Report

Focus on Mathematics Clive Davies Helen Rowland © Clive Davies & Helen Rowland 2014 All rights reserved Reproduction, storage, adaptation or translation, in any form or by any means, of this publication is prohibited without the prior written permission of the publisher. Excerpts may be reproduced for the purpose of research, private study, criticism or review, or by educational institutions solely for educational purposes, without permission, providing full acknowledgement is given. First Published in the UK in 2014 by Focus Education (UK) Ltd Focus Education (UK) Ltd Publishing Talking Point Conference & Exhibition Centre Huddersfield Road Scouthead Saddleworth OL4 4AG Focus Education (UK) Ltd Reg. No 4507968 ISBN 978-1-909038-23-3 Companies, institutions and other organisations wishing to make bulk purchases of books published by Focus Education should contact their local bookstore or Focus Education direct: Customer Services, Focus Education, Talking Point Conference & Exhibition Centre, Huddersfield Road, Scouthead, Saddleworth, OL4 4AG Tel 01457 821818 Fax 01457 878205 www.focus-education.co.uk [email protected] Printed in Great Britain by Focus Education UK Ltd, Scouthead © Focus Education (UK) Ltd 2014 2 ABOUT THE AUTHORS CLIVE DAVIES OBE Clive Davies has a vast experience in primary education. He has inspected more than 200 schools. Whilst a headteacher Clive’s school gained a National Curriculum award and his school was featured in the Times Educational Supplement as one of 3 recognised for its quality practice. The development of pupil autonomy was at the heart of the culture of his successful headships. Clive is well known nationally and internationally having worked in schools throughout England and Wales as well as Dubai, Kuwait, Greece, Turkey, Holland, Cyprus, Germany and Spain. He was awarded an OBE for his services to education in 2007. HELEN ROWLAND Helen is the Academy Improvement Officer for the Focus-Trust and an Associate Consultant for Focus Education. She joined the Focus-Trust from the headship of a school judged outstanding in all aspects. Helen worked in Oldham LA since 1990 and has experience of the full diversity of schools that Oldham offers: English as an additional language, challenging social contexts, village and faith schools. A former headteacher with over 12 years’ experience, Helen now works in partnership with academy leaders, governors and academy teams on developing & improving teaching and leadership for positive impact on children. Helen has led schools in moving from ‘good’ to ‘outstanding’ teaching and learning and implementing the Learning Challenge Curriculum and the new National Curriculum. © Focus Education (UK) Ltd 2014 3 Contents 5 Introduction 8 Year 1 61 Year 2 131 Year 3 195 Year 4 273 Year 5 353 Year 6 © Focus Education (UK) Ltd 2014 4 Introduction • • • • • • Focus on Mathematics is a resource aimed to support schools, academies, staff and pupils to meet the year group expectations set out in the National Curriculum 2014. It is intended for ‘thinking’ teachers and support staff who want to organise the learning for their pupils in a way that will maximise the progress they make. It breaks down the teaching sequences for teachers but gives schools and academies complete autonomy to provide their own methods. In simple terms, Focus on Mathematics takes the year expectations and breaks them down into teaching objectives and provides a framework so that each objective has its own teaching sequence. Most of the teaching objectives are further supported by a series of pre-learning tasks which help teachers decide where to start with different groups of pupils based on their prior knowledge and understanding. In this way pupils should be challenged more rapidly and stretched to reach their full potential. No more than 4 starting positions are suggested in order to make it manageable for staff. In addition Focus on Mathematics provides a target setting continuum which is aimed to help pupils and staff assess progress through each objective. These are referred to as ‘Stepping up to the Challenge’ because they are set in such a way as to suggest pupils are moving onwards and upwards as they progress through each objective. Focus on Mathematics also provides a suggested Assessment procedure which is not based on the old levelling system. It takes, instead, a 3 or a 9-point approach which can then be used to check on key stage, key phase or within year progress. It spells out what has to be done for pupils to meet the year expectations and also explains what it means if they have exceeded these expectations. In short, it provides a valid, but innovative, way of tracking progress and provides a framework for reporting progress to parents. There is strong emphasis placed on the Non-Negotiables¹ and a suggested planning tool is provided to help teachers plan for pupils to meet these expectations. Finally, there is also a Parents’ Guide which aims to help parents understand what learning their children will be experiencing during that year. ¹The Non-Negotiables is a framework written by Simon Camby for Focus Education aimed at helping teachers to ensure pupils are able to meet basic skills in reading, writing and mathematics. © Focus Education (UK) Ltd 2014 5 Focus on Mathematics What the section for each group offers: Year Group Expectations •This section takes the Year Group expectations as outlined in the National Curriculum and where appropriate breaks down the teaching sequence for each. The Objectives related to number then suggest starting points (no more than 4) so that pupils are not covering learning that they are already confident with and are therefore challenged more rapidly. There are 2 groups of expectations, one for number and the other for measurement, geometry and where applicable statistics. Pre- Learning Tasks •These are a series of tasks for many of the ‘number’ year group objectives which aim to help teachers assess the best starting position for each pupil. In this way time is not wasted covering learning already known and understood. The tasks are linked to the teaching sequences by * numbers so that it makes it easier for teachers to decide starting points. What will be interesting is that the groups in classrooms should look different for many objectives because the groupings will be determined by the outcome of the task. It was felt that these would be helpful for the number content but somewhat extravagant for other aspects of mathematics. Step-up to the Challenge •This section provides both teachers and pupils with a resource that helps focus on the progress being made by pupils. It can be used as a self-assessment tool or as check for the teacher. It is designed to break down the progression towards the number, measurement, geometry and statistics objectives. Not all objectives have this resource but the vast majority do. Where they do not exist it was felt that this particular tool was not necessary. This section of the resource can be obtained as individual books for Key Stage 1; Lower Key Stage 2 or Upper Key Stage 2. © Focus Education (UK) Ltd 2014 6 Focus on Mathematics What the section for each group offers (2): NonNegotiables • This section takes the previously published non-negotiables for mathematics and provides a clear framework for planning their use across the year. The expectation is that there will be a focus on the non-negotiables on a daily basis and the framework suggests where the focus ought to be each half term. In addition, there is a parents’ guide provided to help support home school partnership. Assessment •This is potentially the exciting part of this resource. What has been created is a comprehensive overview of how teachers can judge pupils according to how they have met the year group expectations. Schools are then provided with either a 3 or 9-point system aimed at helping assess and track progress. The main focus on assessment will be measuring pupils’ journey towards, and beyond, the Year group expectations. It also has the potential to be used as a tracker going through school. © Focus Education (UK) Ltd 2014 7 Focus on Mathematics Year Group Objectives Year 1 Focus on Mathematics Year 1 Group Objectives Number Year 1 Objectives: Number 1 NUMBER AND PLACE VALUE Objective 1:Counting: 0 to 100, forwards and backwards, from any given number Count on from 0 to 20 *1 Counting: 0 to 100, forwards and backwards, from any given number (continued) Count back from 100 to 0 Count on from 0 to 50 Count back from any number smaller than 10 to 0 Count on from 0 to 100 Count on from any number to 20 NUMBER AND PLACE VALUE *2 Count back from any number smaller than 20 to 0 Count on from any number to 50 Count back from any number smaller than 50 to 0 Count on from any number to 100 Count back from any number smaller than 100 to 0 Count back from 10 to 0 Count back from 20 to 0 Count back from 50 to 0 *3 *4 Count on beyond 100 Count back starting with a number greater than 100 © Focus Education (UK) Ltd 2014 10 Year 1 Objectives : Number 2 NUMBER AND PLACE VALUE Objective 2: Count, read and write to 100; in different multiples including 1s, 2s, 5s and 10s Count in 10s to 50 *1 Count in 10s to 100 NUMBER AND PLACE VALUE Objective 3: Identify one more and one less than a given number Know one more than a given number to 20 Count in 2s to 20 *2 Count in 2s to 50 *1 Know one more than a given number to 50 Know one more than a given number to 100 Count in 2s to 100 Count in 5s to 50 *3 Count in 5s to 100 Know one less than a given number to 20 *2 Know one less than a given number to 50 *3 Know one less than a given number to 100 Write and read all numbers accurately to 10 *4 Write and read all numbers accurately to 20 Write a number that is one more than any given number to 20 *4 Write a number that is one less than any given number to 20 Write and read all numbers accurately to 50 Write and read all numbers accurately to 100 © Focus Education (UK) Ltd 2014 11 Year 1 Objectives : Number 3 NUMBER AND PLACE VALUE Objective 4: Recognise odd and even numbers Know all even numbers to 10 *1 NUMBER AND PLACE VALUE Objective 6: Distinguish between and use: ordinal and cardinal numbers Know all odd numbers to 10 Know all even numbers to 20, then to 50, then to 100 *2 Know all odd numbers to 20, then to 50, then to 100 *3 Know that an even number can be shared between 2 Find missing numbers in a sequence up to 10 *1 Find missing numbers in a sequence up to 20 *2 Order objects using the terms 1st, 2nd, 3rd, etc. *3 Know the 5ness of 5 Know that an odd number cannot be shared equally between 2 Know that a set of 5 objects contains more objects than, say 3, etc. (up to 10) Objective 5: Read and write: 1 to 20 in numerals and words Read all numbers as numerals and words to 10 *1 Write all numbers as numerals and words to 10 *2 Read all numbers as numerals and words to 20 *3 Write all numbers as numerals and words to 20 *4 © Focus Education (UK) Ltd 2014 12 Year 1 Objectives : Number 4 ADDITION AND SUBTRACTION ADDITION AND SUBTRACTION Objective 7: Add and subtract 1-digit and 2digit numbers to 20, including 0 Objective 9: Know and use all number bonds to 20 and related subtraction facts Add two, 1-digit numbers to 10 Know all number bonds to 10, using addition *1 Know all number bonds to 10, using subtraction *2 Know all number bonds to 20, using addition *3 Know all number bonds to 20, using subtraction *4 *1 Add two, 1-digit numbers to 20 (18) Add a 1-digit number to a 2-digit number to 20 *2 Check understanding of 0 (zero) Subtract two, 1-digit numbers *3 Subtract a 1-digit number from a 2-digit number (up to 20) *4 Objective 8: Add three 1-digit numbers Add three, 1-digit numbers (up to 10) *1 Add three, 1-digit numbers to total no more than 20 *2 Objective 10: Solve simple one-step problems that involve addition and subtraction using concrete objects, pictorial representations and missing number problems Solve simple problems involving addition to 10 *1 Solve simple problems involving subtraction to 10 *2 Solve simple problems involving addition to 20 *3 Solve simple problems involving subtraction to 20 *4 © Focus Education (UK) Ltd 2014 13 Year 1 Objectives : Number 5 MULTIPLICATION AND DIVISION FRACTIONS Objective 11: Recognise and write multiplication (x) and division symbols (÷) Know the symbol (x) stands for multiplication Objective 14: Recognise, find and name a half as one of two equal parts of an object, shape or quantity Know the symbol (÷) stands for division Can estimate what half of a given object might be Can estimate what half of a given regular shape might be Objective 12: With support solve onestep problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays With support use practical examples of multiplication and division Using practical materials can show half of a given number of objects *1 *2 *2 Objective 15: Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity Can estimate what a quarter of a given object might be Objective 13: With support solve simple multiplication and division problems With support solve practical examples of multiplication and division up to 20 *1 *1 Can estimate what a quarter of a given regular shape might be Using practical materials can show a quarter of a given number of objects © Focus Education (UK) Ltd 2014 *2 14 Focus on Mathematics Year 1 Pre-Learning Tasks Number Focus on Mathematics: Year 1 Name Date Number Objective 1 Counting: 0 to 100, forwards and backwards, from any given number Can you finish off these sequences? 3, 4, 5, *1 15, 16, 17, 8, 7, 6, *4 16, 15, 14, 33, 34, 35, *2 37, 36, 35, 72, 73, 74, *3 82, 81, 80, Starting Position: © Focus Education (UK) Ltd 2014 16 Focus on Mathematics: Year 1 Name Date Number Objective 2 Count, read and write to 100; in different multiples including 1s, 2s, 5s & 10s Can you finish off these sequences? 10, 20, 30, *1 40, 50, 60, 2, 4, 6, 8, 24, 26, 28, 5, 10, 15, *3 75, 80, 85, *2 Can you read the number twelve and write in the box? *4 Can you read the number fifty- nine and write in the box? Starting Position: © Focus Education (UK) Ltd 2014 17 Focus on Mathematics: Year 1 Name Date Objective 3 Number Identify 1 more than or one less than a given number What is 1 more than…..? 7 What is 1 less than …..? *1 8 13 17 34 46 98 78 Write down a number that is one more than thirteen *2 *3 *4 Write down a number that is one less than twelve Starting Position: © Focus Education (UK) Ltd 2014 18 Focus on Mathematics: Year 1 Name Date Objective 4 Number Recognise odd and even numbers Can you put these numbers in the correct place? 1 2 3 4 5 6 7 8 9 10 36 25 13 41 14 29 32 46 33 15 *1 Even Odd *3 Even Starting Position: Odd 9 12 13 14 15 16 17 18 19 20 Even Odd 34 67 58 17 91 63 28 69 98 77 Even Odd *2 19 Focus on Mathematics: Year 1 Name Objective 5 Date Number Read and write: 1 to 20 in numerals and words Can you read these numbers and put their numerical value in the box? seven *1 six thirteen fourteen Can you read these numerals and write the word (their value) in the box? 8 *2 4 *3 16 *4 12 Write down a number that is one more than fifteen. Write down a number that is one less than eighteen. Starting Position: © Focus Education (UK) Ltd 2014 20 Focus on Mathematics: Year 1 Name Objective 6 Date Number Distinguish between ordinal and cardinal numbers Can you find the missing numbers? 1, 3, 5, …. *1 0, 3, 6, …. 9, 11, 13, 15… 7, 10, 13, 16,… Can you work these out? John won 5 marbles; Claire won 6 marbles and Adin won 4 marbles. Who came first? *3 In a race Abdul was fastest; then India and finally Joe. Who was second? *2 Hussain built a tower with 10 blocks; Jayne’s tower was 7 bocks and Josh’s tower was 3 blocks. Who came first? In a race Sophia filled 3 bottles with water; Amin filled 6 bottles and Charlotte filled 5 bottles. Who was first? Starting Position: © Focus Education (UK) Ltd 2014 21 Focus on Mathematics: Year 1 Name Objective 7 Date Number Add and subtract 1-digit and 2-digit numbers to 20 including 0 Can you add these numbers together? 4 +5 *1 3 +6 7+6 7-5 *3 8-3 *2 12 + 6 Can you add these together: Can you subtract these numbers? 16 - 4 *4 12 - 6 13 + 0 = Can you subtract 0 from 12 Starting Position: © Focus Education (UK) Ltd 2014 22 Focus on Mathematics: Year 1 Name Objective 8 Date Number Add three one-digit numbers Can you add these numbers together? 1 +2+1 *1 7+2+3 2+2+1 8+2+9 1+1+2 6+6+5 0+1+2 7+5+6 *2 Starting Position: © Focus Education (UK) Ltd 2014 23 Focus on Mathematics: Year 1 Name Objective 9 Date Number Know and use all number bonds to 20 and related subtraction facts Can you work these out within 2 seconds? 7+3 *1 3+4 9-4 7-5 12 + 5 *3 11 + 8 *2 17 - 6 *4 18 - 5 Starting Position: © Focus Education (UK) Ltd 2014 24 Focus on Mathematics: Year 1 Name Objective 10 Date Number Solve simple one-step problems that involve addition and subtraction using concrete objects, pictorial representations and missing number problems Can you work these out within 2 seconds? If I have 3 sweets and someone gives me another 5, how many have I altogether? *1 If I score 2 goals in one match and I score 3 in another, how many goals have I scored in the 2 matches? If I have 9 cards and I give 4 away, how many cards have I left? How many coins have I left if I have 7 and I give 3 away? If I have 15 stickers and I buy another 4, how many will I have altogether? *3 If I listen to 12 songs and then another 3, how many will I have listened to altogether? *2 If I have 18 books and give 3 away, how many will I have left? *4 What is 19 take away 5? Starting Position: © Focus Education (UK) Ltd 2014 25 Focus on Mathematics: Year 1 Name Objective 12 and 13 Date Number With support and real objects solve multiplication and division calculations using concrete objects, pictorial representations and arrays Can you work out the answers (using apparatus)? What are 3 lots of 2? *1 Can you share 8 objects between 2 people? What are 2 lots of 5? Can you share 9 objects between 3 people? What are 4 lots of 2? Can you share 12 objects *2 between 3 people? What are 3 lots of 3? Can you divide 15 objects between 5 people? Starting Position: © Focus Education (UK) Ltd 2014 26 Focus on Mathematics: Year 1 Name Date Number Objective 14 Recognise, find and name a half as one of two equal parts of an object, shape or quantity Can you work out the answers (using apparatus)? *1 Can you shade in half of these 2 shapes? *2 What is half of these 2 numbers? How much of the whole shape is red? How much of 12 is 6? 14 16 Starting Position: © Focus Education (UK) Ltd 2014 27 Focus on Mathematics: Year 1 Name Date Number Objective 15 Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity Can you work out the answers (using apparatus)? Can you shade in a quarter of these 2 shapes? What is a quarter of these 2 numbers? *1 12 *2 How much of the circle is missing? How much of 16 is 4? 8 Starting Position: © Focus Education (UK) Ltd 2014 28 Focus on Mathematics Year 1 Group Objectives Measurement and Geometry Year 1 Objectives : Measurement 1 MEASUREMENT Objective 1m - Compare, describe and solve MEASUREMENT practical problems for: Length and height (long/ short, longer/ shorter; tall/short; double/half) Mass/ weight (heavy/ light, heavier than, lighter than) capacity and volume (full/ empty, more than, less than, half, half full, quarter) time (quicker, slower, earlier and later) Objective 2m - Measure and begin to record the Can compare 2 objects and say which is the longer and shorter Can measure the length of an object in m Can compare up to 5 objects and say which is the longest and shortest Can measure the height of an object in cm Can compare 2 objects and say which is the heavier and lighter Can compare up to 5 objects and say which is the heaviest and lightest Can compare 2 containers and say which is full, empty, half full Can describe events which happened earlier and later following: Length and height Mass/ weight Capacity and volume Time (hours, minutes, seconds) Can measure the length of an object in cm Can measure the height of an object in m Can measure the weight of an object in Kg/g Can measure how much liquid is in a container in l/ml Can measure how long it takes to do an activity in hours/minutes/seconds Can compare the movement of 2 objects and describe which is slower, quicker © Focus Education (UK) Ltd 2014 30 Year 1 Objectives : Measurement 2 MEASUREMENT MEASUREMENT Objective 3m - Recognise and know the value of different denominations of coins and notes Objective 5m - Recognise and use language of dates: days of the week, weeks, months and years Recognise 1p, 2p, 5p coins Know days of the week in order Know months of the year in order Recognise 10p, 20p and 50p coins Know that seven days make up one week Recognise a £1 coin Know that there are twelve months in a year Recognise £5 and £10 notes Objective 6m - Tell time: to hour and half past Compare the value of the different denominations of coins and notes Objective 4m - Sequence events in Tell the time to o’clock from one o’clock through to twelve o’clock chronological order using language (e.g. before, after, next, first, today, yesterday, tomorrow, morning, afternoon and evening) Tell the time to half past the hour from half past one through to half past twelve Can order: morning, afternoon and evening Draw hands on the clock to show time to ‘o’clock’ Use terms: before, next and after accurately Draw hands on the clock to show time to ‘half past’ the hour Use terms: today, tomorrow, yesterday accurately Know that key events such as lunchtime happen at 12 o’clock/home time half past 3 © Focus Education (UK) Ltd 2014 31 Year 1 Objectives : Geometry Geometry – Properties of shape Geometry – Position and direction Objective 1g - Recognise and name 2-D shapes: to include: rectangle (including squares), circle and triangle Objective 3g - Describe position, directions and movements including whole, half, quarter and three-quarter turns Know vocabulary: left, right, top, middle, bottom, on top of, in front of, above, between, around, near, close and far, up, down, forwards, backwards, inside and outside Know and name squares Know and name rectangles Know and name circles Can demonstrate a full turn (by moving own body) Know and name triangles Can demonstrate half a turn Objective 2g - Recognise and name 3-D shapes: to include cuboids (including cubes), pyramid and sphere Can demonstrate quarter of a turn Know and name cubes Can hold up right or left hand as required Know and name pyramids Can point to the left or right as required Know and name spheres Can describe position, directions and movements using above vocabulary Can demonstrate three-quarters of a turn © Focus Education (UK) Ltd 2014 32 Focus on Mathematics Step up to the Challenge Year 1 Number Year 1: Can you challenge yourself to meet the Objective? Objective 1: Can you count forwards and backwards 0 to 100 from any given number? Me My Teacher Can you count back from any number smaller than 100 to 0? Can you count back from any number smaller than 50 to 0? Can you count back from any number smaller than 20 to 0? Can you count back from 100 to 0? Can you count back from 50 to 0? Can you count back from 20 to 0? Can you count on from any number to 100? Can you count on from any number to 50? Can you count on from any number to 20? Can you count on from 0 to 100? Can you count on from 0 to 50? Can you count on from 0 to 20? © Focus Education (UK) Ltd 2014 34 Year 1: Can you challenge yourself to meet the Objective? Objective 2: Can you count, read and write to 100, in different multiples of 1, 2s, 5s and 10? Me My Teacher Can you read and write all numbers to 100? Can you read and write all ‘tens’ numbers from 0 to 100? Can you read and write all numbers to 20? Can you read and write all numbers to 10? Can you count in 5s to 100? Can you count in 2s to 100? Can you count in 2s to 50? Can you count in 2s to 20? Can you count in 10s to 100? Can you count in 10s to 50? Can you count from 1 to 100? © Focus Education (UK) Ltd 2014 35 Year 1: Can you challenge yourself to meet the Objective? Objective 3: Can you tell what is ‘one more than’ and ‘one less than’ a number up to 100? Me My Teacher Can you write a number that is ‘one less than’ any number to 100? Can you write a number that is ‘one more than’ any number to 100? Can you say a number that is ‘one less than’ any number to 100? Can you say a number that is ‘one less than’ any number to 50? Can you say a number that is ‘one less than’ any number to 20? Can you say a number that is ‘one more than’ any number up to 100? Can you say a number that is ‘one more than’ any number up to 50? Can you say a number that is ‘one more than’ any number up to 20? © Focus Education (UK) Ltd 2014 36 Year 1: Can you challenge yourself to meet the Objective? Objective 4: Can you recognise odd and even numbers to 100? Me My Teacher Can you explain why an odd number cannot be shared equally by 2? Can you explain why all even numbers can be shared by 2? Can you say all the odd numbers to 100? Can you say all the even numbers to 100? Can you say all the odd numbers to 50? Can you say all the even numbers to 20? Can you say all the odd numbers between 0 and 10? Can you say all the even numbers between 0 and 10? © Focus Education (UK) Ltd 2014 37 Year 1: Can you challenge yourself to meet the Objective? Objective 7: Can you add and subtract 1-digit and 2-digit numbers to 20, including 0? Me My Teacher Me My Teacher Can you subtract a 1-digit number from a 2-digit number? Can you subtract two, 1-digit numbers? Can you add a 1-digit number to a 2-digit number to 20? Can you add two, 1-digit numbers to 20? Can you add two, 1-digit numbers to 10? Objective 8: Can you add three, 1-digit numbers? Can you add three, 1-digit numbers to 20? Can you add three, 1-digit numbers to 10? © Focus Education (UK) Ltd 2014 38 Year 1: Can you challenge yourself to meet the Objective? Objective 9: Can you work out all number bonds to 20? Me My Teacher Me My Teacher Can you work out all subtraction number bonds to 20? Can you work out all addition number bonds to 20? Can you work out all subtraction number bonds to 10? Can you work out all addition number bonds to 10? Objective 10: Can you solve simple word problems involving addition and subtraction to 20? Can you solve simple word problems involving subtraction to 20? Can you solve simple word problems involving addition to 20? Can you solve simple word problems involving subtraction to 10? Can you solve simple word problems involving addition to 10? © Focus Education (UK) Ltd 2014 39 Year 1: Can you challenge yourself to meet the Objective? Objective 11 to 13: Can you do simple multiplications (x) and divisions (÷)? Me My Teacher Can you see that adding in 2s, 5s and 10s is just like multiplication? Without using real objects, can you use division involving numbers to 20? Without using real objects, can you use multiplication involving numbers to 20? Using real objects, can you use division involving numbers to 20? Using real objects, can you use multiplication involving numbers to 20? Do you know that the symbol (÷) stands for division? Do you know that the symbol (x) stands for multiplication? © Focus Education (UK) Ltd 2014 40 Focus on Mathematics Step up to the Challenge Year 1 Measurement and Geometry Year 1: Can you challenge yourself to meet the Objective? Objective 1m and 2m: Can you describe measures and start to use standard measures? Me My Teacher Can you order the time you would do things during a school day? Do you know that time is measured in hours and minutes? Do you know the term litre and can you show some objects that hold more or less than a litre? Do you know the term kilogram and can you show some objects that weigh more or less than a kilogram? Do you know the term metre and can you show objects that are longer or shorter than a metre? Can you order the time it takes to do many things starting with the quickest? Can you work out which object is the heaviest and lightest of a number of objects? Can you work out which object is the longest and shortest of a number of objects? © Focus Education (UK) Ltd 2014 42 Year 1: Can you challenge yourself to meet the Objective? Objective 3m: Can you tell me about money? Me My Teacher Can you work out how many 10p coins is the same as £1? Can you work out how many 50p coins is the same as £1? Can you work out how many £1 coins is the same as a £10 note? Can you point to a £5 note and a £10 note? Can you point to a 10p and a 20p coin? Can you point to a 50p coin? Can you point to a £1 coin? Can you point to a 1p, 2p and 5p coin? © Focus Education (UK) Ltd 2014 43 Year 1: Can you challenge yourself to meet the Objective? Objective 4m to 6m: Can you begin to tell the time? Me My Teacher Can you name the months of the year in order? Can you name the days of the week in order? Can you use the terms before, after and next accurately? Can you use the terms yesterday, today and tomorrow accurately? Can you think of things that normally happen in the morning, afternoon and night time? Can you tell the time to half past the hour from half past one through to half past twelve? Can you tell the time to o’clock from one o’clock through to twelve o’clock? © Focus Education (UK) Ltd 2014 44 Year 1: Can you challenge yourself to meet the Objective? Objective 1g and 2g: Can you recognise 2D and 3D shapes? Me My Teacher Do you know this shape and can you name it? Do you know this shape and can you name it? Do you know this shape and can you name it? Do you know this shape and can you name it? Do you know this shape and can you name it? Do you know this shape and can you name it? Do you know this shape and can you name it? © Focus Education (UK) Ltd 2014 45 Year 1: Can you challenge yourself to meet the Objective? Objective 3g: Can you describe position by using your body? Me My Teacher Can you turn to the left? Can you turn to the right? Can you hold out your left hand? Can you hold out your right hand? Can you turn your body through three-quarters of a turn? Can you turn your body through a quarter of a turn? Can you turn your body through half a turn? Can you turn your body through one full turn? © Focus Education (UK) Ltd 2014 46 Focus on Mathematics Helping pupils meet the (new) National Curriculum Year Objectives Non-Negotiables Year 1 Possible Planning Outline Year 1 Mathematics Non-Negotiables • The following areas of learning are known as the non-negotiables. They have a specific role in helping pupils meet the year group expectations. In a nutshell we are suggesting that if pupils are not confident in these areas then they will find the rest of the curriculum difficult to access. • The non-negotiables are designed to: 1. Identify the essential components that pupils need to become confident with, i.e. be able to demonstrate in independent tasks and be able to apply in other contexts. 2. Unblock learning, i.e. to keep teachers focused on the essential rather than coverage at the expense of progress. 3. Unlock learning and progress. • The non-negotiables are not designed to imply that the rest of the curriculum is an irrelevance – it clearly isn’t. But rather to give a structure for professionals to decide what the right curriculum is for their pupils. © Focus Education (UK) Ltd 2014 48 Year 1 Mathematics Non-Negotiables • Here are the Year 1 mathematics non-negotiables: • • • • • • • Count to and across 100, forwards and backwards from any number. Read and write numbers to 20 in digits and words. Read and write numbers to 100 in digits. Say ‘1 more’ and ‘1 less’ to 100. Count in multiples of 1, 2, 5 and 10. Know bonds to 10 by heart. Use bonds and subtraction facts to 20. • Add and subtract: o 1 digit and 2 digit numbers to 20, including zero. o Add any three 1-digit numbers with a total up to 20. o Solve simple addition and division with apparatus and arrays. • • • • Recognise half and quarter of object, shape or quantity. Sequence events in order. Use language of day, week, month and year. Tell time to hour and half past. © Focus Education (UK) Ltd 2014 49 Planning to meet the requirement of the nonnegotiables The following 3 pages suggest a planning outline for delivering the non-negotiables in classrooms. There should be some element of teaching of these each day. Autumn Term Ist Half Term • • • • • • • 2nd Half Term Count to and across to at least 20 – forwards and backwards beginning with 1 Read and write numbers to 20 in numerals and write numbers in words to 10 Count in 2s to 20 Identify one more and one less than a given number to 20 Order objects using the terms 1st , 2nd, 3rd, 4th, 5th Find the missing number in a sequence up to 10 Add/subtract 2, 1-digit numbers to 10 • • • • • • • • • Count to and across to at least 50 – forwards and backwards beginning with 0 and 1, or from any other given number Read and write numbers to 20 and beyond in numerals and write numbers in words to 10 Count in 2s to 20 and beyond Count in 5s to beyond 20 Count in 10s to 50 Identify one more and less than a given number to 20 and beyond Order objects using the terms 1st , 2nd, 3rd, 4th, 5th and beyond Find the missing number in a sequence up to 10 and beyond Add/subtract 2 1-digit numbers to 10, including 0 © Focus Education (UK) Ltd 2014 50 Planning to meet the requirement of the nonnegotiables Spring Term Ist Half Term • • • • • • • • 2nd Half Term Count to and across to at least 50 – forwards and backwards beginning with 0 and 1 or from any other given number Read and write numbers to 50 in numerals and begin to write numbers in words to 20 Count in 2s and 5s to 50 Count in 10s to 50 and beyond Identify one more and one less than a given number to 50 Order objects using the terms 1st, 2nd, 3rd to 10th Find the missing number in a sequence up to 20 Add/subtract 2-digit and 1-digit numbers to 10 and beyond • • • • • • • • Count to and across to at least 50 – forwards and backwards beginning with 0 and 1 or from any other given number Read and write numbers to 50 and beyond in numerals and continue to write numbers in words to 20 Count in 2s and 5s to 50 and beyond Count in 10s to 100 Identify one more and one less than a given number to 50 and beyond Order objects using the terms 1st , 2nd, 3rd to 10th Find the missing number in a sequence up to 20 and beyond Add/subtract 2-digit and 1-digit numbers to 10 and beyond © Focus Education (UK) Ltd 2014 51 Planning to meet the requirement of the nonnegotiables Summer Term Ist Half Term • • • • • • • • 2nd Half Term Count to and across to at least 100 and beyond forwards and backwards from any given number Read and write numbers to 100 in numerals and write numbers in words to 20 Count in 2s, 5s and 10s to 100 Identify one more and one less than a given number to 100 Find the missing number in a sequence up to 50 Add/subtract 2-digit and 1-digit numbers to 20 Double numbers up to 5 Halve even numbers up to 10 • • • • • • • Count to and across to at least 100 and beyond forwards and backwards beginning with 0 and 1 or from any given number Count in 2s, 5s and 10s to 100 and beyond Identify and write down the number which is one more and less than a given number to 100 Find the missing number in a sequence up to 100 Add/subtract 2-digit and 1-digit numbers to 20 Double numbers up to 10 Halve even numbers up to 20 © Focus Education (UK) Ltd 2014 52 Focus on Mathematics Year 1 Assessment Assessment: Meeting Year 1 Expectations Year 1 Expectations: Number • • • • • The main focus on assessment will be measuring a pupil’s journey towards and beyond the Year 1 expectations. The Year 1 expectations for number are set out on the right hand side of this page. To meet the Year 1 expectations a pupil must be able to meet all of the statements outlined in the table, plus the ones for measurement and geometry, shown later. If they have not met all the statements then they will be deemed to be emerging. If a pupil is meeting the expectations then an assessment needs to made as to whether a pupil is exceeding the expectations. The next page sets out how to assess whether a pupil is exceeding this expectation or whether a pupil is at the emerging stage. The next page also provides you with a 9point scale for deeper analysis, if required. • Count reliably to 100 • Count on and back in 1s, 2s, 5s, and 10s from any given number to 100 • Write all numbers in words to 20 • Say the number that is one more or one less than a number to 100 • Recall all pairs of addition and subtraction number bonds to 20 • Add and subtract 1-digit and 2-digit numbers to 20, including zero • Know the signs (+); (-) and (=) • Solve a missing number problem, such as 5 = 8 - x • Solve a one-step problem involving an addition and subtraction, using concrete objects, pictorial representations and arrays • Solve a one-step problem involving a multiplication and division, using concrete objects, pictorial representations and arrays © Focus Education (UK) Ltd 2014 54 Assessment: Meeting Year 1 Expectations The 3 or 9-point scale Effectively, pupils will be assessed on a 3-point scale: that is, pupils will be judged as having met the expectations; emerging towards the expectations or exceeding the expectations. However, for many schools, this may not give them enough information when tracking pupils through the school. So, if schools desire, the following 9-point system is outlined for them to use. Assessed position Emerging Stage C Emerging Stage B Emerging Stage A Meeting Stage C Meeting Stage B Meeting Stage A Exceeding Stage C Exceeding Stage B Exceeding Stage A Points allocation 1 2 3 4 5 6 7 8 9 • • • • • As is illustrated, Point 4 is the point that indicates that a pupil has met the expectations. If we are to take account of the new Assessment arrangements then it is hoped that 85% of pupils will be at least at this stage by the end of the year. Points 1 to 3 are the ‘emerging’ stages; Points 4 to 6 are the ‘meeting’ expectations stages; and Points 7 to 9 are the ‘exceeding’ stages. The following page sets out what each point actually means and provides clarity about the allocation of the points. © Focus Education (UK) Ltd 2014 55 Assessment: Meeting Year 1 Expectations A pupil will be deemed to be meeting the expectations only if they can satisfy their teacher that they meet all the expectations for their age A pupil will be deemed to be emerging towards the expectations if they do not meet all of the statements outlined for that year group •Meeting the expectations (Stage C) – Point 4 •It is accepted that a pupil might make the occasional error if they are at this stage. However, despite that, the teacher needs to be satisfied that they understand the concept fully. •Meeting the expectations (Stage B) - Point 5 •At this stage a pupil will rarely make mistakes and is very confident at meeting the statements. •Meeting the expectation (Stage A)- Point 6 •At this stage, not only is the pupil confident at meeting the statements but works at a rapid rate. However, they are not yet meeting all the statements for exceeding. •If they meet more than 75% of the statements but not all then they will be described as: •Emerging towards the expectations (Stage C) – Point 3 •If they meet between 50% and 75% of the statements then they will be described as: •Emerging towards the expectations (Stage B) – Point 2 •However if they are not meeting 50% of the expectations they will be described as: •Emerging towards the expectations (Stage A) – Point 1 •There is, therefore, no requirement to write a set of emerging statements © Focus Education (UK) Ltd 2014 A pupil will be deemed to be exceeding the expectations when, in addition to the statements set out for meeting the expectation (Stage A)they meet one or more of three sets of further expectations •Pupils will be deemed to be exceeding expectations if, in addition to what is outlined as Point 6, they show evidence of: •Accessing some of the following year group’s objectives •Being able to use the year group’s expectation within context •Being able to consistently apply the year group objectives in a range of situations. •A set of exceeding statements are set out for you to feel secure about your judgements. •If a pupil is meeting the exceeding statements, they will be deemed to be at Point 7 (Stage C) •If they are very confident and rarely make a mistake in relation to the ‘exceeding’ statements then they will be judged at Point 8 (Stage B) •A few pupils will be judged at Point 9 (Stage A). These will be pupils who are exceptionally confident in handling the exceeding statements and show exceptional mathematical ability for their age 56 Assessment: Meeting Year 1 Expectations Year 1 Expectations: Measurement and Geometry Year 1 Expectations: Number • Count reliably to 100 • Count on and back in 1s, 2s, 5s, and 10s from any given number to 100 • Write all numbers in words to 20 • Say the number that is one more or one less than a number to 100 • Recall all pairs of addition and subtraction number bonds to 20 • Add and subtract 1-digit and 2-digit numbers to 20, including zero • Recognise all coins: £1; 50p; 20p; 10p; 5p and 1p • Recognise and name the 2D shapes: circle; triangle; square and oblong • Recognise and name the 3D shapes: cube; sphere; cuboid • Name the days of the week and months of the year • Tell the time to ‘o’clock’ and half past the hour • Know the signs (+); (-) and (=) • Solve a missing number problem, such as: 5=8• Solve a one-step problem involving an addition and subtraction, using concrete objects, pictorial representations and arrays • Solve a one-step problem involving a multiplication and division, using concrete objects, pictorial representations and arrays © Focus Education (UK) Ltd 2014 57 Assessment: Exceeding Year 1 Expectations Year 1 Exceeding Expectations: • Count reliably well beyond 100 • Count on and back in 3s from any given number to beyond 100 • Say the number that is 10 more or 10 less than a number to 100 • Know the signs (+); (-); (=); (<); (>) • Apply knowledge of number to solve a one-step problem involving an addition, subtraction and simple multiplication and division • Add and subtract 1-digit and 2-digit numbers to 50, including zero • Recognise all coins and notes and know their value • Use coins to pay for items bought up to £1 • Use knowledge of time to know when key periods of the day happen, eg, lunchtime, home time, etc. • Recognise different 2D and 3D shapes in the environment © Focus Education (UK) Ltd 2014 58 Focus on Mathematics Year 1 Parents’ Guide Parents’ Guide ‘Must do’ by the end of Year 1 Number • • • • • • • Shape and Measures Be able to count on in 2s, 5s and 10s to 100 Know one more and one less than any numbers to 100 Know all odd and even numbers to 100 Find missing numbers in sequence up to 20 Add 2, one-digit numbers to 20 Add 3, one-digit numbers to 20 Know all number bonds for numbers to 20, e.g. 2+4, 5+6,17+3, etc. • Name the following shapes: • Tell time to the hour and half past the hour Recognise the £1, 50p, 20p, 10p, 5p, 2p and 1p coins Name the days of the week Name the months of the year • • • © Focus Education (UK) Ltd 2014 60 Focus on Mathematics Year Group Objectives Year 2 Focus on Mathematics Year 2 Group Objectives Number Year 2 Objectives: Number 1 NUMBER AND PLACE VALUE NUMBER AND PLACE VALUE Objective 1: Count on in steps of 2, 3, 5 and 10 from any number Objective 3: Give 10 more or less than any number to 100 Count in 10s to 100 *1 Know 10 more than any number to 50 and then to 100 *1 Count in 2s to 50 then 100 *2 *2 Count in 5s to 50 then 100 *3 Know 10 less than any number from 50 and then from 100 Count in 3s to 30, 60 and then to 99 *4 Objective 2: Recognise the place value of each digit in a two-digit number (tens and ones) Know which is the tens and ones part of a 2-digit number *1 Partition a 2-digit number showing the true value of each digit *2 Objective 4: Use ˂ , ˃ and = signs to compare and order numbers to 100 Know what the = sign stands for *1 Know what the ˃ sign stands for *2 Know what the ˂ sign stands for *3 Use the = sign accurately in simple calculations Use the ˂ sign between 2 numbers accurately Use the ˃ sign between 2 numbers accurately © Focus Education (UK) Ltd 2014 63 Year 2 Objectives : Number 2 NUMBER AND PLACE VALUE ADDITION AND SUBTRACTION Objective 5: Read and write numbers to 100 in numerals and words Objective 8: Recall and use addition and subtraction facts to 20 fluently Read and write all numbers to 20 in numerals and words *1 Know all addition number bonds to 10 instantly *1 Know all addition number bonds to 20 instantly Read and write all numbers to 50 in numerals and words Know all subtraction number bonds to 10 instantly Read and write all numbers to 100 in numerals and words *2 Objective 6: Order, read and write numbers in increasing and decreasing value Order a set of numbers (at least 3) in increasing value using numbers up to 50 *1 Order a set of numbers (at least 3) in decreasing value using numbers up to 50 Order a set of numbers (at least 3) in increasing value using numbers up to 100 *2 Order a set of numbers (at least 3) in decreasing value using numbers up to 100 *2 Know all subtraction number bonds to 20 instantly Relating these number facts to work out larger numbers, if 3 + 5 = 8, then 30 + 50 = 80 *3 Objective 9: Add and subtract mentally up to two-digit numbers using concrete objects and pictorial representations. Complete horizontal addition of a two-digit and a one-digit number with answers up to 50 and then up to 100 *1 Complete horizontal subtraction, taking a onedigit number from a two-digit number with answers of no more than 50 and then with answers of no more than 100 *2 Objective 7: Use number facts and place value to solve number facts Solve problems such as 50 + □ = 54; and □ + 9 = 39 © Focus Education (UK) Ltd 2014 64 Year 2 Objectives : Number 3 NUMBER AND PLACE VALUE ADDITION AND SUBTRACTION Objective 10: Recognise odd and even numbers Recall all even numbers to 10 *1 Recall all odd numbers to 10 Recall rapidly all even numbers to 20, then to 50, then to 100 *2 Recall rapidly all odd numbers to 20, then to 50, then to 100 *3 Know that an even number can be shared between 2 and that an odd number cannot Objective 11: Distinguish between and use: ordinal and cardinal numbers Objective 12: Add and subtract up to two-digit numbers using written methods including columnar addition (without carrying or borrowing). Add a two-digit number and tens with answers of no more than 50 and then with answers of no more than 100 *1 Subtract tens from a two-digit number with answers of no more than 50 and then with answers of no more than 100 *2 Add three one-digit numbers *3 Find missing numbers in a sequence up to 10 Find missing numbers in a sequence up to 20 Order objects using the terms 1st, 2nd, 3rd, etc. Know the 5ness of 5 Know that a set of 5 objects contains more objects than, say 3, etc. (up to 10) Subtract a 2-digit number from another 2-digit number with numbers which do not involve borrowing from the tens column © Focus Education (UK) Ltd 2014 65 Year 2 Objectives : Number 4 ADDITION AND SUBTRACTION ADDITION AND SUBTRACTION Objective 13: Add and subtract mentally: a two-digit number and ones, a two-digit number and tens, 2 two-digit numbers; and 3 one-digit numbers Objective 14: Use subtraction in ‘take away’ and ‘find the difference’ problems Rapid recall of a two-digit number added to a one-digit number *1 Rapid recall of a one-digit number taken away from a two-digit number Rapid recall of 10 added to a two-digit number *1 Complete number problems which require working out the difference between two numbers, e.g. John has read 16 books and Nadir has read 13 books. How many more books has John read? *2 Objective 15: Recognise that addition can be done in any order but subtraction cannot Rapid recall of any 10s number added to a twodigit number (answer no more than 100) Rapid recall of 10 subtracted from a two-digit number Complete number problems which require a number to be taken away from another, e.g. If I have 23 sweets and I eat 5, how many are there left? *2 Rapid recall of any 10s number subtracted from a two-digit number Know that when adding numbers together they can be set out in any order, e.g. 5 + 7 will be same as 7 + 5; or 3 + 5 + 4 will be the same as 5 + 4 + 3 Know that when subtracting the order is very important, e.g. 7 – 5 cannot be set out as 5 - 7 Rapid recall of the addition of any 2 two-digit numbers that do not total above 100 Rapid recall of the addition of any 3 one-digit numbers that do not total above 100 *3 © Focus Education (UK) Ltd 2014 66 Year 2 Objectives : Number 5 ADDITION AND SUBTRACTION MULTIPLICATION AND DIVISION Objective 16: Recognise that subtraction is the inverse of addition and use for checking calculations and solve missing numbers Objective 18: Recall multiplication and division facts for the 2, 5 and 10 times tables Know that 5 + 7 = 12 involves the same process as 12 - 7 = 5, or 12 – 5 = 7 Recite the 2x table rapidly, up to x12, without error Answer rapidly any calculation involving the 2x table out of order Complete calculations such as: If 6 + 8 = 14; what is 14 – 8? Know that 2 x 4 is the same as 4 x 2 Complete calculations such as: If 9 + 6 = 15; what is the missing number in 15 - □ = 9? Recite the 10x table rapidly, up to x12, without error Objective 17: Solve addition and subtraction word problems with up to 2-digits Recognise x2 is doubling Solve simple word problems involving addition to 50 *1 Recognise ÷2 is halving Solve simple word problems involving subtraction to 50 *2 Answer rapidly any calculation involving the 10x table out of order Know that 3 x 10 is the same as 10 x 3 Solve simple word problems involving addition to 100 Solve simple word problems involving subtraction to 100 *1 *3 Recite the 5x table rapidly, up to x12, without error *2 Answer rapidly any calculation involving the 5x table out of order *3 Know that 6 x 5 is the same as 5 x 6 © Focus Education (UK) Ltd 2014 67 Year 2 Objectives : Number 6 MUTIPLICATION AND DIVISION MULTIPLICATION AND DIVISION Objective 19: Use x, ÷ and = signs to read and write mathematical statements Objective 22: Recognise that multiplication can be done in any order but division cannot Know that the ‘x’ sign stands for multiplication *1 Know that 8 x 2 = 16 can be set out as 2 x 8 = 16 Know that the ÷ sign stands for division *2 Know that 20 ÷ 5 = 4 cannot be set out as 5 ÷20= Know that the = sign stands for equals Uses the x, ÷, and = signs in simple calculations for numbers up to 100 Objective 20: Calculate and write multiplication and division statements Calculate and write out simple multiplication statements, such as 6 x 2 = 12 Solve simple word problems involving multiplication to 50 *1 Solve simple word problems involving division to 50 Calculate and write simple division statements, such as 16 ÷ 2 = 8 Objective 21: Recognise that division is the inverse of multiplication and use to check calculations Know that examples such as 8 x 2 = 16 correspond to 16 ÷2 = 8 Objective 23: Solve word problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts Solve simple word problems involving multiplication to 100 Solve simple word problems involving division to 100 *2 Know that if 40 ÷ 2 = 20 then 20 is a half of 40 Know that examples such as 20 ÷ 5 = 4 correspond to 4 x 5 = 20 © Focus Education (UK) Ltd 2014 68 Year 2 Objectives : Number 7 FRACTIONS FRACTIONS Objective 24: Recognise, find, name and write fractions ⅓, ¼, 2/4 and ¾ of a length, shape, set of objects or quantity Objective 25: Recognise, find, name and write fractions ⅓, ¼, 2/4 and ¾ of a length, shape, set of objects or quantity (continued) Know that the symbol ½ stands for half the value of… Calculate 2/4 of a given number up to 100 *1 Calculate ¾ of a given number up to 100 Know that the symbol ¼ stands for a third of the value of… Write simple fractions such as ½ of 6 = 3 Know that the symbol ¾ stands for a quarter of the value of… Recognise the equivalence of 2/4 and ½ Know that the symbol ⅓ stands for a third of the value of… Find ⅓ of a shape *2 Objective 26: Count in halves and quarters to 10 Find ¼ of a shape Count in sequence up to 10: ½; 1; 1½, 2, 2½, …………… Find 2/4 of a shape Count in sequence up to 10: ¼, ½, ¾, 1, 1¼, 1½,…………. Find ¾ of a shape Use the ½ and 2/4 equivalence on a number line, e.g. 1¼ , 12/4 (or 1 ½) , 1¾ , 2 Calculate ⅓ of a given number up to 100 *1 *2 Calculate ¼ of a given number up to 100 © Focus Education (UK) Ltd 2014 69 Focus on Mathematics Year 2 Pre-Learning Tasks Number Focus on Mathematics: Year 2 Name Objective 1 Date Number Count on in steps of 2, 3, 5 and 10 from any number Can you complete these sequences? 20, 30, 40 *1 15, 20, 25 12, 14, 16 *2 17, 22, 27 75, 80, 85 *3 6, 9, 12 35, 38, 41 *4 35, 38, 41 Starting Position: © Focus Education (UK) Ltd 2014 71 Focus on Mathematics: Year 2 Name Date Objective 2 Number Recognise the place value of each digit in a two-digit number (tens and ones) Can you place the tens and the units in the correct place? 17 Tens Units 45 Tens Units 23 Tens Units 67 Tens Units 40 Tens Units 87 Tens Units 61 Tens Units 92 Tens Units *1 *2 © Focus Education (UK) Ltd 2014 72 Focus on Mathematics: Year 2 Name Objective 3 Date Number Give 10 more or less than any number to 100 Can you add 10 to these numbers? 27 Can you take away 10 from these numbers? *1 78 56 45 89 67 67 49 *2 Starting Position: © Focus Education (UK) Ltd 2014 73 Focus on Mathematics: Year 2 Name Date Objective 4 Number Objective 4: Use ˂ , ˃ and = signs to compare and order numbers to 100 Which sign should be used? 8 4+4 *1 9 7 *2 17 18 *3 34 67 Can you complete these? 16 ˃ 23 ˂ ˂ 19 ˃ 56 Starting Position: © Focus Education (UK) Ltd 2014 74 Focus on Mathematics: Year 2 Name Objective 5 Date Number Read and write numbers to 100 in numerals and words Can you write these numbers in numerals? thirteen *1 Can you write these numbers in words? 27 twentyfour 48 forty-two 75 eightyfive *2 92 © Focus Education (UK) Ltd 2014 *1 *2 75 Focus on Mathematics: Year 2 Name Objective 6 Date Number Order, read and write numbers in increasing and decreasing value Can you order these numbers (smallest first)? 23, 1, 46 *1 Can you order these numbers (largest first)? 78, 4, 81 32, 5, 15 77, 6, 89 6, 17, 50 90, 95, 91 41, 8, 23 78, 76, 79 © Focus Education (UK) Ltd 2014 *2 76 Focus on Mathematics: Year 2 Name Date Objective 8 Number Recall and use addition and subtraction facts to 20 fluently Can you work out these answers quickly? (2 minutes) 14 + 5 *1 2 + 15 15 - 3 19 - 12 *2 If 3 + 5 = 8 what is 30 +50? *3 If 7 + 2 = 9 what is 70 +20? If 5 + 2 = 7 what is 50 + 20? If 6 + 4 = 10 what is 60 + 40? Starting Position: © Focus Education (UK) Ltd 2014 77 Focus on Mathematics: Year 2 Name Date Objective 9 Number Add and subtract mentally up to two-digit numbers using concrete objects and pictorial representations. Can you add these numbers? 23 + 5 Can you subtract one number from the other? *1 25 – 7 17 + 9 19 - 6 48 + 9 67 - 6 67 + 6 72 - 7 *2 Starting Position: © Focus Education (UK) Ltd 2014 78 Focus on Mathematics: Year 2 Name Date Objective 10 Number Recognise odd and even numbers to 100 Can you put these numbers in the correct place? 1 2 3 4 5 6 7 8 9 10 36 23 23 43 24 21 22 44 23 18 *1 Even Odd *3 Even Starting Position: Odd 9 12 13 14 15 16 17 18 19 20 Even Odd 34 69 58 27 91 68 28 19 88 67 Even Odd © Focus Education (UK) Ltd 2014 *2 79 Focus on Mathematics: Year 2 Name Date Objective 12 Number Add and subtract up to two-digit numbers using written methods including columnar addition (without carrying or borrowing). What are the answers? 17 + 10 *1 45 - 10 26 + 10 89 - 10 89 + 10 6+7+6 28 - 10 *2 *3 8+9+3 Starting Position: © Focus Education (UK) Ltd 2014 80 Focus on Mathematics: Year 2 Name Date Objective 13 Number Add and subtract mentally: a two-digit number and ones, a two-digit number and tens, 2 two-digit numbers; and 3 one-digit numbers Can you work these out? 17 + 10 *1 25 + 16 26 - 10 89 - 16 69 + 20 4+7+6 48 - 20 *2 23 + 14 Starting Position: *3 7+9+3 9–3-2 © Focus Education (UK) Ltd 2014 81 Focus on Mathematics: Year 2 Name Objective 14 Date Number Use subtraction in ‘take away’ and ‘find the difference’ problems Can you solve these problems? If I have 10 sweets and I give 4 away, how many have I left? *1 What is the difference between 10 and 3? There were 15 biscuits on a plate and 5 people ate one each. How many were left? There are 12 balls in one basket and 5 in another basket. What is the difference? During lunch there were 12 cup cakes on a plate and 8 children had one each. How many are left? Hamza had 15 stickers this week and Helen had 9. What is the difference? John lined up all his play people. There were 23 altogether. Then he took away 5. How many were left? Manchester United scored 14 goals in March and Liverpool scored 10 goals. What is the difference? © Focus Education (UK) Ltd 2014 *2 82 Focus on Mathematics: Year 2 Name Objective 17 Date Number Solve addition and subtraction word problems with up to 2-digits Can you work out the answers? If I have 10 sweets and my mum gives me 13 more. How many have I got? *1 There were 15 biscuits in one packet and 13 in another. How many biscuits altogether? There were 12 cup cakes on one shelf and 8 on another. How many more were on the first shelf? Harry had 12 cars and Abdul had 11. How many did they have altogether? What is the difference between 60 and 13? *3 There are 22 balls in one basket and 50 in another basket. How many are there altogether? *2 Saffiya had 25 stickers this week and Chloe had 19. How many did they have between them? Oldham scored 30 goals this year and Bolton scored 50 goals. Who scored more? How many more? © Focus Education (UK) Ltd 2014 83 Focus on Mathematics: Year 2 Name Date Objective 18 Number Recall multiplication and division facts for the 2, 5 and 10 times tables Can you work these out? 10 x 2 *1 8x2 5x5 7 x 10 *2 11 x 2 How many 2s in 16? How many 5s in 30? How many 10s in 70? *3 Starting Position: © Focus Education (UK) Ltd 2014 84 Focus on Mathematics: Year 2 Name Date Objective 19 Number Use x, ÷ and = signs to read and write mathematical statements Can you work these out? 12 X 2 *1 15 ÷ 5 7X2 25 ÷ 5 10 x 3 24 ÷ 2 8x5 60 ÷ 10 *2 Starting Position: © Focus Education (UK) Ltd 2014 85 Focus on Mathematics: Year 2 Name Objective 23 Date Number Solve word problems involving multiplication and division Can you work out the answers? A mum gave each of her children 2 coins. She had 4 children. How many coins did she give out? *1 Dad had 16 toy cars. He shared them equally with me and my brother. How many did I get? In the PE hall there are different coloured balls: red; yellow; green and blue. There are 5 of each colour. How many are there altogether? In the PE lesson there are 20 bean bags to be shared between 5 children. How many bean bags did each child get? For dinner, everyone had 2 sausages. There were 8 children on the table. How many sausages were there altogether? Five boys shared 25 marbles between them. How many marbles did each boy get? In pre-school 7 mums sat together. They each had 2 children. How many children were there altogether? In the tray there were 15 coloured pencils. 3 boys shared these out. How many pencils did each boy get? © Focus Education (UK) Ltd 2014 *2 86 Focus on Mathematics: Year 2 Name Objective 24 Date Number Recognise, find, name and write fractions ⅓, ¼, 2/4 and ¾ of a length, shape, set of objects or quantity Can you work these out? What is half of 8? *1 Can you colour in a half of this shape? What is a quarter (¼) of 12? Can you colour in a quarter of this shape? What is three quarters (3/4) of 12? Can you colour in three quarters of this shape? What is a third (1/3) of 9? Can you colour in a third of this shape? *2 Starting Position: © Focus Education (UK) Ltd 2014 87 Focus on Mathematics: Year 2 Name Objective 26 Date Number Count in halves and quarters to 10 Can you continue these sequences? ½, 1, 1 ½ , 2, 2 ½ ,…. *1 ¼ , ½, ¾ , 1, 1 ¼, 1 ½, …. 4 ½ , 5, 5 ½ , 6, 6 ½ ,…. 5 ¼, 5 ½, 5 ¾, 6, 6 ¼ ,…. 7, 7 ½ , 8, 8 ½, 9,……. 8, 7 ¾, 7 ½, 7 ¼, 7, 6 ¾,… 5, 4 ½, 4, 3 ½, 3, 2 ½, … 5, 4 ¾, 4 ½, 4 ¼, 4, 3 ¾ ,… *2 Starting Position: © Focus Education (UK) Ltd 2014 88 Focus on Mathematics Year 2 Group Objectives Measurement, Geometry and Statistics Year 2 Objectives : Measurement 1 MEASUREMENT MEASUREMENT Objective 1m: Choose and use appropriate standard units to estimate and measure using rulers, scales, thermometers and measuring vessels, Length/height (m, cm) in any direction Mass (kg, g) Temperature (°C) Capacity (l, ml) to the nearest appropriate unit Objective 2m: Compare and order lengths, mass, volume/capacity and record results using ˂,˃ and = Know 1 m and make reasonable estimates of length/height up to 10m Know 1cm and make reasonable estimates of length/height up to 100cm Know 1kg and make reasonable estimates of weight up to 5kg Order different lengths using metres and centimetres Order different weights using kilograms and grams Use the symbols ˃, ˂, and = to compare two amounts of lengths and weight Record information using ˃, ˂, and = Name objects that weigh more or less than 1kg, 10kg Record amounts of liquid using litres and millilitres Know how much they weigh in kg Use ˃, ˂, and = to compare amounts of liquid Know that kg is a written format for kilogram Objective 3m: Read scales to the nearest numbered unit Know how much 1 litre is Know that many liquids are sold in 1 litre amounts Know amounts that are more or less than 1 litre Know that 0°C is freezing Know that 100°C is boiling Estimate the temperature outside to a reasonable approximation Read weighing scales to the nearest 10 gram units Read lengths to the nearest centimetre Read liquid amounts to the nearest 10 ml © Focus Education (UK) Ltd 2014 90 Year 2 Objectives : Measurement 2 MEASUREMENT MEASUREMENT Objective 4m: Recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value Objective 7m: Estimate and measure using appropriate standard units, using appropriate measuring vessels, rulers and scales: Height/length (m, cm) Mass (kg, g) Temperature (°C) Volume and capacity (l, ml) Know that 1p + 2p = 3p, 10p + 5p = 15p and 50p + 20p = 70p Know that £1 = 50p + 50p Estimate a distance of up to 5 metres Objective 5m: Find different combinations of coins that equal the same amount of money Find all the different ways of using coins to make 20p Name objects that are more or less than a metre long or high Know how long a centimetre is Find all the different ways of using coins to make 50p Know that 100 centimetres make up 1 metre Find all the different ways of using coins to make £1 Objective 6m: Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change Calculate how much Imran spends if he buys an apple for 20p and a banana for 10p. Calculate how much change he would get from 50p Calculate how much change he would get from £1. Use a ruler to measure 5cm, 10cm, 20cm and 30cm accurately Name objects that are approximately 10 cm long Write m and cm to represent metre and centimetres respectively Recognise mm as a very small measurement Know that 10 mm is 1 centimetre © Focus Education (UK) Ltd 2014 91 Year 2 Objectives : Measurement 3 MEASUREMENT Objective 8m: Tell and write the time to 5 minutes (including quarter to and past) MEASUREMENT Read the clock to o’clock and half past Objective 11m: Add and subtract money of the same unit Read the clock to quarter past and quarter to Read the clock in five minute intervals past the hour Add 2 different amounts of money using combinations of £ and 50p Read the clock to five minute intervals to the hour Draw times on clock faces to the intervals of o’clock, half past, quarter past and quarter to the hour Objective 9m: Recognise coins and notes of different values Add 2 different amounts of money using combinations of £ and 10p Add 2 different amounts of money using a combination of notes and coins to the value of £10 Recognise all coins from 1p to £2 Recognise all notes from £5 to £50 Objective 10m: Combine amounts to make values and match combinations of coins to amounts of money Combine coins between the value of 10p and 50p and say how much altogether up to the value of £1 Combine coins between the value of 10p and 50p and say how much altogether up to the value of £5 Combine notes and coins to make up amounts to the value of £10 Combine notes and coins to make up amounts to the value of £50 © Focus Education (UK) Ltd 2014 92 Year 2 Objectives : Geometry 1 PROPERTIES OF SHAPES PROPERTIES OF SHAPES Objective 1g: Recognise and name common 2D and 3D shapes Objective 4g: Identify and describe properties of 3D shapes, including the number of edges, vertices and faces Know and name squares, rectangles, triangles and circles Identify simple 3D shapes according to edges, vertices and faces Know and name cubes, cuboids, spheres, pyramids Use terms vertices and faces when describing 3D shapes Objective 2g: Identify and describe properties of 2D shapes, including the number of sides and line symmetry in a vertical line Identify a line of symmetry in simple shapes Objective 5g: Identify 2D shapes on the surface of 3D shapes Describe 3D shapes according to their 2D make up, e.g. number of squares, triangles, etc. Identify a circle on a cylinder/a triangle on a pyramid, etc. Make up own symmetrical shapes Begin to explore nets of 3D shapes according to 2D shapes contained within them, e.g. a cube has 6 squares Identify 2-D shapes according to sides and number of edges, etc. Describe 2-D shapes including the number of sides and line symmetry Objective 6g: Compare and sort common 2D and 3D shapes Objective 3g: Identify and describe properties of polygons and non-polygons Put together sets of triangles, recognising their similarities and differences Draw lines and shapes using a straight edge Put together sets of rectangles recognising their similarities and differences Put together sets of circles and spheres recognising the differences in their size © Focus Education (UK) Ltd 2014 93 Year 2 Objectives : Geometry 2 POSITION, DIRECTION AND MOTION Objective 7g: Order and arrange combinations of mathematical objects in patterns and sequences Objective 8g: Use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise) Use the term clockwise, anticlockwise, right angle, quarter turn, half turn, three quarter turn, accurately to describe movement © Focus Education (UK) Ltd 2014 94 Year 2 Objectives : Statistics STATISTICS Objective 1s: Interpret and construct simple pictograms, tally charts, block diagrams and simple tables Read information contained within a simple pictogram Read information contained within a simple tally chart Read information contained within a block diagram Read information contained within a simple table Construct a pictogram to show information collected (amounts of less than 20) Construct a tally chart to show information collected (amounts of less than 20) Construct a block diagram to show information collected (amounts of less than 20) Construct a simple table to show information collected (amounts of less than 20) Objective 2s: Ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity Objective 3s: Ask and answer questions about totalling and comparing categorical data © Focus Education (UK) Ltd 2014 95 Making Mathematics Work Step up to the Challenge Year 2 Number Year 2: Can you challenge yourself to meet the Objective? Objective 1: Can you count on in 2s, 3s, 5s, and 10s from any number up to 100? Me My Teacher Can you count on in 3s from any number up to 100? Can you count on in 2s from any number up to 100? Can you count on in 5s from any number up to 100? Can you count on in 10s from any number up to 100? Objective 2: Do you recognise the place value of each digit in a 2digit number (tens and ones)? Can you partition a 2-digit number to show the value of each digit? Can you recognise the ‘tens’ number in a 2-digit number? © Focus Education (UK) Ltd 2014 97 Year 2: Can you challenge yourself to meet the Objective? Objective 3: Can you add or subtract 10 from any number up to 100? Me My Teacher Me My Teacher Can you subtract 10 from any number up to 100? Can you subtract 10 from any number up to 50? Can you add 10 on to any number up to 100? Can you add 10 on to any number up to 50? Objective 4: Can you use ˂ , ˃ and = signs to compare and order numbers to 100? Can you use the ˃ symbol between 2 numbers accurately? Can you use the ˂ symbol between 2 numbers accurately? Can you use the = sign accurately in simple calculations? Do you know what the ˃ symbol stands for? Do you know what the ˂ symbol stands for? Do you know what the = symbol stands for? © Focus Education (UK) Ltd 2014 98 Year 2: Can you challenge yourself to meet the Objective? Objective 5: Can you read and write all numbers to 100 in numerals and words? Me My Teacher Can you read and write all numbers to 100 in numerals and words? Can you read and write all numbers to 50 in numerals and words? Can you read and write all numbers to 20 in numerals and words? Objective 6: Can you order, read and write numbers in increasing and decreasing value Me My Teacher Can you order a set of numbers (at least 3) in decreasing value using numbers up to 100? Can you order a set of numbers (at least 3) in increasing value using numbers up to 100? Can you order a set of numbers (at least 3) in decreasing value using numbers up to 50? Can you order a set of numbers (at least 3) in increasing value using numbers up to 50? © Focus Education (UK) Ltd 2014 99 Year 2: Can you challenge yourself to meet the Objective? Objective 8: Can you rapidly recall and use addition and subtraction facts to 20? Me My Teacher Can you relate number facts (within bonds of 20) to working out larger numbers, e.g. If 3 + 5 = 8, then 30 + 50 = 80? Do you know all subtraction number bonds to 20 instantly? Do you know all subtraction number bonds to 10 instantly? Do you know all addition number bonds to 20 instantly? Do you know all addition number bonds to 10 instantly? © Focus Education (UK) Ltd 2014 100 Year 2: Can you challenge yourself to meet the Objective? Objective 10: Do you recognise all odd and even numbers to 100? Me My Teacher Do you know that an even number can be shared between 2? Do you know all odd numbers to 20, then to 50, then to 100? Do you know all even numbers to 20, then to 50, then to 100? Do you know all odd numbers to 11? Do you know all even numbers to 10? Objective 12: Can you add and subtract up to 2-digit numbers using written methods including columnar addition (without carrying or borrowing)? Can you subtract a 2-digit number from another 2-digit number with numbers which do not involve borrowing from the tens column? Can you add two 2-digit numbers together using columnar addition (where the two units do not add up to 10)? Can you complete horizontal subtraction, taking a 1-digit number from a 2-digit number with answers of no more than 50? Can you complete horizontal addition of a 1-digit and a 2-digit number with answers up to 50; and then up to 100? © Focus Education (UK) Ltd 2014 101 Year 2: Can you challenge yourself to meet the Objective? Objective 13: Can you add and subtract mentally: a 2-digit number and ones, a 2-digit number and tens, two 2-digit numbers? Me My Teacher Can you add any two, 2-digit numbers that do not total above 100 and give the answer rapidly? Can you take away any 10s number from a 2-digit number and give the answer rapidly? Can you take away 10 from a 2-digit number and give the answer rapidly? Can you add any 10s number to a 2-digit number (answer no more than 100) and give the answer rapidly? Can you add 10 to a 2-digit number and give the answer rapidly? Can you take away a 1-digit number from a 2-digit number and give the answer rapidly? Can you add a 2-digit number to a 1-digit number and give the answer rapidly? © Focus Education (UK) Ltd 2014 102 Year 2: Can you challenge yourself to meet the Objective? Objective 14: Do you recognise subtraction as ‘taking away’ and ‘finding’ the difference’? Me My Teacher Can you complete a subtraction problem requiring you to find the difference in value between two numbers? Can you complete a subtraction problem requiring you to ‘take away’ one number from another? Objective 15: Do you know that addition can be done in any order, but subtraction cannot? Do you know that when subtracting you must always take the smaller number from the larger one? Do you know that when adding you can start with any number? Objective 16: Do you know that subtraction is the inverse of addition and can be used for checking calculations Do you know that in the calculation ‘a + b = c’; that c – a = b and c- b = a? © Focus Education (UK) Ltd 2014 103 Year 2: Can you challenge yourself to meet the Objective? Objective 17: Can you solve addition and subtraction word problems with up to 2-digits? Me My Teacher Can you solve simple word problems involving subtraction to 100? Can you solve simple word problems involving addition to 100? Can you solve simple word problems involving subtraction to 50? Can you solve simple word problems involving addition to 50? © Focus Education (UK) Ltd 2014 104 Year 2: Can you challenge yourself to meet the Objective? Objective 18: Can you recall multiplication and division facts for the 2, 5 and 10 times tables? Me My Teacher Can you answer rapidly any calculation involving the 5x table out of order? Can you recite the 5x table rapidly, up to x12, without error? Can you answer rapidly any calculation involving the 10x table out of order? Do you recognise that ÷2 is halving? Do you recognise that x2 is doubling? Can you recite the 10x table rapidly, up to x12, without error? Do you know the inverse rule; i.e. that 2 x 4 is the same as 4 x 2? Can you answer rapidly any calculation involving the 2x table out of order? Can you recite the 2x table rapidly, up to x12, without error? © Focus Education (UK) Ltd 2014 105 Year 2: Can you challenge yourself to meet the Objective? Objective 19: Can you use x, ÷ and = signs to read and write mathematical statements? Me My Teacher Can you use the x, ÷, and = signs in simple calculations for numbers up to 100? Do you know that the = sign stands for equals? Do you know that the ÷ sign stands for division? Do you know that the ‘x’ sign stands for multiplication? Objective 20: Can you calculate and write multiplication and division statements? Can you calculate and write simple division statements, such as 15 ÷ 3 = 5? Can you calculate and write out simple multiplication statements, such as 8 x 2 = 16? Objective 21: Do you recognise that division is the inverse of multiplication and use to check calculations? Do you know the inverse rule; i.e. that examples such as 35 ÷ 5 = 7 correspond to 7 x 5 = 35? Do you know the inverse rule; i.e. that examples such as 9 x 2 = 18 correspond to 18 ÷ 2 = 9? © Focus Education (UK) Ltd 2014 106 Year 2: Can you challenge yourself to meet the Objective? Objective 24: Can you recognise, name and write fractions ¼, ⅓, ½, ⅔ and ¾ of a whole? Me My Teacher Can you calculate ⅔ of a given number up to 100? Can you calculate ¾ of a given number up to 100? Can you calculate ¼ of a given number up to 100? Can you calculate ⅓ of a given number up to 100? Can you calculate ½ of a given number up to 100? Do you know that the symbol ⅔ stands for two-thirds of the value of a number or object? Do you know that the symbol ¾ stands for three-quarters of the value of a number or object? Do you know that the symbol ¼ stands for a quarter of the value of a number or object? Do you know that the symbol ⅓ stands for a third of the value of a number or object? Do you know that the symbol ½ stands for half the value of a number or object? © Focus Education (UK) Ltd 2014 107 Year 2: Can you challenge yourself to meet the Objective? Objective 26: Can you count in halves, quarters and thirds to 10? Me My Teacher Can you count in thirds sequence up to 10: ⅓, ⅔, 1, 1⅓, 1⅔,………….? Can you count in quarters sequence up to 10: ¼, ½, ¾, 1, 1¼, 1½,………….? Can you count in half sequence up to 10: ½; 1; 1½, 2, 2½, ……………? © Focus Education (UK) Ltd 2014 108 Making Mathematics Work Step up to the Challenge Year 2 Measurement, Geometry and Statistics Year 2: Can you challenge yourself to meet the Objective? Objective 1m: Can you estimate and measure using appropriate standard units, using appropriate measuring vessels, rulers and scales? Me My Teacher Do you know that 10 mm is 1 centimetre? Do you recognise mm as a very small amount? Can you write m and cm to represent metre and centimetres respectively? Can you name objects that are approximately 10 cm long? Can you use a ruler to measure 5cm, 10cm, 20cm and 30cm accurately? Do you know that 100 centimetres make up 1 metre? Do you know how long a centimetre is? Can you name objects that are more or less than a metre long or high? Can you estimate a distance of up to 5 metres? © Focus Education (UK) Ltd 2014 110 Year 2: Can you challenge yourself to meet the Objective? Objective 2m: Can you compare and order lengths, mass, volume/capacity and record results (using ˂,˃ and =)? Me My Teacher Can you use ˃, ˂, and = to compare amount of liquid? Can you record amounts of liquid using litres and millilitres? Can you record information using ˃, ˂, and =? Can you use the symbols ˃, ˂, and = to compare two amounts of lengths and weight? Can you order different weights using kilograms and grams? Can you order different lengths using metres and centimetres? Objective 3m: Can you read scales to the nearest numbered unit? Can you read weighing scales to the nearest 10 gram units? Can you read lengths to the nearest centimetre? Can you read liquid amounts to the nearest 10ml? © Focus Education (UK) Ltd 2014 111 Year 2: Can you challenge yourself to meet the Objective? Objective 7m: Can you estimate and measure using appropriate standard units, using appropriate measuring vessels, rulers and scales? (continued) Me My Teacher Can you estimate the temperature outside to a reasonable approximation? Do you know that 0°C is freezing and that 100°C is boiling? Do you know amounts that are more or less than 1 litre? Do you know that many liquids are sold in 1 litre amounts? Do you know how much 1 litre is? Do you know that kg is a written format for kilogram? Do you know how much you weigh in kg? Can you name objects that weigh more or less than 1kg, 10kg? Do you know 1kg and make reasonable estimates of weight up to 5kg? © Focus Education (UK) Ltd 2014 112 Year 2: Can you challenge yourself to meet the Objective? Objective 8m: Can you tell and write the time to 5 minutes (including quarter to and past)? Me My Teacher Can you draw times on clock faces to the intervals of o’clock, half past, quarter past and quarter to the hour? Can you read the clock in five minute intervals to the hour? Can you read the clock in five minute intervals past the hour? Can you read the clock to quarter past and quarter to? Can you read the clock to o’clock and half past? Objective 9m: Do you recognise coins and notes of different values? Can you recognise all notes from £5 to £50? Can you recognise all coins from 1p to £2? © Focus Education (UK) Ltd 2014 113 Year 2: Can you challenge yourself to meet the Objective? Objective 10m: Can you combine amounts to make values and match combinations of coins to amounts of money? Me My Teacher Can you combine notes and coins to make up amounts to the value of £50? Can you combine notes and coins to make up amounts to the value of £10? Can you combine coins between the value of 10p and 50p and say how much altogether up to the value of £5? Can you combine coins between the value of 10p and 50p and say how much altogether up to the value of £1? Objective 11m: Can you add and subtract money of the same unit? Can you add 2 different amounts of money using combinations of notes and coins to the value of £10 Can you add 2 different amounts of money using combinations of £ and 10p? Can you add 2 different amount of money using combinations of £ and 50p? © Focus Education (UK) Ltd 2014 114 Year 2: Can you challenge yourself to meet the Objective? Objective 2g: Can you identify and describe properties of 2D and 3D shapes (sides, lines of symmetry)? Me My Teacher Can you identify simple 3-D shapes according to sides, edges, faces, etc.? Can you identify 2-D shapes according to sides and number of edges, etc.? Can you make up your own symmetrical shapes? Can you identify a line of symmetry in simple shapes? Objective 3g: Can you identify and describe properties of 3D shapes (edges, vertices and faces)? Do you use the terms ‘vertices’ and ‘faces’ when describing 3D shapes? Can you identify simple 3D shapes according to sides, edges, faces, etc.? © Focus Education (UK) Ltd 2014 115 Year 2: Can you challenge yourself to meet the Objective? Objective 1s: Can you interpret and construct simple pictograms, tally charts, block diagrams and tables? Me My Teacher Can you read information contained within a pictogram? Can you read information contained within a simple tally chart? Can you read information contained within a block diagram? Can you read information contained within a simple table? Can you construct a pictogram to show information collected (amounts of less than 20)? Can you construct a tally chart to show information collected (amounts of less than 20)? Can you construct a tally chart to show information collected (amounts of less than 20)? Can you construct a block diagram to show information collected (amounts of less than 20)? Can you construct a simple table to show information collected (amounts of less than 20)? © Focus Education (UK) Ltd 2014 116 Focus on Mathematics Non-Negotiables Year 2 Possible Planning Outline Year 2 Mathematics Non-Negotiables • The following areas of learning are known as the non-negotiables. They have a specific role in helping pupils meet the year group expectations. In a nutshell, we are suggesting that if pupils are not confident in these areas then they will find the rest of the curriculum difficult to access. • The non-negotiables are designed to: 1. Identify the essential components that pupils need to become confident with, i.e. be able to demonstrate in independent tasks and be able to apply in other contexts. 2. Unblock learning, i.e. to keep teachers focused on the essential rather than coverage at the expense of progress. 3. Unlock learning and progress. • The non-negotiables are not designed to imply that the rest of the curriculum is an irrelevance – it clearly isn’t. But rather to give a structure for professionals to decide what the right curriculum is for their pupils. © Focus Education (UK) Ltd 2014 118 Year 2 Mathematics Non-Negotiables • Compare and order numbers up to 100. • Read and write all numbers to 100 in digits and words. • Say 10 more/less than any number to 100. • Count in multiples of 2, 3, 5 and 10 from any number up to 100. • Recall and use multiplication and division facts for 2, 5 and 10 tables. • Recall and use addition and subtraction facts to 20. • Derive and use related facts to 100. • Recognise place value of any 2-digit number. • Use the < > and = signs correctly • Add and subtract: o 2-digit numbers and ones o 2-digit numbers and tens o Two 2-digit numbers o Three 1-digit numbers • Recognise and use inverse for addition and subtraction • Calculate and write multiplication and division calculations using multiplication tables. • Recognise and use inverse for multiplication and division • Recognise, find, name and write 1/3; 1/4; 2/4; 3/4. • Recognise equivalence of simple fractions. • Tell time to five minutes, including quarter past and to the hour. © Focus Education (UK) Ltd 2014 119 Planning to meet the requirement of the nonnegotiables The following 3 pages suggest a planning outline for delivering the nonnegotiables in classrooms. There should be some element of teaching of these each day. Autumn Term Ist Half Term 2nd Half Term • Count on/back in steps of 2s and 5s to 100 from 0; and in 10s to 100 and beyond from 0 and any given number • Read and write all numbers to 100 in numerals and write all numbers in words to 30 • Order a set of numbers (at least 3) to 50 in increasing value • Recall fluently all addition number bonds to 10 and know all the subtraction number bonds to 10 • Add/subtract 2-digit and 1-digit numbers to 20 • Find 1/10 more/less than a given number up to 30 • Recall the 2 times tables up to 12x12 • Double any number up to 20 • Halve any even 2-digit number up to 40 • Count on/back in steps of 2s and 5s to 100, 3s to 30 from 0; and in 10s to 100 and beyond from 0 and any given number • Identify even and odd numbers to 20 • Read and write all numbers to 100 and beyond accurately in numerals and write all numbers in words to 30 and beyond • Order a set of numbers (at least 3) to 50 in decreasing value • Recall fluently all addition number bonds to 10 and beyond and know all the subtraction number bonds to 10 • Add/subtract 2-digit and 1-digit numbers to 20 and beyond • Find 1/10 more/less than a given number up to 30 • Recite the 2 times tables and answer any calculation involving the 2 times table in any order • Recite the 10 times tables • Double any number up to 30 • Halve any even 2-digit number up to 60 © Focus Education (UK) Ltd 2014 120 Planning to meet the requirement of the nonnegotiables Spring Term Ist Half Term 2nd Half Term • Count on/back in steps of 2s and 5s to 100; 3s to 30 and beyond from 0; and in 10s to 100 and beyond from 0 and any given number • Identify even and odd numbers to 20 and beyond • Read and write all numbers to 100 and beyond in numerals and write all numbers in words to 50 • Order a set of numbers (at least 3) to 100 in increasing value • Compare numbers up to 20 using =, <, > symbols • Recall fluently all addition number bonds to 15 and beyond and know all the subtraction number bonds to 15 • Find 1/10 more/less than 50 • Round numbers to the nearest 10 up to 50 • Add/subtract : 2-digit and 1-digit numbers, a 2-digit number and ten and add 3 one digit numbers • Recite the 2 and 10 times tables and answer any calculation involving the 2 and 10 times table in any order • Double any number up to 40 • Halve any even 2-digit number up to 80 • Count on/back in steps of 2s and 5s to 100, 3s to 60 from 0; and in 10s to 100 and beyond from 0 and any given number • Count in ½s to 5 • Identify even and odd numbers to 50 • Read and write all numbers to 100 and beyond in numerals and write all numbers in words to 50 and beyond • Order a set of numbers (at least 3) to 50 and beyond in decreasing value • Compare numbers up to 50 using =, <, > symbols • Round numbers to the nearest 10 up to at least 50 • Recall fluently all addition number bonds to 20 and know all the subtraction number bonds to 20 • Find 1/10 more/less than a given number up to 50 and beyond • Add/subtract 2-digit and 1-digit numbers to 20; a 2-digit number and tens • Add/subtract: 2-digit and 1-digit numbers, a 2-digit number and tens and add 3 one digit numbers • Recite the 2 and 10 times tables and answer any calculation involving the 2 and 10 times table in any order • Recite the 5 times tables • Double any number up to at least 40 • Halve any even 2-digit number up to 80 © Focus Education (UK) Ltd 2014 121 Planning to meet the requirement of the nonnegotiables Summer Term Ist Half Term • • • • • • • • • • • • • • • 2nd Half Term Count on/back in steps of 2s and 5s to 100 and beyond, 3s to 60 from 0; and in 10s to 100 and beyond from 0 and any given number Count in ½s to 10 Count in 1p, 2p, 5p, 10p and £1 Identify even and odd numbers to 50 and beyond Read and write all numbers to 100 and beyond in numerals and write all numbers in words to 100 Order a set of numbers (at least 3) to 100 in increasing and decreasing value Round numbers to the nearest 10 up to 100 Compare numbers up to 100 using =, <, > symbols Recognise the place value of a 2 digit number (tens and ones) Find 1/10 more/less than a given number up to 100 Recall fluently all addition number bonds to 20 and know all the subtraction number bonds to 20 to begin to become fluent in deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30) Add/subtract: 2-digit and 1-digit numbers, a 2-digit number and tens, two 2- digit numbers which do not involve bridging/exchanging across the 10s boundary and add 3 one digit numbers Recite the 2, 10 and 5 times tables and answer any calculation involving the 2, 10 and 5 times table in any order Double any number up to 50 Halve any even 2-digit number up to 100 • Count on/back in steps of 2s and 5s to 100 and beyond, 3s to 99 from 0; and in 10s to 100 and beyond from 0 and any given number • Count in 1p, 2p, 5p, 10p and £1 • Count in ½s to 10; in ¼s to 5 • Read and write all numbers to 100 and beyond in numerals and write all numbers in words to 100 and over • Order a set of numbers (4 and/or) to 100 in increasing and decreasing value • Round numbers to the nearest 10 up to at least 100 • Compare numbers up to 100 using =, <, > symbols • Begin to recognise the place value of a 3 digit number (hundreds, tens and ones) • Find 1/10 more/less than a given number up to 100 and beyond • Recall fluently all addition number bonds to 20 and know all the subtraction number bonds to 20 to begin to become fluent in deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30) • Add/subtract: 2-digit and 1-digit numbers, a 2-digit number and tens, two 2- digit numbers and add 3 one digit numbers • Recite the 2, 10 and 5 times tables and answer any calculation involving the 2, 10 and 5 times table in any order • Identify even and odd numbers to 100 • Double any number up to at least 50 • Halve any even 2-digit number up to 100 © Focus Education (UK) Ltd 2014 122 Focus on Mathematics Year 2 Assessment Assessment: Meeting Year 2 Expectations Year 2 Expectations: Number • • • • • • The main focus on assessment will be measuring a pupil’s journey towards and beyond the Year 2 expectations. The Year 2 expectations for number are set out on the right hand side of this page. To meet the Year 2 expectations a pupil must be able to meet all of the statements outlined in the table, plus the ones for measurement and geometry, shown later. If they have not met all the statements then they will be deemed to be emerging. If a pupil is meeting the expectations then an assessment needs to made as to whether a pupil is exceeding the expectations. The next page sets out how to assess whether a pupil is exceeding this expectation or whether a pupil is at the emerging stage. The next page also provides you with a 9point scale for deeper analysis, if required. • Read and write numbers to at least 100 in numerals and words • Recognise odd and even numbers to 100 • Count in steps of 2, 3 and 5 from 0 • Recognise place value of each digit in 2-digit numbers • Compare and order numbers from 0 to 100 using the >; <; and = signs • Name the fractions 1/3 ; ¼ ; ½ and ¾ and find fractional values of shapes; lengths and numbers • Recall and use multiplication and division facts for the 2, 5 and 10x multiplication tables • Add and subtract: two 1-digit; 2-digit and a 1 digit; 2-digit and 10s; two 2-digit and three 1-digit numbers • Solve problems with addition and subtraction • Understand commutativity in relation to addition, subtraction, multiplication and division © Focus Education (UK) Ltd 2014 124 Assessment: Meeting Year 2 Expectations The 3 or 9-point scale Effectively, pupils will be assessed on a 3-point scale: that is, pupils will be judged as having met the expectations; emerging towards the expectations or exceeding the expectations. However, for many schools, this may not give them enough information when tracking pupils through the school. So, if schools desire, the following 9-point system is outlined for them to use. Assessed position Emerging Stage C Emerging Stage B Emerging Stage A Meeting Stage C Meeting Stage B Meeting Stage A Exceeding Stage C Exceeding Stage B Exceeding Stage A Points allocation 1 2 3 4 5 6 7 8 9 • • • • • As is illustrated, Point 4 is the point that indicates that a pupil has met the expectations. If we are to take account of the new Assessment arrangements then it is hoped that 85% of pupils will be at least at this stage by the end of the year. Points 1 to 3 are the ‘emerging’ stages; Points 4 to 6 are the ‘meeting’ expectations stages; and Points 7 to 9 are the ‘exceeding’ stages. The following page sets out what each point actually means and provides clarity about the allocation of the points. © Focus Education (UK) Ltd 2014 125 Assessment: Meeting Year 2 Expectations A pupil will be deemed to be meeting the expectations only if they can satisfy their teacher that they meet all the expectations for their age A pupil will be deemed to be emerging towards the expectations if they do not meet all of the statements outlined for that year group •Meeting the expectations (Stage C) – Point 4 •It is accepted that a pupil might make the occasional error if they are at this stage. However, despite that, the teacher needs to be satisfied that they understand the concept fully. •Meeting the expectations (Stage B) - Point 5 •At this stage a pupil will rarely make mistakes and is very confident at meeting the statements. •Meeting the expectation (Stage A)- Point 6 •At this stage, not only is the pupil confident at meeting the statements but works at a rapid rate. However, they are not yet meeting all the statements for exceeding. •If they meet more than 75% of the statements but not all then they will be described as: •Emerging towards the expectations (Stage C) – Point 3 •If they meet between 50% and 75% of the statements then they will be described as: •Emerging towards the expectations (Stage B) – Point 2 •However if they are not meeting 50% of the expectations they will be described as: •Emerging towards the expectations (Stage A) – Point 1 •There is, therefore, no requirement to write a set of emerging statements © Focus Education (UK) Ltd 2014 A pupil will be deemed to be exceeding the expectations when, in addition to the statements set out for meeting the expectation (Stage A)they meet one or more of three sets of further expectations •Pupils will be deemed to be exceeding expectations if, in addition to what is outlined as Point 6, they show evidence of: •Accessing some of the following year group’s objectives •Being able to use the year group’s expectation within context •Being able to consistently apply the year group objectives in a range of situations. •A set of exceeding statements are set out for you to feel secure about your judgements. •If a pupil is meeting the exceeding statements, they will be deemed to be at Point 7 (Stage C) •If they are very confident and rarely make a mistake in relation to the ‘exceeding’ statements then they will be judged at Point 8 (Stage B) •A few pupils will be judged at Point 9 (Stage A). These will be pupils who are exceptionally confident in handling the exceeding statements and show exceptional mathematical ability for their age 126 Assessment: Meeting Year 2 Expectations Year 2 Expectations: Number • Read and write numbers to at least 100 in numerals and words • Recognise odd and even numbers to 100 Year 2 Expectations: Measurement, Geometry and Statistics • Choose and use appropriate standard units to estimate length/ height/ temperature and capacity • Count in steps of 2, 3 and 5 from 0 • Tell and write the time to 5 minute intervals • Recognise place value of each digit in 2-digit numbers • Recognise and use the symbols £ and p when solving problems involving addition and subtraction of money • Compare and order numbers from 0 to 100 using the >; <; and = signs • Name the fractions 1/3 ; ¼ ; ½ and ¾ and find fractional values of shapes; lengths and numbers • Recall and use multiplication and division facts for the 2, 5 and 10x multiplication tables • Describe the properties of 2D and 3D shapes to include: edges, vertices and faces • Interpret and construct pictograms, tally charts, block diagrams and simple tables • Add and subtract: two 1-digit; 2-digit and a 1 digit; 2-digit and 10s; two 2-digit and three 1-digit numbers • Solve problems with addition and subtraction • Understand commutativity in relation to addition, subtraction, multiplication and division © Focus Education (UK) Ltd 2014 127 Assessment: Exceeding Year 2 Expectations Year 2 Exceeding Expectations: • Count reliably up to 1000 in 2s, 5s and 10s • Count on and back in multiples of 4, 8, 25, 50 and 100 from any given number to beyond 1000 • Add and subtract fractions with a common denominator • Apply knowledge of number up to 100 to solve a one-step problem involving a addition, subtraction and simple multiplication and division • Apply knowledge of addition and subtraction to pay for items, up to £10, within a problem solving context • Add and subtract two 2-digit and numbers to 100 • Use an appropriate strategy to add and subtract numbers that move between and through 100, eg, 97 + 7; 103 - 8 • Know about right angles and where they can be seen in the environment • Tell time to 5 minute intervals in both analogue and digital and relate one to the other • Measure, compare, add and subtract using common metric measures © Focus Education (UK) Ltd 2014 128 Focus on Mathematics Year 2 Parents’ Guide Parents’ Guide ‘Must do’ by the end of Year 2 • • • • • • • • • • • • • • • Count on in 2s, 3s, 5s and 10s to 100 Find 10 more than a given number to 100 Find 10 less than a given number to 100 Use the < > and = signs correctly Order a set of 3 numbers in increasing and decreasing value Know all addition bonds to 20 Know all subtraction bonds to 20 Add a 1-digit number to a 2-digit number to 100 Add 2, 2-digit numbers using column addition Subtract a 1-digit number from a 2-digit number using columns with no carry over Rapid recall of 2-digit number add a 1-digit number Rapid recall of a 2-digit number add 10 Rapid recall of 2-digit add 2-digit number Rapid recall of 2-digit number take away 1digit number Rapid recall of a 2-digit number take away 10 • • • • • • • • Know all odd and even numbers to 100 Write any written number as digits Problem solving involving take away or difference Know the 2x, 5x and 10x tables Know the fractions: ½; ¼; ¾; ⅓; ⅔ Tell time to 5 minute intervals Recognise all coins from 1p to £2 Add and subtract money values involving 10p, 50p, and £notes © Focus Education (UK) Ltd 2014 130 Focus on Mathematics Year Group Objectives Year 3 Year 3 Objectives: Number NUMBER AND PLACE VALUE NUMBER AND PLACE VALUE Objective 1: Read and write numbers up to 1000 in numerals and words Objective 3: Compare and order numbers up to 1000 Read and write all numbers to 100 *1 Read and write all numbers in 100s from 100 to 1000 Read and write all numbers in 50s from 50 to 1000 Know which of two 3-digit numbers is the greater and smaller *1 *2 Order a set of 3-digit numbers from smallest to largest *2 *3 Order a set of 3-digit numbers from largest to smallest Read and write all numbers in 10s from 10 to 1000 Read and write all numbers to the value of 1000 Objective 4: Count in multiples of 4, 8, 50 and 100 from 0 *4 Objective 2: Recognise place value of each digit in a 3-digit number (hundreds, tens, ones) Count on and back in 10s from 0 to 1000 *1 Count on and back in 100s from 0 to 1000 *2 Count on and back in 50s from 0 to 1000 Know and use terms: units, tens and hundreds correctly *1 Count on and back in 4s from 0 to 1000 *3 Partition any number up to 999 showing the value of each digit *2 Count on and back in 8s from 0 to 1000 *4 © Focus Education (UK) Ltd 2014 132 Year 3 Objectives : Number 2 ADDITION AND SUBTRACTION NUMBER AND PLACE VALUE Objective 5: Find 10 or 100 more or less than a given number Objective 6: Mental addition and subtraction: pairs of one and 2-digit numbers; a 3-digit number and ones; a 3-digit number and tens; a 3-digit number and hundreds Add rapidly any 2 single-digit numbers Find 10 more than a given number between 0 and 1000 *1 Subtract rapidly any 2 single-digit number Find10 less than a given number between 0 and 1000 *2 Add together mentally any single-digit and any 2digit number Find100 more than a given number between 0 and 1000 Subtract any single-digit number from a 2-digit number Find100 less than a given number between 0 and 1000 Add together mentally any 3-digit number and any single-digit number *1 *2 *3 Subtract any single-digit number from a 3-digit number Add together mentally any 3-digit number and any 10s number Subtract any 10s number from a 3-digit number *4 Add together mentally any 3-digit number and any 100s number Subtract any 100s number from a 3-digit number © Focus Education (UK) Ltd 2014 133 Year 3 Objectives : Number 3 NUMBER AND PLACE VALUE Objective 7: Identify, represent and estimate numbers using different representations, including those related to measure Know that 7 tens and 3 ones is 73 *1 Know that 6 hundreds, 5 tens and 2 ones is 652 Know that an object of 4.8m is longer than one of 356cm *2 Know that 257cm is 2.57m *3 Objective 8: Solve number problems and practical problems involving numbers up to 1000 Solve problems such as which is greater: 3 hundreds, 6 tens and 4 ones or 578? Use everyday situations to solve problems involving addition with answers no greater than 1000 Use everyday situations to solve problems involving subtraction using numbers that are no greater than 1000 © Focus Education (UK) Ltd 2014 134 Year 3 Objectives : Number 4 ADDITION AND SUBTRACTION ADDITION AND SUBTRACTION Objective 9: Add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction Objective 10: Solve word problems, including missing numbers, using number facts, place value, and more complex addition and subtraction Add 2 numbers with 2-digits together using columnar addition without exchange between units and tens *1 Solve simple word problems involving missing numbers Subtract a 2-digit number from another using columnar subtraction which requires no exchange between the units, tens or hundreds Solve simple word problems involving place value Solve simple word problems involving complex addition to 1000 Add 2 numbers with 3-digits together using columnar addition without exchange between units and tens Add 2 numbers with 3-digits together using columnar addition, where the units and tens when added make more than 10. *2 Solve simple word problems involving complex subtraction to 1000 Add 3 numbers with 3-digits using columnar addition where the units or tens make more than 10 Subtract a 3-digit number from another using columnar subtraction which requires no exchange between the units, tens or hundreds *3 Subtract a 3-digit number from another using columner subtraction which requires exchange between the units, tens or hundreds *4 © Focus Education (UK) Ltd 2014 135 Year 3 Objectives : Number 5 ADDITION AND SUBTRACTION ADDITION AND SUBTRACTION Objective 11: Estimate the answer to a calculation and use inverse operations to check answers Objective 12: Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction *1 Estimate the answer to 65 add 32 Estimate the answer to 76 subtract 44 Solve simple word problems involving missing numbers Estimate the answer to 673 add 25 Solve simple word problems involving place value Estimate the answer to 864 subtract 523 *2 Know that 500 + 300 = 800 involves the same process as 800 - 300 = 500, or 800 – 500 = 300 Subtract any single-digit number from a 3-digit number Solve simple word problems involving complex addition to 1000 Solve simple word problems involving complex subtraction to 1000 © Focus Education (UK) Ltd 2014 136 Year 3 Objectives : Number 6 MULTIPLICATION AND DIVISION MULTIPLICATION AND DIVISION Objective 13: Know all table calculations for 2, 3, 4, 5, 8 and 10 Objective 15: Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for 2-digit times one-digit numbers, using mental and progressing to formal written methods Recite all multiplication facts for the x2 table *1 Recite all multiplication facts for the x5 table Multiply a 10s number by a single-digit number mentally, using 2, 3, 4, 5, 8 and 10x *1 Multiply a 2-digit number by a single-digit number using 2, 3, 4, 5, 8 and 10x *2 *3 Recite all multiplication facts for the x4 table Divide 2, 3, 4, 5, 8 and 10 into any 10s number (no remainder) Recite all multiplication facts for the x8 table Divide 2, 3, 4, 5, 8 and 10 into any 2-digit number (no remainder) *4 Recall all number facts for the 2, 3, 4, 5, 8 and 10x table out of sequence Objective 16: Solve word problems involving 4 operations, including missing number problems Recite all multiplication facts for the x10 table Recite all multiplication facts for the x3 table Know the inverse of all table facts involving 2, 3, 4, 5, 8 and 10x table, eg. how many 4s in 24? *2 Solve word problems involving addition with numbers up to 1000 Know the inverse of all table facts involving 2, 3, 4, 5, 8 and 10x table, eg. What is 48÷8? Solve word problems involving subtraction with numbers up to 1000 Objective 14: Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects Solve word problems involving multiplication with numbers up to 100 Solve word problems involving division with numbers up to 100 © Focus Education (UK) Ltd 2014 137 Year 3 Objectives : Number 7 FRACTIONS FRACTIONS Objective 17: Count up and down in tenths Objective 20: Recognise and show, using diagrams, equivalent fractions with small denominators Count up in tenths *1 Count down in tenths *2 Know that ½ is the same as 2/4, etc. Know that tenths arise from dividing an object into 10 equal parts *3 Be able to show 1/3 of a square and 2/6 of a square Objective 18: Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators Objective 19: Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators Know what fractional values are: eg. ¼ is one part of four, etc. Name all fractions from ½ to 1/12 Find ½,¼,⅕ of a given 2-digit number Objective 21: Add and subtract fractions with same denominator within one whole Add 2 fractions with the same denominator that add up to no more than 1 whole, eg. 5/7 + 1/7 = 6/7 *1 Subtract one fraction from another of the same denominator, eg. ⅘ – 2/5 = 2/5 *2 Objective 22: Compare and order unit fractions, and fractions with the same denominators Order any fraction between ½ to 1/12 Order any fraction where the denominator is the same (between ½ to 1/12th) Objective 23: Solve problems that © Focus Education involve (UK) Ltd 2014all of the above 138 Focus on Mathematics Year 3 Pre-Learning Tasks Number Focus on Mathematics: Year 3 Name Objective 1 Date Number Read and write numbers to 1000 in numerals and words Can you write these numbers in numerals? sixty-four *1 89 *3 247 one hundred three hundred and eighty- three Can you write these numbers in words? *2 392 Six hundred and five 709 eight hundred and eighteen 968 © Focus Education (UK) Ltd 2014 *4 140 Focus on Mathematics: Year 3 Name Date Objective 2 Number Recognise place value of each digit in a 3-digit number (hundreds, tens, ones) Can you place the hundreds, tens and the units in the correct place? 317 Hundreds Tens Units *1 Partition the following numbers 415 670 300 Hundreds Tens Units 426 Hundreds Tens Units 87 615 Hundreds Tens Units 902 © Focus Education (UK) Ltd 2014 *2 (400 + 10 + 5) 141 Focus on Mathematics: Year 3 Name Date Objective 3 Number Compare and order numbers up to 1000 Can you say which is the greater and the smaller number? Greater Smaller *1 Can you order these numbers (smallest first)? 26, 134, 98 132 or 235 202, 506, 113 132 or 569 67, 980, 127 657 or 234 803, 296, 105 113 or 233 230, 788, 982 109 or 201 115, 78, 902 100 or 98 67, 98, 230 207 or 702 119, 657, 458 666 or 444 201, 506, 561 17 or 767 205, 290, 256 © Focus Education (UK) Ltd 2014 *2 142 Focus on Mathematics: Year 3 Name Objective 4 Date Number Count on in steps of 4, 8, 50 and 100 from 0 Can you count on or back as required? 0, 100, 200 *1 0, 50,100 400,300,200 200,150,100 0, 4, 8 *3 16, 12, 8 *2 0, 8, 16 *4 32,24,16 Starting Position: © Focus Education (UK) Ltd 2014 143 Focus on Mathematics: Year 3 Name Objective 5 Date Number Find 10 or any 100 more or less than a given number Can you find the number 10 more than? 56 *1 Can you find the number 10 less than? 78 98 17 786 876 395 905 291 503 © Focus Education (UK) Ltd 2014 *2 144 Focus on Mathematics: Year 3 Name Date Objective 6 Number Mental addition and subtraction: pairs of one and 2-digit numbers; a 3-digit number and ones; a 3-digit number and tens; a 3-digit number and hundreds Can you complete these very quickly? (2 minutes) 7+6 *1 9-3 23 + 6 345 + 40 492 + 30 *2 569 - 50 56 + 9 348 - 90 67 - 5 363 + 200 45 - 9 875 + 300 129 + 6 *3 *4 560 - 200 345 + 9 789 - 300 124 - 8 678 -200 © Focus Education (UK) Ltd 2014 145 Focus on Mathematics: Year 3 Name Objective 7 Date Number Identify, represent and estimate numbers using different representations, including those related to measure Can you put each number in the correct column? H T U *1 51 579 911p 760 167p or £1.23 45cm or 1m 16cm 3m 78cm or 567cm 6m or 567cm *3 823cm 106 145p or £3.21 493p 178cm 63 Which is the greater? Can you write these as £ and p or as m and cm? *2 378cm 208p 134p 78cm © Focus Education (UK) Ltd 2014 146 Focus on Mathematics: Year 3 Name Date Objective 9 Number Add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction Can you calculate these accurately? *1 321 137 223+ 345 124 228+ 156 216 422+ 138 212 114+ 23 14+ 35 14+ 62 25+ 72 23+ 37 14- 48 25- 27 16- 18 12- 345 112- 789 356- 389 272- 479 345- *3 345 242+ 236 342+ 123 356+ 321 321+ 535 246- 621 373- 735 567- 843 467- *4 345 136+ 236 437+ 123 458+ 321 559+ *2 © Focus Education (UK) Ltd 2014 147 Focus on Mathematics: Year 3 Name Objective 11 Date Number Estimate the answer to a calculation and use inverse operations to check answers Can you quickly estimate the answers to these calculations? 77 + 65 39 - 13 *1 What do you notice about these calculations? 100 + 200 *2 300 - 100 123 + 65 256 + 99 250 + 130 367 - 50 380 - 130 345 - 90 429 + 60 560 - 200 345 + 90 760 - 560 424 - 8 © Focus Education (UK) Ltd 2014 148 Focus on Mathematics: Year 3 Name Objective 13 Date Number Know all table calculations for 2, 3, 4, 5, 8 and 10 Can you complete these very quickly? (2 minutes maximum) 5x5 *1 Can you complete these very quickly? (2 minutes maximum) How many 5s in 35? 9x3 How many 4s in 24? 10 x 8 How many 2s in 16? 6 x 10 How many 8s in 64? 7x8 How many 3s in 27? 7x4 How many 5s in 35? 4x3 How many 3s in 21? 10 x 4 How many 8s in 32? 10 x 10 How many 10s in 90? © Focus Education (UK) Ltd 2014 *2 149 Focus on Mathematics: Year 3 Name Objective 15 Date Number Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for 2-digit times one-digit numbers, using mental and progressing to formal written methods Can you complete these calculations? 20 x 3 *1 Can you complete these calculations? 50 ÷ 2 30 x 5 150 ÷ 3 40 x 8 240 ÷ 8 70 x 10 250 ÷ 5 24 x 8 *2 27 ÷ 3 41 x10 88 ÷ 8 35 x 5 72 ÷ 4 17 x 4 55 ÷ 5 © Focus Education (UK) Ltd 2014 *3 *4 150 Focus on Mathematics: Year 3 Name Objective 17 Date Number Count up and down in tenths Can you complete the sequences? 1/10; 2/10; 3/10 *1 7/10; 6/10; 5/10 1 3/10; 1 4/10; 1 5/10 2 3/10 ; 2 2/10 1 8/10; 1 9/10; 2; How many tenths in 2 and a half? 7 9/10; 8; 8 1/10 How many tenths in 4 and 3 tenths? *2 *3 Starting Position: © Focus Education (UK) Ltd 2014 151 Focus on Mathematics: Year 3 Name Objective 21 Date Number Add and subtract fractions with same denominator within one whole Can you add these fractions? 3/5 + 1/5 = *1 Can you subtract these fractions? 6/10 - 5/10 = 5/8 + 1/8 = 8/9 - 1/9 = 2/7 + 4/7 = 5/6 – 2/6 = 2/9 + 5/9 = 6/7 – 2/7 = *2 Starting Position: © Focus Education (UK) Ltd 2014 152 Focus on Mathematics Year 3 Group Objectives Measurement, Geometry and Statistics Year 3 Objectives : Measurement MEASUREMENT MEASUREMENT Objective 1m: Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg, g); volume and capacity (l/ ml) Objective 2m: Measure the perimeter of simple 2D shapes Practise using appropriate tools to measure distances and weight Know the term ‘perimeter’ Recognise 1m as having 100cm Know that the perimeter is the distance around the four sides of a rectangle Know that 50cm is ½ a metre Know that the perimeter is the distance around the outside of any shape Measure to the nearest metre a distance of up to 10m Measure accurately each side of a 2D shape and add up all the sides to find the perimeter Measure accurately a distance of up to 30cm using a ruler Measure a distance of up to 5m using a tape measure giving the answer in m and cm Objective 3m: Add and subtract amounts of money to give change, using both £ and p in practical contexts Recognise 1Kg as having 1000g Add any two amounts of money using notes and coins Know that 500g is ½ a Kg Sort out an amount of money by organising it into sets of the same coins and then making up sets of pounds, etc. Measure to the nearest Kg a weight of up to 10Kg on a weighing machine From a given amount give change from £1, £5, £10 Measure accurately a weight of up to 500g on a weighing scale Measure a weight of up to 5Kg using a weighing machine giving the answer in Kg and g © Focus Education (UK) Ltd 2014 154 Year 3 Objectives : Measurement 2 MEASUREMENT Objective 4m: Tell and write the time from an analogue clock, using Roman numerals 1 to X11, and 12 hour & 24 hour clocks MEASUREMENT Objective 6m: Record and compare time in terms of seconds, minutes, hours Recognise all Roman numerals from 1 to 12 and their associated place on a clock Know that 60 seconds is one minute and that 60 minutes is one hour Can tell the time on an analogue clock and write down its equivalent, e.g. ten past two can be written as 2:10 Know that quarter past is 15 minutes past; and that half past is 30 minutes past Know that 90 seconds is a minute and a half Understand the 24 hour system, e.g. 2pm is 1400 hours Know that 75 minutes is one hour and a quarter Objective 5m: Estimate and read time with increasing accuracy to the nearest minute Revise reading the time in five minute intervals Read the time to one minute intervals Objective 7m: Use vocabulary such as: o’clock, am, pm, morning, afternoon, noon and midnight Know that am represents time from midnight to noon Know that pm represents time from noon to midnight Estimate the time to the nearest five minutes, eg, it is almost ten past three © Focus Education (UK) Ltd 2014 155 Year 3 Objectives : Measurement 4 MEASUREMENT Objective 8m: Know the number of seconds in a minute; minutes in an hour; and the number of days in each month, year and leap year Know that 60 minutes make 1 hour; and that 60 seconds make 1 minute Know that the number of days per month varies between 28 to 31 Know that the number of days in a year varies between 365 and 366 and know the term leap year Know the rhyme associated with days of the month Objective 9m: Compare durations of events, e.g. calculate time taken by particular events or tasks Measure in minutes and seconds any duration using a stop watch or hand held clock Know that certain events last a given time: e.g. lunch hour = 60 minutes, playtime = quarter of an hour, football match = 90 minutes © Focus Education (UK) Ltd 2014 156 Year 3 Objectives : Geometry PROPERTIES OF SHAPES PROPERTIES OF SHAPES Objective 1g: Draw 2D shapes and make 3D shapes using modelling materials Objective 4g: Identify right angles; know that 2 and 4 right angles make half and a full turn respectively Draw 2D shapes and name them Know a right angle as having 90 degrees which is written as 90˚ Make a range of 3D shapes using playdough, clay Objective 2g: Recognise 3D shapes in different orientations and describe them Describe a range of 3D shapes set out in different ways Objective 3g: Recognise angles as a property of shape or a description of a turn Know that the opening between two lines joined at a point is known as an angle and can be measured in degrees Know that the measurement in degrees is greater when the opening is wider Know that two right angles effectively make a straight line and is equivalent to 180˚ Know that 2 right angles make a half-turn Know that three right angles make three quarters of a turn Know that 4 right angles is a complete turn Objective 5g: Identify whether angles are greater or less than a right angle Identify angles that are smaller than a right angle Identify angles that are larger than a right angle Know that an angle smaller than a right angle is known as an acute angle Know that an angle larger than a right angle is known as an obtuse angle © Focus Education (UK) Ltd 2014 157 Year 3 Objectives : Geometry 2/ Statistics PROPERTIES OF SHAPES STATISTICS Objective 6g: Identify horizontal and vertical lines and pairs of perpendicular and parallel lines Objective 1s: Interpret and present data using bar charts, pictograms and tables Know the terms: horizontal and vertical Read information set out in a bar chart, pictogram or table Read information from a bar chart that has a scale on the vertical axes Recognise horizontal and vertical in everyday situations, e.g. telephone pole being vertical, the sea being horizontal Present information in a pictogram, bar chart or table Know the relationship between horizontal and horizon Present information on a bar chart where there is a scale on the vertical axes Know the terms perpendicular and parallel Draw lines that are perpendicular and parallel to a given line Objective 2s: Solve one-step and two-step questions using information presented in scaled bar charts, pictograms and tables Objective 7g: Recognise and use abbreviations of metric units of measure Solve problems involving pictograms, bar charts and tables Know that metres, centimetres and millimetres are written as : m, cm, mm. respectively Work out the answer to: ‘How many more children like carrots than potatoes?’ Know that grams and Kilograms are written a: g. and Kg respectively Work out the answer to: ‘How many fewer children travel to school by car than walk?’ Know that litres and millilitres and written as: l, ml, respectively © Focus Education (UK) Ltd 2014 158 Focus on Mathematics Step up to the Challenge Year 3 Number Year 3: Can you challenge yourself to meet the Objective? Objective 1: Can you read and write numbers : to at least a 1000 in numerals and words? Me My Teacher Can you read and write all numbers to the value of 1000? Can you read and write all numbers in 10s from 10 to 1000? Can you read and write all numbers in 50s from 50 to 1000? Can you read and write all numbers in 100s from 100 to 1000? Can you read and write all numbers to 100? Objective 2: Can you recognise place value of each digit in a 3-digit number? Can you partition any number up to 999 showing the value of each digit? Do you know and use terms: units; tens and hundreds correctly? © Focus Education (UK) Ltd 2014 160 Year 3: Can you challenge yourself to meet the Objective? Objective 3: Can you compare and order numbers up to 1000? Me My Teacher Can you order a set of 3-digit numbers from largest to smallest? Can you order a set of 3-digit numbers from smallest to largest? Do you know which of two 3-digit numbers is the greater and smaller? Objective 4: Can you count in multiples of: 2, 3, 4, 5, 8, 10, 50 and 100 from 0? Can you count on and back in 8s from 0 to 96? Can you count on and back in 5s from 0 to 100? Can you count on and back in 4s from 0 to 100? Can you count on and back in 3s from 0 to 99? Can you count on and back in 50s from 0 to 1000? Can you count on and back in 10s from any given number between 0 and 1000? Can you count on and back in 10s from 0 to 100? Can you count on and back in 100s from 0 to 1000? © Focus Education (UK) Ltd 2014 161 Year 3: Can you challenge yourself to meet the Objective? Objective 5: Do you know 10 or 100 more or less than a given number? Me My Teacher Do you know 100 less than a given number between 0 and 1000? Do you know 100 more than a given number between 0 and 1000? Do you know 10 less than a given number between 0 and 1000? Do you know 10 more than a given number between 0 and 1000? © Focus Education (UK) Ltd 2014 162 Year 3: Can you challenge yourself to meet the Objective? Objective 6: Can you work out these mental addition and subtraction: pairs of one and 2-digit numbers; 3-digit numbers and ones; 3-digit numbers and tens; 3-digit numbers and hundreds? Me My Teacher Can you subtract any 100s number from a 3-digit number? Can you add together mentally any 100s number and any 3-digit number? Can you subtract any 10s number from a 3-digit number? Can you add together mentally any 10s number and any 3-digit number? Can you subtract any single-digit number from a 3-digit number? Can you add together mentally any single-digit and any 3-digit number? Can you subtract any single-digit number from a 2-digit number? Can you add together mentally any single-digit and any 2-digit number? Can you subtract rapidly any 2 single-digit numbers? Can you add rapidly any 2 single-digit numbers? © Focus Education (UK) Ltd 2014 163 Year 3: Can you challenge yourself to meet the Objective? Objective 8: Can you solve word problems, including missing numbers, using number facts, place value, and more complex addition and subtraction? Me My Teacher Can you solve simple word problems involving complex subtraction to 1000? Can you solve simple word problems involving complex addition to 1000? Can you solve simple word problems involving place value? Can you solve simple word problems involving missing numbers? © Focus Education (UK) Ltd 2014 164 Year 3: Can you challenge yourself to meet the Objective? Objective 9: Add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction Me My Teacher Can you subtract a 3-digit number from another using column subtraction which requires exchange between the units, tens or hundreds ? Can you subtract a 3-digit number from another using columnar subtraction which requires no exchange between the units, tens or hundreds? Can you add 3 numbers with 3-digits using columnar addition where the units or tens make more than 10? Can you add 2 numbers with 3-digits together using columnar addition, where the units and tens when added make more than 10? Can you add 2 numbers with 3-digits together using columnar addition without exchange between units and tens? Can you subtract a 2-digit number from another using columnar subtraction which requires no exchange between the units, tens or hundreds? Can you add 2 numbers with 2-digits together using columnar addition without exchange between units and tens? © Focus Education (UK) Ltd 2014 165 Year 3: Can you challenge yourself to meet the Objective? Objective 10: Can you solve word problems involving 4 operations, including missing number problems? Can you solve word problems involving division with numbers up to 100? Can you solve word problems involving multiplication with numbers up to 100? Can you solve word problems involving subtraction with numbers up to 1000? Can you solve word problems involving addition with numbers up to 1000? © Focus Education (UK) Ltd 2014 166 Year 3: Can you challenge yourself to meet the Objective? Objective 11: Estimate the answer to a calculation and use inverse operations to check answers Me My Teacher Can you subtract any single-digit number from a 3-digit number? Do you know that 500 + 300 = 800 involves the same process as 800 - 300 = 500, or 800 – 500 = 300? Can you estimate the answer when subtracting one 3-digit number from another 3digit number? Can you estimate the answer when adding a 3-digit number to a 2-digit numbers? Can you estimate the answer when subtracting one 2-digit number from another 2-digit number? Can you estimate the answer when adding 2, 2-digit numbers? Objective 12: Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction Can you solve simple word problems involving complex subtraction to 1000? Can you solve simple word problems involving complex addition to 1000? Can you solve simple word problems involving place value? Can you solve simple word problems involving missing numbers? © Focus Education (UK) Ltd 2014 167 Year 3: Can you challenge yourself to meet the Objective? Objective 13: Can you recall and use multiplication and division facts for: 2, 3, 4, 5, 8 and 10? Me My Teacher Do you know the inverse of all table facts involving 2, 3, 4, 5, 8 and 10x table, e.g. how many 4s in 24? Can you recall all number facts for the 2, 3, 4, 5, 8 and 10x table out of sequence? Can you recite all multiplication facts for the x8 table? Can you recite all multiplication facts for the x4 table? Can you recite all multiplication facts for the x3 table? Can you recite all multiplication facts for the x10 table? Can you recite all multiplication facts for the x5 table? Can you recite all multiplication facts for the x2 table? © Focus Education (UK) Ltd 2014 168 Year 3: Can you challenge yourself to meet the Objective? Objective 15: Can you write and calculate using multiplication and division within multiplication tables; 2-digit x one-digit; using mental and written methods? Me My Teacher Me My Teacher Can you divide 2, 3, 4, 5, 8 and 10 into any 2-digit number (no remainder)? Can you divide 2, 3, 4, 5, 8 and 10 into any 10s number (no remainder)? Can you multiply a 2-digit number by a single-digit number using 2, 3, 4, 5, 8 and 10x ? Can you multiply a 10s number by a single-digit number mentally, using 2, 3, 4, 5, 8 and 10x? Objective 16: Solve word problems involving 4 operations, including missing number problems Can you solve word problems involving division with numbers up to 100? Can you solve word problems involving multiplication with numbers up to 100? Can you solve word problems involving subtraction with numbers up to 1000? Can you solve word problems involving addition with numbers up to 1000? © Focus Education (UK) Ltd 2014 169 Year 3: Can you challenge yourself to meet the Objective? Objective 17: Count up and down in tenths Me My Teacher Do you know that tenths arise from dividing an object into 10 equal parts? Can you count down in tenths? Do you know what fractional values are: eg ¼ is one part of four, etc.? Objective 19: Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators Can you find ½,¼,⅕ of a given 2-digit number Can you name and order any fraction between ½ to 1/12? Do you know what fractional values are: eg. ¼ is one part of four, etc.? © Focus Education (UK) Ltd 2014 170 Making Mathematics Work Step up to the Challenge Year 3 Measurement, Geometry and Statistics Year 3: Can you challenge yourself to meet the Objective? Objective 1m: Can you measure, compare, add and subtract: lengths (m/cm/mm); masses (kg, g); volume and capacity (l/ ml); and time (hr/mins/sec)? Me My Teacher Do you know that 60 minutes make 1 hour; and that 60 seconds make 1 minute? Can you measure a weight of up to 5Kg using a weighing machine giving the answer in Kg and g? Can you measure accurately a weight of up to 500g on a weighing scale? Can you measure to the nearest Kg a weight of up to 10Kg on a weighing machine? Do you know that 500g is ½ a Kg? Do you recognise 1Kg as having 1000g? Can you measure a distance of up to 5m using a tape measure giving the answer in m and cm? Can you measure accurately a distance of up to 30cm using a ruler? Can you measure to the nearest metre a distance of up to 10m? Do you know that 50cm is ½ a metre? Do you recognise 1m as having 100cm? Can you practise using appropriate tools to measure distances © Focus Education (UK) Ltd 2014 and weight? 172 Year 3: Can you challenge yourself to meet the Objective? Objective 2m: Can you measure perimeter of simple 2D shapes? Me My Teacher Can you measure accurately each side of a 2D shape and add up all the sides to find the perimeter? Do you know that the perimeter is the distance around the outside of any shape? Do you know that the perimeter is the distance around the four sides of a rectangle? Do you know the term perimeter? Objective 3m: Can you add and subtract amounts of money to give change, using £ and p? From a given amount can you give change from £1, £5, £10 ? Can you sort out an amount of money by organising it into sets of the same coins and then making up sets of pounds, etc.? Can you add any two amounts of money using notes and coins? © Focus Education (UK) Ltd 2014 173 Year 3: Can you challenge yourself to meet the Objective? Objective 4m: Can you tell and write the time from an analogue clock, using Roman numerals 1 to X11, and 12 hour & 24 hour digital clocks? Can you tell the time in digital format and write it down? Do you understand the 24 hour system, e.g. 2pm is 1400 hours? Can you tell the time on an analogue clock and write down its equivalent, e.g. ten past two can be written as 2:10? Do you recognise all Roman numerals from 1 to 12 and their associated place on a clock? © Focus Education (UK) Ltd 2014 174 Year 3: Can you challenge yourself to meet the Objective? Objective 5m: Can you estimate and read time to the nearest minute? Me My Teacher Can you estimate the time to the nearest five minutes, eg, it is almost ten past three? Can you read the time to one minute intervals? Can you revise reading the time in five minute intervals? Objective 6m: Can you compare time in terms of seconds, minutes, hours and o’clock? Do you know that 90 seconds is a minute and a half? Do you know that quarter past is 15 minutes past; and that half past is 30 minutes past? Do you know that 60 seconds is one minute and that 60 minutes is one hour? Objective 7m: Do you use terms such as: am, pm, morning, afternoon, noon and midnight? Do you know that pm represents time from noon to midnight? Do you know that am represents time from midnight to noon? © Focus Education (UK) Ltd 2014 175 Year 3: Can you challenge yourself to meet the Objective? Objective 8m: Know the number of seconds in a minute; minutes in an hour; and the number of days in each month, year and leap year Do you know the rhyme associated with days of the month? Do you know that the number of days in a year varies between 365 and 366 and know the term leap year? Do you know that the number of days per month varies between 28 to 31? Do you know that 60 minutes make 1 hour; and that 60 seconds make 1 minute? Objective 9m: Can you compare duration of events, e.g. calculate time taken up by particular events or tasks? Me My Teacher Do you know that certain events last a given time: e.g. lunch hour; football match = 90 minutes? Can you measure in minutes and seconds any duration using a stop watch or hand held clock? © Focus Education (UK) Ltd 2014 176 Year 3: Can you challenge yourself to meet the Objective? Objective 3g: Do you recognise angles as a property of shape and as an amount of turning? Me My Teacher Do you know that the measurement in degrees is greater when the opening is wider? Do you know that the opening between two lines joined at a point is known as an angle and can be measured in degrees? Objective 4g: Can you identify right angles; know that 2 and 4 right angles make half and a full turn respectively? Do you know that 4 right angles is a full turn? Do you know that 2 right angles is half a turn? Do you know that two right angles make a straight line and is equivalent to 180˚? Do you know a right angle has 90 degrees which is written as 90˚? © Focus Education (UK) Ltd 2014 177 Year 3: Can you challenge yourself to meet the Objective? Objective 5g: Can you identify whether angles are greater or less than a right angle? Me My Teacher Do you know that an angle larger than a right angle is known as an obtuse angle? Do you know that an angle smaller than a right angle is known as an acute angle? Can you identify angles that are larger than a right angle? Can you identify angles that are smaller than a right angle? Objective 6g: Can you identify horizontal, vertical, perpendicular, parallel, and curved lines? Can you draw lines that are perpendicular and parallel to a given line? Do you know the terms perpendicular and parallel? Do you know the relationship between horizontal and horizon? Can you recognise horizontal and vertical in everyday situations, eg, telephone pole being vertical, the sea being horizontal? Do you know the terms: horizontal and vertical? © Focus Education (UK) Ltd 2014 178 Year 3: Can you challenge yourself to meet the Objective? Objective 7g: Recognise and use abbreviations of metric units of measure Me My Teacher Do you know that litres and millilitres and written as: l and ml, respectively? Do you know that grams and Kilograms are written a: g and Kg respectively? Do you know that metres, centimetres and millimetres are written as : m, cm and mm respectively? © Focus Education (UK) Ltd 2014 179 Year 3: Can you challenge yourself to meet the Objective? Objective 1s: Can you read, interpret and present data using pictograms and bar charts with scales? Me My Teacher Can you present information on a bar chart where there is a scale on the vertical axes? Can you present information in a pictogram or bar chart? Can you read information from a bar chart that has a scale on the vertical axes? Can you read information set out in a bar chart or pictogram? Objective 2s: Solve one-step and two-step questions using information presented in scaled bar charts, pictograms and tables Work out the answer to: ‘How many fewer children travel to school by car than walk?’ Work out the answer to: ‘How many more children like carrots than potatoes?’ Solve problems involving pictograms, bar charts and tables © Focus Education (UK) Ltd 2014 180 Focus on Mathematics Non-Negotiables Year 3 Possible Planning Outline Year 3 Mathematics Non-Negotiables • The following areas of learning are known as the non-negotiables. They have a specific role in helping pupils meet the year group expectations. In a nutshell we are suggesting that if pupils are not confident in these areas then they will find the rest of the curriculum difficult to access. • The non-negotiables are designed to: 1. Identify the essential components that pupils need to become confident with, i.e. be able to demonstrate in independent tasks and be able to apply in other contexts. 2. Unblock learning, i.e. to keep teachers focused on the essential rather than coverage at the expense of progress. 3. Unlock learning and progress. • The non-negotiables are not designed to imply that the rest of the curriculum is an irrelevance – it clearly isn’t. But rather to give a structure for professionals to decide what the right curriculum is for their pupils. © Focus Education (UK) Ltd 2014 182 Year 3 Mathematics Non-Negotiables • Compare and order numbers up to 1000. • Read and write all numbers to 1000 in digits and words. • Find 10 or 100 more/less than a given number. • Count from 0 in multiples of 4, 8, 50 & 100. • Recall and use multiplication & division facts for 3, 4, 8 tables. • Recognise place value of any 3-digit number. • Add and subtract: o 3-digit numbers and ones o 3-digit numbers and tens o 3-digit numbers and hundreds • Add and subtract: o Numbers with up to 3-digits using efficient written method (column). • Use inverse to check. • Multiply: o 2-digit by 1-digit • Count up/down in tenths. • Compare and order fractions with same denominator. • Addition and subtraction of fractions with same denominator with whole. • Know pairs of fractions that total 1. • Tell time using 12 and 24 hour clocks; and using Roman numerals. • Tell time to nearest minute. • Know number of days in each month. © Focus Education (UK) Ltd 2014 183 Planning to meet the requirement of the nonnegotiables The following 3 pages suggest a planning outline for delivering the non-negotiables in classrooms. There should some element of teaching of these each day. Autumn Term Ist Half Term 2nd Half Term • Count on/back in steps of 2s, 5s, 10s, 3s to 100 and beyond, from 0 and any given number • Count on/back in 4s from 0 to 100 • Count on/back in 50s and 100s from 0 to 1000 • Find 10/100 more or less than a given number up to 500 • Read and write all numbers to 1000 in numerals and write all numbers in words to 200 and over • Order a set of numbers (4 and/or 5 ) to at least 1000 in increasing and decreasing value • Compare numbers up to 200 using =, <, > symbols • Round numbers to the nearest 10 to at least 200 • Partition 3 digit numbers (hundreds, tens and ones) • Recall fluently all addition number bonds to 20 and know all the subtraction number bonds to 20 to begin to become fluent in deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30 and 300 + 700 = 1000; 1000 – 700 = 300 and 700 = 1000 – 300) • Add/subtract: 2-digit and 1-digit numbers, a 2-digit number and tens, two 2- digit numbers and add 3 one digit numbers • Recall the 2, 5 and 10 times tables and the derived division facts and begin to learn the 4 and 3 times tables • Double any number up to 50 and halve any even 2-digit number up to 100 • • • • • • • • • • • • • • • Count on/back in steps of 2s, 5s, 10s, 3s to 100 and beyond, from 0 and any given number Count on/back in multiples of 4 and 8 from 0 Count on/back in 50s, 100s from 0 to 1000 Find 10/100 more or less than a given number up to 500 Count on/back in tenths Read and write all numbers to 1000 in numerals and write all numbers in words to 400 and over Order a set of numbers (4 and/or 5 ) to at least 1000 in increasing and decreasing value Compare numbers up to 200 and beyond using =, <, > symbols Round numbers to the nearest 10 to at least 500 and to the nearest 100 to 500 Partition 3 digit numbers (hundreds, tens and ones) Recall fluently all addition number bonds to 20 and know all the subtraction number bonds to 20 to begin to become fluent in deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30 and 300 + 700 = 1000; 1000 – 700 = 300 and 700 = 1000 – 300) Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and tens and a 3-digit number and hundreds Count on/back in ½s , ¼s and 1/3s including on a number line Recall the 2, 3, 4, 5 and 10 times tables and the derived division facts Double any number up to 50 and halve any even 2-digit number up to 100 © Focus Education (UK) Ltd 2014 184 Planning to meet the requirement of the nonnegotiables Spring Term Ist Half Term • • • • • • • • • • • • • • 2nd Half Term Count on/back in steps of 2s,5s, 10s, 3s to 100 and beyond, from 0 and any given number Count on/back in multiples of 4 and 8 from 0 Count on/back in 50s, 100s from 0 to 1000 Find 10/100 more or less than a given number up to 500 and more Read and write all numbers to 1000 in numerals and write all numbers in words to 500 Order a set of numbers (4 and/or 5 ) to at least 1000 in increasing and decreasing value Compare numbers up to 500 using =, <, > symbols Round numbers to the nearest 10 to at least 1000 and to the nearest 100 to 1000 Recognise the place value of each digit (hundreds, tens and ones) Recall fluently all addition number bonds to 20 and know all the subtraction number bonds to 20 to begin to become fluent in deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30 and 300 + 700 = 1000; 1000 – 700 = 300 and 700 = 1000 – 300) Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and tens and a 3-digit number and hundreds Recall the 2, 3, 4, 5 and 10 times tables and the derived division facts Double any number up to 100; double any multiple of 50 up to 500 and halve any number up to 100 Find complements to 100 and recall addition and subtraction facts for 100 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 – 63 = 37) • • • • • • • • • • • • • • • Count on/back in steps of 2s, 5s, 10s, 3s to 100 and beyond, from 0 and any given number Count on/back in multiples of 4 and 8 from 0 Count on/back in 50s, 100s from 0 to 1000 Find 10/100 more or less than a given number up to 500 and more Read and write all numbers to 1000 in numerals and write all numbers in words to 500 and over Order a set of numbers (4 and/or 5 ) to at least 1000 in increasing and decreasing value Compare numbers up to 500 and beyond using =, <, > symbols Round numbers to the nearest 10 to at least 1000 and to the nearest 100 to 1000 Partition 3 digit numbers (hundreds, tens and ones) and partition numbers in different ways Recall fluently all addition number bonds to 20 and know all the subtraction number bonds to 20 to begin to become fluent in deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30 and 300 + 700 = 1000; 1000 – 700 = 300 and 700 = 1000 – 300) Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and tens and a 3-digit number and hundreds Count on/back in ½s , ¼s and 1/3s including on a number line Recall the 2, 3, 4, 5, and 10 times tables and the derived division facts Double any number up to 100; double any multiple of 50 up to 500 and halve any number up to 100 Find complements to 100 and recall addition and subtraction facts for 100 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 – 63 = 37) © Focus Education (UK) Ltd 2014 185 Planning to meet the requirement of the nonnegotiables Summer Term Ist Half Term • • • • • • • • • • • • • • 2nd Half Term Count on/back in steps of 1s, 10s, or 100 from any 2/3 digit numbers Count on/back in 50s, 100s from 0 to 1000 Find 10/100 more or less than a given number up to 1000 Read and write all numbers to 1000 in numerals and write all numbers in words to at least 1000 Order a set of numbers (4 and/or 5 ) to at least 1000 in increasing and decreasing value Compare numbers up to 1000 using =, <, > symbols Round numbers to the nearest 10 to 1000 and beyond and to the nearest 100 to 1000 and beyond Partition 3 digit numbers (hundreds, tens and ones) and partition numbers in different ways Count in tenths, read and write numbers with 1 decimal place and compare numbers with one decimal place Recall fluently all addition number bonds to 20 and know all the subtraction number bonds to 20 to begin to become fluent in deriving facts ( e.g. 3 + 7 = 10; 10 – 7 = 3 and 7 = 10 -3 to calculate 30 + 70 = 100; 100 – 70 = 30 and 70 = 100 – 30 and 300 + 700 = 1000; 1000 – 700 = 300 and 700 = 1000 – 300) Find complements to 100 and recall addition and subtraction facts for 100 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 – 63 = 37) Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and tens and a 3-digit number and hundreds Recall the 2, 3, 4, 5, 8 and 10 times tables and the derived division facts Double any number up to 100; double any multiple of 50 up to 500 and halve any number up to 200 • • • • • • • • • • • • • • • Count on/back in steps of 2s,5s, 10s, 3s to 100 and beyond, from 0 and any given number Count on/back in multiples of 4 and 8 from 0 Count on/back in 50s, 100s from 0 to 1000 Find 10/100 more or less than a given number up to 1000 and more Read and write all numbers to 1000 in numerals and write all numbers in words to at least 1000 Order a set of numbers (4 and/or 5 ) to 1000 and beyond in increasing and decreasing value Compare numbers up to 1000 and beyond using =, <, > symbols Round numbers to the nearest 10 to 1000 and beyond and to the nearest 100 to 1000 and beyond Begin to partition 4 digit numbers (thousands, hundreds, tens and ones) Count in tenths, read and write numbers with 1 decimal place and compare numbers with one decimal place Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and tens and a 3-digit number and hundreds Count on/back in ½s , ¼s , 1/3s and 1/10s including on a number line Find complements to 100 and recall addition and subtraction facts for 100 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 – 63 = 37) Recall the 2, 3, 4, 5, 8 and 10 times tables and the derived division facts Double any number up to 100; double any multiple of 50 up to 500 and halve any number up to 200 © Focus Education (UK) Ltd 2014 186 Focus on Mathematics Year 3 Assessment Assessment: Meeting Year 3 Expectations Year 3 Expectations: Number • • • • • • The main focus on assessment will be measuring a pupil’s journey towards and beyond the Year 3 expectations. The Year 3 expectations for number are set out on the right hand side of this page. To meet the Year 3 expectations a pupil must be able to meet all of the statements outlined in the table, plus the ones for measurement and geometry, shown later. If they have not met all the statements then they will be deemed to be emerging. If a pupil is meeting the expectations then an assessment needs to made as to whether a pupil is exceeding the expectations. The next page sets out how to assess whether a pupil is exceeding this expectation or whether a pupil is at the emerging stage. The next page also provides you with a 9point scale for deeper analysis, if required. • Compare and order numbers to 1000 and read and write numbers to 1000 in numerals and words • Count from 0 in multiples of 4, 8, 50 and 100 • Recognise the value of each digit in a 3-digit number • Understand and count in tenths, and find the fractional value of a given set • Add and subtract fractions with a common denominator • Derive and recall multiplication facts for 3, 4 and 8x multiplication tables • Add and subtract mentally combinations of 1digit and 2-digit numbers • Add and subtract numbers with up to 3-digits using formal written methods • Write and calculate mathematical statements for multiplication and division; including 2-digit number with a 1-digit number (from multiplication tables they know, ie, 2, 3, 4, 5, 8 and 10) • Solve number problems using one and two step operations © Focus Education (UK) Ltd 2014 188 Assessment: Meeting Year 3 Expectations The 3 or 9-point scale Effectively, pupils will be assessed on a 3-point scale: that is, pupils will be judged as having met the expectations; emerging towards the expectations or exceeding the expectations. However, for many schools, this may not give them enough information when tracking pupils through the school. So, if schools desire, the following 9-point system is outlined for them to use. Assessed position Emerging Stage C Emerging Stage B Emerging Stage A Meeting Stage C Meeting Stage B Meeting Stage A Exceeding Stage C Exceeding Stage B Exceeding Stage A Points allocation 1 2 3 4 5 6 7 8 9 • • • • • As is illustrated, Point 4 is the point that indicates that a pupil has met the expectations. If we are to take account of the new Assessment arrangements then it is hoped that 85% of pupils will be at least at this stage by the end of the year. Points 1 to 3 are the ‘emerging’ stages; Points 4 to 6 are the ‘meeting’ expectations stages; and Points 7 to 9 are the ‘exceeding’ stages. The following page sets out what each point actually means and provides clarity about the allocation of the points. © Focus Education (UK) Ltd 2014 189 Assessment: Meeting Year 3 Expectations A pupil will be deemed to be meeting the expectations only if they can satisfy their teacher that they meet all the expectations for their age A pupil will be deemed to be emerging towards the expectations if they do not meet all of the statements outlined for that year group •Meeting the expectations (Stage C) – Point 4 •It is accepted that a pupil might make the occasional error if they are at this stage. However, despite that, the teacher needs to be satisfied that they understand the concept fully. •Meeting the expectations (Stage B) - Point 5 •At this stage a pupil will rarely make mistakes and is very confident at meeting the statements. •Meeting the expectation (Stage A)- Point 6 •At this stage, not only is the pupil confident at meeting the statements but works at a rapid rate. However, they are not yet meeting all the statements for exceeding. •If they meet more than 75% of the statements but not all then they will be described as: •Emerging towards the expectations (Stage C) – Point 3 •If they meet between 50% and 75% of the statements then they will be described as: •Emerging towards the expectations (Stage B) – Point 2 •However if they are not meeting 50% of the expectations they will be described as: •Emerging towards the expectations (Stage A) – Point 1 •There is, therefore, no requirement to write a set of emerging statements © Focus Education (UK) Ltd 2014 A pupil will be deemed to be exceeding the expectations when, in addition to the statements set out for meeting the expectation (Stage A)they meet one or more of three sets of further expectations •Pupils will be deemed to be exceeding expectations if, in addition to what is outlined as Point 6, they show evidence of: •Accessing some of the following year group’s objectives •Being able to use the year group’s expectation within context •Being able to consistently apply the year group objectives in a range of situations. •A set of exceeding statements are set out for you to feel secure about your judgements. •If a pupil is meeting the exceeding statements, they will be deemed to be at Point 7 (Stage C) •If they are very confident and rarely make a mistake in relation to the ‘exceeding’ statements then they will be judged at Point 8 (Stage B) •A few pupils will be judged at Point 9 (Stage A). These will be pupils who are exceptionally confident in handling the exceeding statements and show exceptional mathematical ability for their age 190 Assessment: Meeting Year 3 Expectations Year 3 Expectations: Number • Compare and order numbers to 1000 and read and write numbers to 1000 in numerals and words • Count from 0 in multiples of 4, 8, 50 and 100 • Recognise the value of each digit in a 3-digit number • Understand and count in tenths, and find the fractional value of a given set • Add and subtract fractions with a common denominator • Derive and recall multiplication facts for 3, 4 and 8x multiplication tables Year 3 Expectations: Measurement, Geometry and Statistics • Identify right angles; compare other angles to being greater or smaller than a right angle • Identify horizontal and vertical lines and pairs of perpendicular and parallel lines • Tell time to nearest minute and use specific vocabulary: seconds, am and pm • Measure, compare, add and subtract using common metric measures • Solve one-step and two step problems using information presented in scaled bar charts, pictograms and tables • Add and subtract mentally combinations of 1digit and 2-digit numbers • Add and subtract numbers with up to 3-digits using formal written methods • Write and calculate mathematical statements for multiplication and division; including 2-digit number with a 1-digit number (from multiplication tables they know, ie, 2, 3, 4, 5, 8 and 10) • Solve number problems using one and two step operations © Focus Education (UK) Ltd 2014 191 Assessment: Exceeding Year 3 Expectations Year 3 Exceeding Expectations • Recognise the value of each digit in a 4-digit number and the value of a tenth • Know all multiplication facts up to 10 x 10 and be able to instantaneously answer questions such as, how many 7s in 42? • Add and subtract numbers with any number of digits using formal written methods • Begin to have an understanding about negative numbers recognising they are smaller than zero • Multiply and divide any 2-digit number by a single digit number and have an understanding of ‘remainder’ • Can find fractional values (from ½ to 1/10 )of amounts up to 1000 • Use knowledge of number to solve problems related to money, time and measures • Know that the total internal angles of a triangle measure 180° and can measure each • Can relate knowledge of time to problems related to timetables • Measure, compare, add and subtract more complex problems using common metric measures set out in Kg, g; Kl, l; Km and m, etc. © Focus Education (UK) Ltd 2014 192 Focus on Mathematics Year 3 Parents’ Guide ‘Must Dos’ by the end of Year 3 • • • • • • • • • Write down all numbers said to them up to 1000 Know place value of each digit in a 3-digit number Order a set of 3-digit numbers: greatest first, smallest first Count on and back from any number in 2s, 3s, 4s, 5s, 8s, 10s, 50s, and 100s up to 1000 Know 100 more than a given number to 1000 Know 100 less than a given number to 1000 Add 2 or 3 numbers with 3-digits, using column addition Subtract 2 numbers with 3-digits using column subtraction Rapid recall: Add rapidly a 3-digit number to a 1-digit number; to a 10s number; and to a 100s number • • • • • • • • • • Subtract rapidly a 1-digit number from a 3-digit number; a 10s number and a 100s number Rapid Recall: 2x, 3x, 4x, 5x, 8x, 10s tables and their inverses Multiply a 2-digit number by a 1-digit number Divide 2, 3, 4, 5, 8 and 10 into a 2-digit number (no remainder) Fractions: Find ½,¼, 1/5 of a 2-digit number Order fractions from ½ to 1/12 Know pairs of fractions that make up 1 whole Know equivalent fractions of ½,¼,⅕ and 1/10 Add 2 fractions with same denominator Subtract 1 fraction from another with same denominator © Focus Education (UK) Ltd 2014 194 Focus on Mathematics Year Group Objectives Year 4 Year 4 Objectives: Number 1 NUMBER AND PLACE VALUE NUMBER AND PLACE VALUE Objective 1: Count in multiples of 6, 7, 8, 9, 10, 25, 50, 100 and 1000 from any given number. Objective 2: Read and write numbers to at least 10,000 Count on and back in 1000s from 0 to 10,000 *1 Count on and back in 10s from any given number between 0 and 10,000 Count on and back in 100s from 0 to 10,000 Count on and back in 50s from 0 to 1000 starting at any given number *2 Read and write numbers to 5000 *2 Read and write numbers to 10,000 *3 Objective 3: Find a 1000 more or less than a given number *1 Find 100 more or less than any 4-digit number *3 Find 1000 more or less than any 4-digit number Count on in 8s from 0 to 1000 starting at any given number Count on in 7s from 0 to 1000 starting at any given number *1 Find 100 more or less than any 3-digit number Count on and back in 25s from 0 to 1000 starting at any given number Count on and back in 9s from 0 to 1000 starting at any given number Revise reading and writing numbers to: 100 and then to 1000; *2 Find 1000 more than any 2 or 3-digit number *4 Count on in 6s from 0 to 1000 starting at any given number © Focus Education (UK) Ltd 2014 196 Year 4 Objectives: Number 2 NUMBER AND PLACE VALUE NUMBER AND PLACE VALUE Objective 4: Recognise the place value of each digit in a 4-digit number (thousands, hundreds, tens and ones) Objective 6: Identify, represent and estimate numbers using different representations Know and use terms: units, ones, tens, hundreds and thousands correctly *1 Know that 6 thousands, 3 hundreds, 2 tens and 5 ones is 6325 Partition any number up to 9,999 showing the value of each digit *2 Know that an object of 74.8m is longer than one of 476cm *2 Know that 8562cm is 85.62m *3 Objective 5: Order and compare numbers beyond 1000 Know which of two 4-digit numbers is the greater and smaller *1 Order a set of 4-digit numbers from smallest to largest *2 Order a set of 4-digit numbers from largest to smallest Know that 5 hundred, 6 tens and 3 ones is 563 *1 Know that 9042ml is 9.042l Objective 7: Round any number to the nearest 10, 100 or 1000 Round any number up to 100 to the nearest 10 *1 Round any number up to 1000 to the nearest 10 Round any number up to 1000 to the nearest 100 *2 Round any number up to 10,000 to the nearest 1000 *3 © Focus Education (UK) Ltd 2014 197 Year 4 Objectives : Number 3 NUMBER AND PLACE VALUE NUMBER AND PLACE VALUE Objective 8: Count backwards through zero to include negative numbers Objective 10: Read Roman numerals to 100 (1 to C) and know that, over time, the numeral system changed to include the concept of zero and place value Know that the value of any negative number is less than 0 *1 Know which of 2 negative numbers is the greater, eg. -2 is greater than -5 Know the Roman numerals from 1 to 10 *1 Know which of 2 negative numbers is the smaller, eg. -7 is smaller than -4 Know the Roman numerals for 50 *2 Count accurately forwards from any negative number to any positive number, moving across the 0 *2 Know the Roman numerals for 100 Count accurately backwards from any positive number to any negative number, moving across the 0 Order a set of negative and positive numbers showing largest or smallest first Objective 9: Solve word problems involving all of the above and increasingly large positive numbers Solve problems which require movement between negative and positive numbers © Focus Education (UK) Ltd 2014 198 Year 4 Objectives : Number 4 ADDITION AND SUBTRACTION Objective 11: Add and subtract numbers with up to 4-digits using the formal written methods of columnar addition and subtraction where appropriate Objective 12: Add and subtract numbers mentally including two 2-digit numbers (with increasingly larger numbers) (Non- statutory) Add 2 numbers with 4-digits together using columnar addition without exchange between units and tens *1 Add together mentally any single-digit and any 2-digit number Add 2 numbers with 4-digits together using columnar addition, where the units, tens or hundreds when added make more than 10. *2 Subtract any single-digit number from a 2-digit number Add together mentally any single-digit and any 3-digit number Add 3 numbers with 4-digits using columnar addition where the units, tens or hundreds make more than 10 Subtract any single-digit number from a 3-digit number Subtract a 4-digit number from another using columnar subtraction which requires no exchange between the units, tens, hundreds or thousands *3 Subtract a 4-digit number from another using columnar subtraction which requires exchange between the units, tens, hundreds or thousands (or any two of these) *4 Add together mentally any two 2-digit numbers Subtract mentally any two 2-digit numbers Add together mentally any 1000s number and any 4-digit number Subtract any 1000s number from a 4-digit number © Focus Education (UK) Ltd 2014 199 Year 4 Objectives : Number 5 ADDITION AND SUBTRACTION ADDITION AND SUBTRACTION Objective 13: Estimate and use inverse operations to check answers to a calculation Objective 14: Solve addition and subtraction two-step problems in contexts, deciding which operations to use and why Estimate the answer to any given addition involving two 2-digit numbers to the nearest 10 *1 Solve two-step word problems involving addition with numbers up to 1000 Estimate the answer to any given addition involving two 3-digit numbers to the nearest 100 *2 Solve two-step word problems involving subtraction with numbers up to 1000 Estimate the answer to any given addition involving two 3-digit numbers to the nearest 10 Solve two-step word problems involving addition and subtraction with numbers up to 1000 Estimate the answer to any given subtraction involving two 2-digit numbers to the nearest 10 Estimate the answer to any given subtraction involving two 3-digit numbers to the nearest 100 Estimate the answer to any given subtraction involving two 3-digit numbers to the nearest 10 Know the meaning of the term ‘inverse’ *3 Check the answer to any given addition involving 2 numbers by using the inverse method Check the answer to any given subtraction by using the inverse method © Focus Education (UK) Ltd 2014 200 Year 4 Objectives : Number 6 Objective 15: Recall multiplication and division facts for tables up to 12 x 12 MULTIPLICATION AND DIVISION Recite all multiplication facts for the x9 table Objective 17: Multiply and divide 2-digit and 3digit numbers by 1-digit number using formal written layout Multiply a 100s number by a single-digit number mentally, using 2, 3, 4, 5, 6, 7, 8, and 9x *1 Recite all multiplication facts for the x11 table Recite all multiplication facts for the x7 table Multiply a 2-digit number by a single-digit number using 2, 3, 4, 5, 6, 7, 8, and 9x *2 Recite all multiplication facts for the x12 table Multiply a 3-digit number by a single-digit number using 2, 3, 4, 5, 6, 7, 8, and 9x Recall all number facts for the 6, 7, 9, 11 and 12x table out of sequence Divide 2, 3, 4, 5, 6, 7, 8, 9 and 10 into any 10s number (no remainder) *3 Divide 2, 3, 4, 5, 6, 7, 8, 9 and 10 into any 2-digit number (no remainder) *4 Recite all multiplication facts for the x6 table *1 Know the inverse of all table facts involving 6, 7, 9, 11 and 12x table, eg. how many 7s in 63? *2 Objective 16: Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1; dividing by 1; multiplying together three numbers Use all table facts up to 12x in calculations involving multiplication and division Divide 2, 3, 4, 5, 6, 7, 8, 9 and 10 into any 3-digit number (no remainder) Objective 18: Recognise and use factor pairs and commutativity in mental calculations Know the term ‘prime factor’ and what it means Know what happens when multiplying by 0 or 1 Know all the factors within all numbers to 10 Know what happens when dividing by 1 Work out all the factors within any number up to 144 Know what happens when 3 numbers are multiplied together Know the term ‘square number’ and know all the square numbers associated with numbers 1 to 144 © Focus Education (UK) Ltd 2014 201 Year 4 Objectives : Number 7 MULTIPLICATION AND DIVISION Objective 19: Solve problems involving multiplying and dividing including using the distributive law to multiply two digits by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects Solve word problems involving multiplication with numbers up to 1000 Solve word problems involving division with numbers up to 1000 Use the distributive law to solve problems, eg. 39 x 7 = 30 x7+9x7 Use the associative law to solve problems, eg. (2x3) x 4 = 2 x (3x4) Solve mental and written calculations, eg. 2 x 6 x 5 = 10 x 6 = 60 Solve a range of two-step problems, choosing the appropriate operation © Focus Education (UK) Ltd 2014 202 Year 4 Objectives : Number 8 FRACTIONS FRACTIONS Objective 20: Recognise and show, using diagrams, families of common equivalent fractions with denominators up to and including 12 Objective 22: Move up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten Know all the equivalent fractions of ½ up to and including the denominator 12 *1 Count from 1/100 to 99/100 Know all the equivalent fractions of ¾ up to and including the denominator 12 *2 Know all the equivalent fractions of ⅓ up to and including the denominator 12 *3 Objective 23: Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number Know all the equivalent fractions of ⅔ up to and including the denominator 12 *4 Know all the equivalent fractions of ¼ up to and including the denominator 12 Objective 21: Write equivalent fraction of a fraction given the denominator or numerator Objective 24: Recognise fractions in their simplest form Reduce any fraction with a denominator of up to 12 to its simplest form Write the equivalent fraction when given the denominator Objective 25: Add and subtract 2 fractions with the same denominator Write the equivalent fraction when given the numerator Add two fractions with a denominator of 4, 5, 6, 10 where the answer is less than 1 whole *1 Subtract any two fractions with a denominator of 4, 5, 6, 10 *2 © Focus Education (UK) Ltd 2014 203 Year 4 Objectives : Number 9 DECIMALS Objective 26: Recognise and write decimal equivalents of any number of tenths and hundredths Know that 1/10 is 0.1 *1 Know that 6/10 is 0.6 Know that 0.01 is 1/100 *2 Know that 3/100 is 0.03 Objective 27: Recognise and write decimal equivalents to ¼, ½, ¾ Know that ½ is 0.5 Know that ¼ is 0.25 Know that ¾ is 0.75 Objective 28: Find the effect of dividing a 1 or 2-digit number by 10 and 100; identify the value of the digits in the answer as ones, tenths and hundredths Divide any 2-digit number by 10 and express answer in terms of tenths *1 Divide any 2-digit number by 100 and express answer in terms of tenths and hundredths *2 DECIMALS Objective 29: Estimate, compare and calculate different measures, including money in pounds and pence Carry out simple problems involving money, length, weight, and time Objective 30: Compare numbers with the same number of decimal places up to 2 decimal places Given 3 numbers with one decimal place, eg. 34.2; 45.7; 12.8; work out the smallest and largest number and put them in order *1 Given 3 numbers with two decimal places, eg. 15.67; 19.56; 12.78; work out the smallest and largest number and put them in order *2 Given a set of numbers with either 1 or 2 decimal places put them in order of either largest first or smallest first *3 204 © Focus Education (UK) Ltd 2014 Focus on Mathematics Year 4 Pre-Learning Tasks Number Focus on Mathematics: Year 4 Name Objective 1 (i) Date Number Count in multiples of 6, 7, 8, 9, 10, 25, 50, 100 and 1000 from any given number. Can you count on or back as required? 3000, 4000 *1 200, 300 2315, 3315 173, 273 8000, 7000 500, 400 4136, 3136 883, 783 *2 Starting Position: © Focus Education (UK) Ltd 2014 206 Focus on Mathematics: Year 4 Name Objective 1(ii) Date Number Count in multiples of 6, 7, 8, 9, 10, 25, 50, 100 and 1000 from any given number. Can you count on or back as required? 150, 200 *3 75, 100 231, 281 67, 92 850, 800 500, 475 413, 363 883, 858 Starting Position: © Focus Education (UK) Ltd 2014 207 Focus on Mathematics: Year 4 Name Objective 1(iii) Date Number Count in multiples of 6, 7, 8, 9, 10, 25, 50, 100 and 1000 from any given number. Can you count on or back as required? 36, 45, 54 *4 64, 72, 80 41, 50, 59 165,173 72, 63, 54 880, 872 177,168,159 673, 665 Starting Position: © Focus Education (UK) Ltd 2014 208 Focus on Mathematics: Year 4 Name Objective 1(iv) Date Number Count in multiples of 6, 7, 8, 9, 10, 25, 50, 100 and 1000 from any given number. Can you count on or back as required? 49, 56, 63 *4 66, 72, 78 89, 96,103 168,174 84, 77, 70 881, 875 176,169,162 693, 687 Starting Position: © Focus Education (UK) Ltd 2014 209 Focus on Mathematics: Year 4 Name Objective 2 Date Number Read and write numbers to 10,000 in numerals and words Can you write these numbers in numerals? Can you write these numbers in words? Two hundred and fourteen *1 461 One thousand, three hundred and sixty-four *2 79 Nine thousand, one hundred and two 1,247 Four thousand, three hundred and eighty- three 8,392 Sixteen thousand, four hundred and five *3 9,709 © Focus Education (UK) Ltd 2014 *2 *3 210 Focus on Mathematics: Year 4 Name Objective 3 Date Number Find a 1000 more or less than a given number Can you find the number 100 more or less than? *1 100 more than 356 Can you find the number 1000 less than? 100 less than 498 1000 less than 3417 100 more than 1786 1000 more than 876 100 less than 3395 1000 more than 85 100 more and then 100 less than 2291 more less *2 1000 more than 2478 1000 more and then 1000 less than 2503 © Focus Education (UK) Ltd 2014 more less 211 Focus on Mathematics: Year 4 Name Date Objective 4 Number Recognise place value of each digit in a 4-digit number (thousands, hundreds, tens, ones) Can you place the thousands, hundreds, tens and the units in the correct place? 2317 Thousands Hundreds Tens Units Partition these numbers *1 4315 3100 Thousands Hundreds Tens Units *2 (4000 + 300 + 10 +5) 6670 5682 6426 Thousands Hundreds Tens Units 8723 1873 6150 Thousands Hundreds Tens Units 9902 8953 © Focus Education (UK) Ltd 2014 212 Focus on Mathematics: Year 4 Name Date Objective 5 Number Order and compare numbers beyond 1000 Can you say which is the greater and the smaller number? Greater Smaller *1 Can you order these numbers (smallest first)? 206, 1340, 980 1432 or 2135 2012, 1506, 1113 6132 or 5690 267, 9280, 1227 6357 or 2234 8303, 3296, 1305 1139 or 2393 2430, 4788, 9824 1095 or 2091 1155, 578, 5902 1000 or 908 675, 958, 5230 207 or 7023 6119, 6657, 5458 6626 or 4404 2015, 5806, 5961 175 or 7670 2075, 2970, 2576 © Focus Education (UK) Ltd 2014 *2 213 Focus on Mathematics: Year 4 Name Date Objective 6 Number Identify, represent and estimate numbers using different representations Can you put each digit in the correct column? Th H T U Can you write these as £ and p or as m and cm? *1 551 *3 1728cm 663 7579 8323cm 1086 9411p 7960 Which is the greater? 4913p *2 1145p or £31.21 3785cm 6208p 1167p or £1.23 1374p 450cm or 1m 19cm 4m 78cm or 587cm 878cm 61m or 5567cm © Focus Education (UK) Ltd 2014 214 Focus on Mathematics: Year 4 Name Date Objective 7 Number Round any number to the nearest 10, 100 or 1000 Can you round these numbers to the nearest 10, 100 or 1000? 67 to the nearest 10 *1 771 to the nearest 100 72 to the nearest 10 1987 to the nearest 1000 145 to the nearest 10 8756 to the nearest 1000 567 to the nearest 10 9385 to the nearest 1000 234 to the nearest 100 *2 *3 3567 to the nearest 1000 © Focus Education (UK) Ltd 2014 215 Focus on Mathematics: Year 4 Name Objective 8 Date Number Count backwards through zero to include negative numbers. Can you tell me which is the greatest? 0, 2, -2 *1 What comes next in these sequences? 3, 2, 1, 0, -1, -4, 0, -5 -5, -4, -3, -2, -1 9, -4, 0, -14 -2, -3, -4, -5 -8, 0, 6, -3 1, 0, -1, -2, -3 *2 Starting Position: © Focus Education (UK) Ltd 2014 216 Focus on Mathematics: Year 4 Name Date Objective 10 Number Read Roman numerals to 100 (1 to C) and know that over time, the numeral system changed to include the concept of zero and place value Can you write these numbers as Roman numerals? 5 *1 23 9 19 3 75 10 92 6 100 © Focus Education (UK) Ltd 2014 *2 217 Focus on Mathematics: Year 4 Name Date Objective 11 Number Add and subtract numbers with up to 4-digits using the formal written methods of columnar addition and subtraction where appropriate Can you calculate these accurately? 1323 1234+ 1135 1412+ 1062 2025+ 1172 4123+ 1237 1459+ 1648 1225+ 2723 1645+ 1175 1236+ 3451 2429+ 2356 3482+ 1273 3566+ 3291 3251+ 5672 1345 1436+ 7562 2386 4375+ 8943 1923 4578+ 9532 7321 5659+ *1 3276 1033- 3459 1246- 1569 2163- 4777 1555- *3 *2 3450 1126- 7892 3569- 3819 2720- 4279 3458- *4 5353 2466- 6211 3736- 7351 5675- 8432 4677- © Focus Education (UK) Ltd 2014 218 Focus on Mathematics: Year 4 Name Objective 13 Date Number Estimate and use inverse operations to check answers to a calculation Can you quickly estimate the answers to these calculations to the nearest 10? 27 + 65 *1 39 - 13 What do you notice about these calculations? 67 + 35 *3 102 - 67 35 + 56 26 + 19 135 + 121 256 - 135 Can you quickly estimate the answers to these calculations to the nearest 100? 345 - 190 *2 729 + 260 760 - 205 845 + 190 205 + 555 724 - 128 © Focus Education (UK) Ltd 2014 219 Focus on Mathematics: Year 4 Name Objective 15 Date Number Recall multiplication and division facts for tables up to 12 x 12 Can you complete these very quickly? (2 minutes maximum) 5x7 *1 Can you complete these very quickly? (2 minutes maximum) How many 7s in 35? 9x3 How many 12s in 24? 11 x 8 How many 2s in 36? 6 x 10 How many 8s in 64? 7 x 12 How many 9s in 27? 9x4 How many 11s in 33? 4x8 How many 3s in 27? 10 x 9 How many 8s in 88? 10 x 10 How many 6s in 42? © Focus Education (UK) Ltd 2014 *2 220 Focus on Mathematics: Year 4 Name Date Objective 17 Number Multiply and divide 2-digit and 3-digit numbers by 1-digit number using formal written layout Can you multiply or divide these accurately? 200 3x 400 5x 600 4x 300 8x 37 9x 48 5x 72 6x 75 8x 51 9x 56 7x 73 6x 91 5x 672 6x 562 7x 943 8x 532 9x *1 90 ÷ 9 50 ÷ 2 60 ÷ 3 80 ÷ 4 *3 *2 12 ÷ 6 87 ÷ 3 84 ÷ 7 56 ÷ 8 *4 324 ÷ 4 720 ÷ 9 865 ÷ 5 658 ÷ 7 © Focus Education (UK) Ltd 2014 221 Focus on Mathematics: Year 4 Name Date Objective 20 Number Recognise and show, using diagrams, families of common equivalent fractions with denominators up to and including 12 Can you work out the missing numbers to complete these fractions? 2 4 = 3 = 6 2 8 = 3 = 6 8 = 9 = 3 2 6 = 3 = 4 4 6 = 6 = 8 = 1 *1 1 3 6 = 3 = 12 *2 9 = 12 = 1 *3 3 9 = = 2 *4 6 9 = = 4 8 8 = = = 6 6 © Focus Education (UK) Ltd 2014 = 12 = 2 *1 4 *2 4 12 12 = = 3 3 *3 *4 222 Focus on Mathematics: Year 4 Name Date Objective 25 Number Add and subtract 2 fractions with the same denominator Can you work out the missing numbers to complete these fractions? 2 4 +1 4 = 3 6 - 1 6 = 1 6 + 2 6 = 3 4 - 1 4 = 3 10 + 1 10 = 7 10 - 3 10 = 1 5 + 3 5 = 3 5 - 1 5 = 1 6 + 5 6 = 9 10 - *1 © Focus Education (UK) Ltd 2014 4 10 *2 = 223 Focus on Mathematics: Year 4 Name Date Objective 26 Number Recognise and write decimal equivalents of any number of tenths and hundredths Can you write the decimal equivalents of these fractions? 1/10 *1 3/100 3/10 6/100 7/10 5/100 9/10 7/100 5/10 8/100 © Focus Education (UK) Ltd 2014 *2 224 Focus on Mathematics: Year 4 Name Objective 28 Date Number Find the effect of dividing a 1 or 2-digit number by 10 and 100; identify the value of the digits in the answer as ones, tenths and hundredths Can you work out the answers to these divisions? 60 ÷ 10 *1 300 ÷ 100 700 ÷ 10 62 ÷ 100 7 ÷ 10 5÷ 100 91 ÷ 10 79 ÷ 100 85 ÷ 10 87 ÷ 100 © Focus Education (UK) Ltd 2014 *2 225 Focus on Mathematics: Year 4 Name Date Objective 30 Number Compare numbers with the same number of decimal places up to 2 decimal places Can you tell me which is the greatest; and then order them? 4.2; 5.3; 2.7 *1 13.3; 2.17; 2.9, 6.8; 3.1; 9.4 45.1; 4.51; 1.45 5.3; 5.2; 6.1 7.2; 7.19; 7.17 7.27; 7.15; 7.16 8.23; 7.34; 7.43 *2 *3 31.3; 6.17; 3.13 7.21; 5.5; 3.23 Starting Position: © Focus Education (UK) Ltd 2014 226 Focus on Mathematics Year 4 Group Objectives Measurement, Geometry and Statistics Year 4 Objectives : Measurement 1 MEASUREMENT MEASUREMENT Objective 1m: Convert between different units of measure e.g. km to m; m to cm; cm to mm; kg to g; l to ml; hour to min; min to sec; year to month; week to days Objective 2m: Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres Revise relationships between measure, ie. 1000m = 1Km; 100cm = 1m; 10mm = 1cm; 1000g = 1kg; 60 min = 1 hour; 60sec = 1 min; 12 month = 1 year; etc. Know that the perimeter of a rectangle can be measured by a simple formula of 2 x length + 2 x width Express a distance of more than 1Km in metres Express a distance of more than 1 cm in mm Know the term ‘perimeter’ Know that the perimeter of an irregular shape can be measured by adding each individual side together Express a weight of more than 1Kg in grams Objective 3m: Find area of rectilinear shapes by counting squares Express an amount of more than 1l in ml Know that the area of a square is measured in squared cm or squared meters, etc. Express the passing of time of more than 1 hour in minutes Express the passing of time of more than 1 minute in seconds Know the formula for measuring the area of a square and the area of a rectangle Objective 4m: Estimate, compare and calculate different measures, including money in pounds and pence Carry out simple problems involving money, length, weight, and time © Focus Education (UK) Ltd 2014 228 Year 4 Objectives : Measurement 2 MEASUREMENT Objective 5m: Read, write and convert time between analogue and digital 12- and 24- hour clocks Know how to set out each analogue time in digital format, eg. ten past two = 02:10 Can convert between analogue and digital in this way Know how a 24 hour clock system works, eg. ten past two in the afternoon = 02:10pm = 1410 hours Objective 6m: Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days Convert hours into minutes, eg, 4 hours = 240 minutes Convert minutes to seconds, eg, 10 minutes = 600 seconds Convert years to months, eg, 3 years = 36 months Convert weeks to days, eg, 8 weeks = 56 days © Focus Education (UK) Ltd 2014 229 Year 4 Objectives : Geometry PROPERTIES AND SHAPE PROPERTIES AND SHAPE Objective 1g: Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes Objective 3g: Identify lines of symmetry in 2D shapes presented in different orientations Relate number of angles and sides associated with triangles; squares; oblongs; circles Objective 2g: Identify acute and obtuse angles and compare and order angles up to two right angles by size Know what the term symmetry is Show lines of symmetry in a equilateral or isosceles triangle Show lines of symmetry in a square and oblong Understand about lines of symmetry within a circle Know how to describe an acute angle Know how to describe an obtuse angle Recognise how angles are measured Compare angles by size © Focus Education (UK) Ltd 2014 230 Year 4 Objectives : Geometry 2 Objective 4g: Complete a simple symmetric figure with respect to a specific line of symmetry Create simple symmetrical figures and show line of symmetry Recognise line/s of symmetry in given shapes POSITION AND DIRECTION Objective 5g: Describe positions on a 2-D grid as coordinates in the first quadrant Pinpoint a position on a quadrant using numbers along the axes Objective 6g: Describe movements between positions as translations of a given unit to the left/right and up/down Explain a change in a given position by the movement made along each axes of the quadrant Objective 7g: Plot specified points and draw sides to complete a given polygon Use the numbers along the axes of a quadrant to complete a given polygon © Focus Education (UK) Ltd 2014 231 Year 4 Objectives : Statistics STATISTICS Objective 1s: Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs Read a bar chart accurately with no scales on the axes Read a bar chart accurately with scales on the axes Read a time graph accurately with no scales on the axes Read a time graph accurately with scales on the axes © Focus Education (UK) Ltd 2014 232 Focus on Mathematics Step up to the Challenge Year 4 Number Year 4: Can you challenge yourself to meet the Objective? Objective 1: Count in multiples of 6, 7, 8, 9, 10, 25, 50, 100 and 1000 from any given number. Me My Teacher Can you count on in 6s from 0 to 1000 starting at any given number? Can you count on in 7s from 0 to 1000 starting at any given number? Can you count on in 8s from 0 to 1000 starting at any given number? Can you count on and back in 9s from 0 to 1000 starting at any given number? Can you count on and back in 25s from 0 to 1000 starting at any given number? Can you count on and back in 50s from 0 to 1000 starting at any given number? Can you count on and back in 100s from 0 to 10,000? Can you count on and back in 10s from any given number between 0 and 10,000? Can you count on and back in 100s from 0 to 1000? © Focus Education (UK) Ltd 2014 234 Year 4: Can you challenge yourself to meet the Objective? Objective 2: Read and write numbers to at least 10,000 Me My Teacher Can you write all numbers in words up to 10,000? Can you write all numbers in numerals up to 10,000? Can you write all numbers to 5,000 in words? Can you write all numbers in numerals up to 5,000? Can you remember how to write all numbers up to 1,000 in numerals and in words? Can you remember how to write all numbers up to 100 in numerals and in words? © Focus Education (UK) Ltd 2014 235 Year 4: Can you challenge yourself to meet the Objective? Objective 3: Find1000 more or less than a given number Me My Teacher Can you find 1000 more than any 2 or 3-digit number Can you find 1000 less than any 4-digit number? Can you find 1000 more than any 4-digit number? Can you find 100 less than any 4-digit number? Can you find 100 more than any 4-digit number? Can you find 100 less than any 3-digit number? Can you find 100 more than any 3-digit number? © Focus Education (UK) Ltd 2014 236 Year 4: Can you challenge yourself to meet the Objective? Objective 4: Recognise the place value of each digit in a 4-digit number (thousands, hundreds, tens and ones) Me My Teacher Me My Teacher Can you partition any number up to 9,999 showing the value of each digit? Do you know and use terms: units, ones, tens, hundreds and thousands correctly? Objective 5: Order and compare numbers beyond 1000 Can you order a set of 4-digit numbers from largest to smallest? Can you order a set of 4-digit numbers from smallest to largest? Can you work out which of two 4-digit numbers is the greater and smaller? © Focus Education (UK) Ltd 2014 237 Year 4: Can you challenge yourself to meet the Objective? Objective 6: Identify, represent and estimate numbers using different representations Me My Teacher Me My Teacher Do you know that 9042ml is 9.042 l? Do you know that 8562cm is 85.62m? Do you know that an object of 74.8m is longer than one of 476cm? Do you know that 6 thousands, 3 hundreds, 2 tens and 5 ones is 6325? Do you that 5 hundred, 6 tens and 3 ones is 563? Objective 7: Round any number to the nearest 10, 100 or 1000 Can you round any number up to 10,000 to the nearest 1000? Can you round any number up to 1000 to the nearest 100? Can you round any number up to 1000 to the nearest 10? Can you round any number up to 100 to the nearest 10? © Focus Education (UK) Ltd 2014 238 Year 4: Can you challenge yourself to meet the Objective? Objective 8: Count backwards through zero to include negative numbers Me My Teacher Can you order a set of negative and positive numbers showing largest or smallest first? Can you count accurately backwards from any positive number to any negative number, moving across the 0? Can you count accurately forwards from any negative number to any positive number, moving across the 0? Do you know which of 2 negative numbers is the smaller, e.g. -7 is smaller than -4? Do you know which of 2 negative numbers is the greater, e.g. -2 is greater than -5? Do you know that the value of any negative number is less than 0? © Focus Education (UK) Ltd 2014 239 Year 4: Can you challenge yourself to meet the Objective? Objective 10: Read Roman numerals to 100 (1 to C) and know that over time, the numeral system changed to include the concept of zero and place value Me My Teacher Can you write out all Roman numerals between 0 and 100? Do you know the Roman numerals for 100? Can you write out all Roman numerals between 0 and 50? Do you know the Roman numerals for 50? Do you know the Roman numerals from 1 to 10? © Focus Education (UK) Ltd 2014 240 Year 4: Can you challenge yourself to meet the Objective? Objective 11: Add and subtract numbers with up to 4-digits using the formal written methods of columnar addition and subtraction where appropriate Me My Teacher Can you subtract a 4-digit number from another using columnar subtraction which requires exchange between the units, tens, hundreds or thousands (or any two of these)? Can you subtract a 4-digit number from another using columnar subtraction which requires no exchange between the units, tens, hundreds or thousands? Can you add 3 numbers with 4-digits using columnar addition where the units, tens or hundreds make more than 10? Can you add 2 numbers with 4-digits together using columnar addition, where the units, tens or hundreds when added make more than 10? Can you add 2 numbers with 4-digits together using columnar addition without exchange between units and tens? © Focus Education (UK) Ltd 2014 241 Year 4: Can you challenge yourself to meet the Objective? Objective 12: Add and subtract numbers mentally including two 2digit numbers (with increasingly larger numbers) (Non- statutory) Me My Teacher Can you subtract any 1000s number from a 4-digit number? Can you add together mentally any 1000s number and any 4-digit number? Can you subtract mentally any two 2-digit numbers? Can you add together mentally any two 2-digit numbers? Can you subtract any single-digit number from a 3-digit number? Can you add together mentally any single-digit and any 3-digit number? Can you subtract any single-digit number from a 2-digit number? Can you add together mentally any single-digit and any 2-digit number? © Focus Education (UK) Ltd 2014 242 Year 4: Can you challenge yourself to meet the Objective? Objective 13: Estimate and use inverse operations to check answers to a calculation Me My Teacher Can you check the answer to any given subtraction by using the inverse method? Can you check the answer to any given addition involving 2 numbers by using the inverse method? Do you know the meaning of the term ‘inverse’? Can you estimate the answer to any given subtraction involving two 3digit numbers to the nearest 10? Can you estimate the answer to any given subtraction involving two 3-digit numbers to the nearest 100? Can you estimate the answer to any given subtraction involving two 2-digit numbers to the nearest 10? Can you estimate the answer to any given addition involving two 3digit numbers to the nearest 10? Can you estimate the answer to any given addition involving two 3-digit numbers to the nearest 100? Can you estimate the answer to any given addition involving two 2-digit numbers to the nearest 10? © Focus Education (UK) Ltd 2014 243 Year 4: Can you challenge yourself to meet the Objective? Objective 14: Solve addition and subtraction two-step problems in contexts, deciding which operations to use and why Me My Teacher Can you solve two-step word problems involving addition and subtraction with numbers up to 1000? Can you solve two-step word problems involving subtraction with numbers up to 1000? Can you solve two-step word problems involving addition with numbers up to 1000? © Focus Education (UK) Ltd 2014 244 Year 4: Can you challenge yourself to meet the Objective? Objective 15: Recall multiplication and division facts for tables up to 12 x 12 Me My Teacher Do you know the inverse of all table facts involving 6, 7, 9, 11 and 12x table, e.g. how many 7s in 63? Can you recall all number facts for the 6, 7, 9, 11 and 12x table out of sequence? Can you recite all multiplication facts for the x12 table? Can you recite all multiplication facts for the x11 table? Can you recite all multiplication facts for the x9 table? Can you recite all multiplication facts for the x7 table? Can you recite all multiplication facts for the x6 table? © Focus Education (UK) Ltd 2014 245 Year 4: Can you challenge yourself to meet the Objective? Objective 16: Use place value, known and derived facts to multiply and divide mentally, including multiplying by 0 and 1; dividing by 1; multiplying together three numbers Me My Teacher Do you know what happens when 3 numbers are multiplied together? Do you know what happens when dividing by 1? Do you know what happens when multiplying by 0 or 1? Can you use all table facts up to 12x in calculations involving multiplication and division? © Focus Education (UK) Ltd 2014 246 Year 4: Can you challenge yourself to meet the Objective? Objective 17: Multiply and divide 2-digit and 3-digit numbers by 1digit number using formal written layout Me My Teacher Can you divide 2, 3, 4, 5, 6, 7, 8, 9 and 10 into any 3-digit number (no remainder) ? Can you divide 2, 3, 4, 5, 6, 7, 8, 9 and 10 into any 2-digit number (no remainder) ? Can you divide 2, 3, 4, 5, 6, 7, 8, 9 and 10 into any 10s number (no remainder) ? Can you multiply a 3-digit number by a single-digit number using 2, 3, 4, 5, 6, 7, 8, and 9x ? Can you multiply a 2-digit number by a single-digit number using 2, 3, 4, 5, 6, 7, 8, and 9x ? Can you multiply a 100s number by a single-digit number mentally, using 2, 3, 4, 5, 6, 7, 8, and 9x ? © Focus Education (UK) Ltd 2014 247 Year 4: Can you challenge yourself to meet the Objective? Objective 18: Recognise and use factor pairs and commutativity in mental calculations Me My Teacher Do you know the term ‘square number’ and know all the square numbers associated with numbers 1 to 144 ? Can you work out all the factors within any number up to 144? Do you know all the factors within all numbers to 10? Do you know the term ‘prime factor’ and what it means? © Focus Education (UK) Ltd 2014 248 Year 4: Can you challenge yourself to meet the Objective? Objective 19: Solve problems involving multiplying and dividing including using the distributive law to multiply two digits by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects Me My Teacher Can you solve a range of two-step problems, choosing the appropriate operation? Can you solve mental and written calculations, eg. 2 x 6 x 5 = 10 x 6 = 60? Can you use the associative law to solve problems, eg. (2x3) x 4 = 2 x (3x4)? Can you use the distributive law to solve problems, eg. 39 x 7 = 30 x 7 + 9 x 7? Can you solve word problems involving division with numbers up to 1000? Can you solve word problems involving multiplication with numbers up to 1000? © Focus Education (UK) Ltd 2014 249 Year 4: Can you challenge yourself to meet the Objective? Objective 20: Recognise and show, using diagrams, families of common equivalent fractions with denominators up to and including 12 Me My Teacher Do you know all the equivalent fractions of ⅔ up to and including the denominator 12? Do you know all the equivalent fractions of ⅓ up to and including the denominator 12? Do you know all the equivalent fractions of ¾ up to and including the denominator 12? Do you know all the equivalent fractions of ¼ up to and including the denominator 12? Do you know all the equivalent fractions of ½ up to and including the denominator 12? © Focus Education (UK) Ltd 2014 250 Year 4: Can you challenge yourself to meet the Objective? Objective 26: Recognise and write decimal equivalents of any number of tenths and hundredths Me My Teacher Me My Teacher Do you know that 3/100 is 0.03? Do you know that 0.01 is 1/100? Do you know that 6/10 is 0.6? Do you know that 1/10 is 0.1? Objective 27: Recognise and write decimal equivalents to ¼, ½, ¾ Do you know that ¾ is 0.75? Do you know that ¼ is 0.25? Do you know that ½ is 0.5? © Focus Education (UK) Ltd 2014 251 Year 4: Can you challenge yourself to meet the Objective? Objective 28: Find the effect of dividing a 1 or 2-digit number by 10 Me My Teacher Me My Teacher and 100; identify the value of the digits in the answer as ones, tenths and hundredths Can you divide any 2-digit number by 100 and express answer in terms of tenths and hundredths? Can you divide any 2-digit number by 10 and express answer in terms of tenths? Objective 30: Compare numbers with the same number of decimal places up to 2 decimal places Given a set of numbers with either 1 or 2 decimal places can you put them in order of either largest first or smallest first? Given 3 numbers with two decimal places, eg. 15.67, 19.56, 12.78, can you work out the smallest and largest number and put them in order? Given 3 numbers with one decimal place, eg. 34.2, 45.7, 12.8, can you work out the smallest and largest number and put them in order? © Focus Education (UK) Ltd 2014 252 Making Mathematics Work Step up to the Challenge Year 4 Measurement, Geometry and Statistics Year 4: Can you challenge yourself to meet the Objective? Objective 1m: Convert between different units of measure e.g. km to m; m to cm; cm to mm; kg to g; l to ml; hour to min; min to sec; year to month; week to days Me My Teacher Can you express the passing of time of more than 1 minute in seconds? Can you express the passing of time of more than 1 hour in minutes? Can you express an amount of more than 1l in ml? Can you express a weight of more than 1Kg in grams? Can you express a distance of more than 1 cm in mm? Can you express a distance of more than 1Km in metres? Do you remember that: 1000m = 1Km; 100cm = 1m; 10mm = 1cm; 1000g = 1kg; 60 min = 1 hour; 60sec = 1 min; 12 month = 1 year; etc.? © Focus Education (UK) Ltd 2014 254 Year 4: Can you challenge yourself to meet the Objective? Objective 2m: Measure and calculate the perimeter of a rectilinear shape (including squares) in centimetres and metres Me My Teacher Me My Teacher Do you know that the perimeter of an irregular shape can be measured by adding each individual side together? Do you know that the perimeter of a rectangle can be measured by a simple formula of 2 x length + 2 x width? Do you know the term ‘perimeter’? Objective 3m: Find area of rectilinear shapes by counting squares Do you know the formula for measuring the area of a square and the area of a rectangle? Do you know that the area of a square is measured in squared cm or squared meters, etc.? © Focus Education (UK) Ltd 2014 255 Year 4: Can you challenge yourself to meet the Objective? Objective 5m: Read, write and convert time between analogue Me My Teacher Me My Teacher and digital 12- and 24- hour clocks Do you know how a 24 hour clock system works, e.g. ten past two in the afternoon = 02:10pm = 14:10 hours? Can you convert between analogue and digital in this way? Do you know how to set out each analogue time in digital format, eg. ten past two = 02:10? Objective 6m: Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days Can you convert weeks to days? Can you convert years to months? Can you convert minutes to seconds? Can you convert hours into minutes? © Focus Education (UK) Ltd 2014 256 Year 4: Can you challenge yourself to meet the Objective? Objective 2g: Identify acute and obtuse angles and compare and order angles up to two right angles by size Me My Teacher Me My Teacher Can you compare angles by size? Do you know how angles are measured? Do you know how to describe an obtuse angle? Do you know how to describe an acute angle? Objective 3g: Identify lines of symmetry in 2D shapes presented in different orientations Do you understand about lines of symmetry within a circle? Can you show lines of symmetry in a square and oblong? Can you show lines of symmetry in a equilateral or isosceles triangle? Can you explain what the term symmetry is? © Focus Education (UK) Ltd 2014 257 Year 4: Can you challenge yourself to meet the Objective? Objective 1s: Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs Me My Teacher Can you read a time graph accurately with scales on the axes? Can you read a time graph accurately with no scales on the axes? Can you read a bar chart accurately with scales on the axes? Can you read a bar chart accurately with no scales on the axes? © Focus Education (UK) Ltd 2014 258 Focus on Mathematics Non-Negotiables Year 4 Possible Planning Outline Year 4 Mathematics Non-Negotiables • The following areas of learning are known as the non-negotiables. They have a specific role in helping pupils meet the year group expectations. In a nutshell we are suggesting that if pupils are not confident in these areas then they will find the rest of the curriculum difficult to access. • The non-negotiables are designed to: 1. Identify the essential components that pupils need to become confident with, i.e. be able to demonstrate in independent tasks and be able to apply in other contexts. 2. Unblock learning, i.e. to keep teachers focused on the essential rather than coverage at the expense of progress. 3. Unlock learning and progress. • The non-negotiables are not designed to imply that the rest of the curriculum is an irrelevance – it clearly isn’t. But rather to give a structure for professionals to decide what the right curriculum is for their pupils. © Focus Education (UK) Ltd 2014 260 Year 4 Mathematics Non-Negotiables • Count backwards through zero to include negative numbers. • Compare and order numbers beyond 1000. • Compare and order numbers with 2 decimal places. • Read Roman numerals to 100. • Find 1000 more/less than a given number. • Count in multiples of 6, 7, 8, 9, 25 & 1000. • Recall and use multiplication and division facts all tables to 12x12. • Recognise place value of any 4-digit number. • Round any number to the nearest 10, 100 or 1000. • Round decimals with 1decimal place (dp) to nearest whole number. • Add and subtract: o Numbers with up to 4-digits using efficient written method (column). o Numbers with up to 1dp. • Multiply: o 2-digit by 1-digit o 3-digit by 1-digit • Divide: o 3-digit by 1-digit • Count up/down in hundredths. • Write equivalent fractions • Add and subtract fractions with same denominator. • Read, write and convert time between analogue and digital 12 and 24 hour clocks. © Focus Education (UK) Ltd 2014 261 Planning to meet the requirement of the nonnegotiables The following 3 pages suggest a planning outline for delivering the non-negotiables in classrooms. There should be some element of teaching of these each day. Autumn Term Ist Half Term • • • • • • • • • • • • • • 2nd Half Term Count on/back in steps of 2s, 3s, 4s 5s, 8s, 10s, 6s and 9s (through zero to include negative numbers) Recall the 2, 3, 4, 5, 8 and 10 times tables and the derived division facts Count on/back in multiples of 6 and 9 from 0 Count on/back in 25s, 50s, 100s from 0 to 5000 and in 1000s from 0 to 10,000 and beyond Find 10/100/1000 more or less than a given number beyond 1000 Read and write all numbers to at least 10,000 in both numerals and words Partition 4 digit numbers (thousands, hundreds, tens and ones) Partition in different ways Order a set of numbers (4 and/or 5 ) to 10,000 and beyond in increasing and decreasing value Compare numbers up to 10,000 and beyond using =, <, > symbols Round numbers up to 10,000 to the nearest 10, 100 or 1000 Count in tenths, read and write numbers with 1 decimal place and compare numbers with one decimal place Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and tens and a 3-digit number and hundreds, combinations of 2 and 3 digit numbers Find complements to 100 and to 1000 and recall addition and subtraction facts for 100 and 1000 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 – 63 = 37, 530 + 470 = 1000) Double any number up to 100; double any multiple of 50 up to 500 and halve any number up to 200 • • • • • • • • • • • • • Count on/back in steps of 2s, 3s, 4s 5s, 8s, 10s Count on/back in multiples of 6 and 9 from 0 Recall the 2, 3, 4, 5, 6, 8 and 10 times tables and the derived division facts Count on/back in 25s, 50s, 100s from 0 to 5000 and in 1000s from 0 to 10,000 and beyond Find 10/100/1000 more or less than a given number beyond 1000 Read and write all numbers to at least 10,000 in both numerals and words Order a set of numbers (4 and/or 5 ) to 10,000 and beyond in increasing and decreasing value Compare numbers up to 10,000 and beyond using =, <, > symbols Round numbers up to 10,000 to the nearest 10, 100 or 1000 Count in tenths, hundredths, read and write numbers with up to 2 decimal places and compare numbers with the same number of decimal places up to 2 decimal places Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and tens and a 3-digit number and hundreds, combinations of 2 and 3 digit numbers Count on/back in ½s , ¼s , 1/3s , 1/10s and other unit fractions including on a number line Find complements to 100 and to 1000 and recall addition and subtraction facts for 100 and 1000 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 – 63 = 37, 530 + 470 = 1000) © Focus Education (UK) Ltd 2014 262 Planning to meet the requirement of the nonnegotiables Spring Term Ist Half Term • • • • • • • • • • • • • 2nd Half Term Count on/back in steps of 2s, 3s, 4s 5s, 8s, 10s, 6s, 9s Recall the 2, 3, 4, 5, 6, 8, 9 and 10 times tables and the derived division facts Count on/back in multiples of 7 from 0 Count on/back in 25s, 50s, 100s from 0 to 10,000 and in 1000s from 0 to 10,000 and beyond Find 10/100/1000 more or less than a given number beyond 5000 Read and write all numbers to at least 10,000 in both numerals and words Partition 4 digit numbers (thousands, hundreds, tens and ones) Partition in different ways Order a set of numbers (4 and/or 5) to 50,000 and beyond in increasing and decreasing value Compare numbers up to 50,000 and beyond using =, <, > symbols Round numbers up to and beyond 10,000 to the nearest 10, 100 or 1000 Count in tenths, hundredths, read and write numbers with up to 2 decimal places and compare numbers with the same number of decimal places up to 2 decimal places Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and tens and a 3-digit number and hundreds, combinations of 2 and 3 digit numbers Find complements to 100 and to 1000 and recall addition and subtraction facts for 100 and 1000 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 – 63 = 37, 530 + 470 = 1000) • • • • • • • • • • • • • Count on/back in steps of 2s, 3s, 4s 5s, 8s, 10s, 6s, 9s Recall the 2, 3, 4, 5, 6, 8, 9 and 10 times tables and the derived division facts Count on/back in multiples of 7 from 0 Count on/back in 25s, 50s, and 100s from 0 to 10,000 and in 1000s from 0 to 10,000 and beyond Count in tenths, hundredths, read and write numbers with up to 2 decimal places and compare numbers with the same number of decimal places up to 2 decimal places Find 10/100/1000 more or less than a given number beyond 5000 Read and write all numbers to at least 10,000 in both numerals and words Order a set of numbers (4 and/or 5) to 50,000 and beyond in increasing and decreasing value Compare numbers up to 50,000 and beyond using =, <, > symbols Round numbers up to and beyond 10,000 to the nearest 10, 100 or 1000 Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and tens and a 3-digit number and hundreds, combinations of 2 and 3 digit numbers Count on/back in ½s , ¼s , 1/3s , 1/10s and other unit fractions including on a number line Find complements to 100 and to 1000 and recall addition and subtraction facts for 100 and 1000 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 – 63 = 37, 530 + 470 = 1000) © Focus Education (UK) Ltd 2014 263 Planning to meet the requirement of the nonnegotiables Summer Term Ist Half Term • • • • • • • • • • • • • 2nd Half Term Count on/back in steps of 2s, 3s, 4s 5s, 8s, 10s, 6s, 9s, 7s Recall the 2, 3, 4, 5, 6, 7, 8, 9 and 10 times tables and the derived division facts Multiply and divide numbers mentally using place value and known facts including multiplying by 1 and 0 and dividing by 1 Count on/back in 25s, 50s, and 100s from 0 to 10,000 and in 1000s from 0 to 10,000 and beyond Count in tenths, hundredths, read and write numbers with up to 2 decimal places and compare numbers with the same number of decimal places up to 2 decimal places Find 10/100/1000 more or less than a given number up to 10,000 Read and write all numbers to at least 10,000 in both numerals and words Partition 4 and begin to partition 5 digit numbers (thousands, hundreds, tens and ones) Partition in different ways Order a set of numbers (4 and/or 5)up to 100,000 in increasing and decreasing value Compare numbers up to 100,000 using =, <, > symbols Round numbers up to 50,000 to the nearest 10, 100 or 1000 Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and tens and a 3-digit number and hundreds, combinations of 2 and 3 digit numbers Find complements to 100 and to 1000 and recall addition and subtraction facts for 100 and 1000 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 – 63 = 37, 530 + 470 = 1000) Count on/back in steps of 11 and 12 Recall the 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 times tables and the derived division facts Multiply and divide numbers mentally using place value and known facts including multiplying by 1 and 0 and dividing by 1 Multiply together three numbers by using place value and known facts Partition 4 and begin to partition 5 digit numbers Count on/back in 25s, 50s, and 100s from 0 to 10,000 and in 1000s from 0 to 10,000 and beyond Count in tenths, hundredths, read and write numbers with up to 2 decimal places and compare numbers with the same number of decimal places up to 2 decimal places Find 10/100/1000 more or less than a given number beyond 10,000 Read and write all numbers to at least 10,000 in both numerals and words Order a set of numbers (4 and/or 5) to 100,000 and beyond in increasing and decreasing value Compare numbers up to 100,000 and beyond using =, <, > symbols Round numbers up to and beyond 100,000 to the nearest 10, 100 or 1000 Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and tens and a 3-digit number and hundreds, combinations of 2 and 3 digit numbers Count on/back in ½s , ¼s , 1/3s , 1/10s and other unit fractions including on a number line Find complements to 100 and to 1000 and recall addition and subtraction facts for 100 and 1000 (e.g. 37 + 63 = 100, 63 + 37 = 100, 100 – 37 = 63, 100 – 63 = 37, 530 + 470 = 1000) © Focus Education (UK) Ltd 2014 264 Focus on Mathematics Year 4 Assessment Assessment: Meeting Year 4 Expectations • • • • • • The main focus on assessment will be measuring a pupil’s journey towards and beyond the Year 4 expectations. The Year 4 expectations for number are set out on the right hand side of this page. To meet the Year 4 expectations a pupil must be able to meet all of the statements outlined in the table, plus the ones for measurement and geometry, shown later. If they have not met all the statements then they will be deemed to be emerging. If a pupil is meeting the expectations then an assessment needs to made as to whether a pupil is exceeding the expectations. The next page sets out how to assess whether a pupil is exceeding this expectation or whether a pupil is at the emerging stage. The next page also provides you with a 9point scale for deeper analysis, if required. Year 4 Expectations: Number • Recall all multiplication facts to 12 x 12 • Round any number to the nearest 10, 100 or 1000 and decimals with one decimal place to the nearest whole number • Count backwards through zero to include negative numbers • Compare numbers with the same number of decimal places up to 2 decimal places • Recognise and write decimal equivalents of any number of tenths or hundredths • Add and subtract with up to 4 decimal places using formal written methods of columnar addition and subtraction • Divide a 1 or 2-digit number by 10 or 100 identifying the value of the digits in the answer as Units, tenths and hundredths • Multiply 2-digit and 3-digit numbers by a 1-digit number using formal written layout • Solve addition and subtraction two-step problems in context and solve problems involving multiplication and division • Solve simple measures and money problems involving fractions and decimals to 2 decimal places © Focus Education (UK) Ltd 2014 266 Assessment: Meeting Year 4 Expectations The 3 or 9-point scale Effectively, pupils will be assessed on a 3-point scale: that is, pupils will be judged as having met the expectations; emerging towards the expectations or exceeding the expectations. However, for many schools, this may not give them enough information when tracking pupils through the school. So, if schools desire, the following 9-point system is outlined for them to use. Assessed position Emerging Stage C Emerging Stage B Emerging Stage A Meeting Stage C Meeting Stage B Meeting Stage A Exceeding Stage C Exceeding Stage B Exceeding Stage A Points allocation 1 2 3 4 5 6 7 8 9 • • • • • As is illustrated, Point 4 is the point that indicates that a pupil has met the expectations. If we are to take account of the new Assessment arrangements then it is hoped that 85% of pupils will be at least at this stage by the end of the year. Points 1 to 3 are the ‘emerging’ stages; Points 4 to 6 are the ‘meeting’ expectations stages; and Points 7 to 9 are the ‘exceeding’ stages. The following page sets out what each point actually means and provides clarity about the allocation of the points. © Focus Education (UK) Ltd 2014 267 Assessment: Meeting Year 4 Expectations A pupil will be deemed to be meeting the expectations only if they can satisfy their teacher that they meet all the expectations for their age A pupil will be deemed to be emerging towards the expectations if they do not meet all of the statements outlined for that year group •Meeting the expectations (Stage C) – Point 4 •It is accepted that a pupil might make the occasional error if they are at this stage. However, despite that, the teacher needs to be satisfied that they understand the concept fully. •Meeting the expectations (Stage B) - Point 5 •At this stage a pupil will rarely make mistakes and is very confident at meeting the statements. •Meeting the expectation (Stage A)- Point 6 •At this stage, not only is the pupil confident at meeting the statements but works at a rapid rate. However, they are not yet meeting all the statements for exceeding. •If they meet more than 75% of the statements but not all then they will be described as: •Emerging towards the expectations (Stage C) – Point 3 •If they meet between 50% and 75% of the statements then they will be described as: •Emerging towards the expectations (Stage B) – Point 2 •However if they are not meeting 50% of the expectations they will be described as: •Emerging towards the expectations (Stage A) – Point 1 •There is, therefore, no requirement to write a set of emerging statements © Focus Education (UK) Ltd 2014 A pupil will be deemed to be exceeding the expectations when, in addition to the statements set out for meeting the expectation (Stage A)they meet one or more of three sets of further expectations •Pupils will be deemed to be exceeding expectations if, in addition to what is outlined as Point 6, they show evidence of: •Accessing some of the following year group’s objectives •Being able to use the year group’s expectation within context •Being able to consistently apply the year group objectives in a range of situations. •A set of exceeding statements are set out for you to feel secure about your judgements. •If a pupil is meeting the exceeding statements, they will be deemed to be at Point 7 (Stage C) •If they are very confident and rarely make a mistake in relation to the ‘exceeding’ statements then they will be judged at Point 8 (Stage B) •A few pupils will be judged at Point 9 (Stage A). These will be pupils who are exceptionally confident in handling the exceeding statements and show exceptional mathematical ability for their age 268 Assessment: Meeting Year 4 Expectations Year 4 Expectations: Number Year 4 Expectations: Measurement, Geometry and Statistics • Recall all multiplication facts to 12 x 12 • Round any number to the nearest 10, 100 or 1000 and decimals with one decimal place to the nearest whole number • Compare and classify geometrical shapes, including quadrilaterals and triangles, based on their properties and sizes • Count backwards through zero to include negative numbers • Know that angles are measured in degrees and identify acute and obtuse angles and compare and order angles up to two right angles by size • Compare numbers with the same number of decimal places up to 2 decimal places • Measure and calculate the perimeter of a rectilinear shape in centimetres and metres • Recognise and write decimal equivalents of any number of tenths or hundredths • Read, write and convert between analogue and digital 12 and 24 hour clocks • Add and subtract with up to 4 decimal places using formal written methods of columnar addition and subtraction • Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs • Divide a 1 or 2-digit number by 10 or 100 identifying the value of the digits in the answer as units, tenths and hundredths • Multiply 2-digit and 3-digit numbers by a 1-digit number using formal written layout • Solve addition and subtraction two-step problems in context and solve problems involving multiplication and division • Solve simple measures and money problems involving fractions and decimals to 2 decimal places © Focus Education (UK) Ltd 2014 269 Assessment: Exceeding Year 4 Expectations Year 4 Exceeding Expectations: • Use tenths, hundredths and thousandths when comparing values and solving addition and subtraction problems • Round any number to 100,000 to the nearest 10, 100, 1,000 or 10,000 • Relate tenths and hundredths to fractional values • Rapidly recall answer when multiplying and dividing a whole or decimal number by 10 • Solve multi-step problems involving more than one of the operations • Work out simple percentage values of whole numbers as is related to on-going learning in science, history and geography • Compare and add fractions whose denominators are all multiples of the same number • Use a 24-hour timetable to find out times for a journey between various places • Use knowledge of perimeter to work out perimeter of large areas around school using meters and centimetres • Collect own data on given project and present information in graphical formats of their choosing © Focus Education (UK) Ltd 2014 270 Focus on Mathematics Year 4 Parents’ Guide Parents’ Guide ‘Must Dos’ by the end of Year 4 Number • • • • • • • • • • • Number Read and write all numbers to 10,000 Know place value of each digit in a 4digit number Order a set of 4-digit numbers: greatest first, smallest first Count on and back from any number in 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s,10s, 25s, 50s, 100s and 1000s up to 10,000 Round a number to the nearest 10 or 100 Read and write negative numbers Count on and back in negative numbers Add a number of 4-digit numbers using formal methods Subtract 2, 4-digit numbers using formal methods Estimate the answer to additions with up to 3-digit numbers Estimate the answer to subtractions with up to 3-digit numbers • • • • • • • • • Rapid Recall: All table facts up to 12x, including their inverses Multiply 2-digit and 3-digit numbers by a 1-digit number Divide 2-digit numbers by a 1-digit number Recognise and use factor pairs within 144 Fractions: Identify and name equivalent fractions with the same denominator up to and including 12 Add and subtract fractions with the same denominator (within 1 whole) Decimal Fractions: Order decimal fractions up to tenths and hundredths Multiply and divide decimal fractions by 10 and 100 Recognise fractional value of decimal fractions © Focus Education (UK) Ltd 2014 272 Focus on Mathematics Year Group Objectives Year 5 Year 5 Objectives: Number NUMBER AND PLACE VALUE NUMBER AND PLACE VALUE Objective 1: Read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit Objective 2: Count forwards and backwards in steps of powers of 10 (100, 1000, 10,000 ) for any given number up to 1,000,000 Revise reading and writing numbers to: 1000 and then to 10,000. *1 Read and write numbers to 50,000 Read and write numbers to 1,000,000 Recognise the value of each digit up to 1,000,000 Know and use terms: units; tens, hundreds, thousands, ten thousands, hundred thousands and one million correctly *2 Count onwards and backwards from a given number in steps of 100s *1 Count onwards and backwards from a given number in steps of 1000s *2 Count onwards and backwards from a given number in steps of 10,000s *3 Count onwards and backwards from a given number in steps of 100,000s *4 Count onwards and backwards from a given number in steps of 1,000,000s Partition any number up to 1,000,000 showing the value of each digit © Focus Education (UK) Ltd 2014 274 Year 5 Objectives : Number 2 NUMBER AND PLACE VALUE NUMBER AND PLACE VALUE Objective 3: Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero Objective 5: Estimate the answers to calculations involving addition, subtraction, multiplication and division Interpret temperatures at minus ⁰C on a thermometer *1 Count forwards from - 20 to + 20 *2 Count backwards from + 30 to -30 Objective 4: Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000 Round any number up to 100 to the nearest 10 *1 Round any number up to 1000 to the nearest 10 Round any number up to 100,000 to the nearest 10,000, 1000, 100 or 10 Round any number up to 1,000,000 to the nearest 100,000, 10,000, 1000, 100 or 10 *1 Estimate the answer to any given addition or subtraction involving two 3-digit numbers to the nearest 100 *2 Estimate the answer to any given addition or subtraction involving two 3-digit numbers to the nearest 10 *3 Estimate the answer to any given multiplication involving two 2-digit numbers to the nearest 10 *4 Estimate the answer to any given multiplication involving two 3-digit numbers to the nearest 100 Estimate the answer to any given multiplication involving two 3-digit numbers to the nearest 10 Round any number up to 1000 to the nearest 100 Round any number up to 10,000 to the nearest 1,000, 100 or 10 Estimate the answer to any given addition or subtraction involving two 2-digit numbers to the nearest 10 *2 Estimate the answer to any given division involving a 2digit number divided by a 1-digit number to the nearest 10 Estimate the answer to any given division involving a 3digit number divided by a 1-digit number to the nearest 100 Estimate the answer to any given division involving a 3digit number divided by a 1-digit to the nearest 10 © Focus Education (UK) Ltd 2014 275 Year 5 Objectives : Number 3 NUMBER AND PLACE VALUE ADDITION AND SUBTRACTION Objective 6: Solve number problems and practical problems that involve all of the above, including addition, subtraction, multiplication and division Objective 8: Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) Calculate the answer to any given addition involving two 2-digit numbers to the nearest 10 Add 2 numbers with 5-digits together using column addition without exchange between units and tens *1 Calculate the answer to any given addition involving two 3-digit numbers to the nearest 10 Add 2 numbers with 5-digits together using column addition, where the units, tens or hundreds when added make more than 10. *2 Objective 7: Read Roman numerals to 1000 (M) and recognise years written in Roman numerals Add 3 numbers with 5-digits using column addition where the units, tens or hundreds make more than 10 Calculate the answer to any given addition involving two 3-digit numbers to the nearest 100 Remember the Roman numerals from 1 to 10 *1 Remember the Roman numerals for 50 *2 Remember the Roman numerals for 100 *3 Know all Roman numerals up to 1000 *4 Subtract a 5-digit number from another using column subtraction which requires no exchange between the units, tens, hundreds or thousands *3 Subtract a 5-digit number from another using column subtraction which requires exchange between the units, tens, hundreds or thousands (or any two of these) *4 © Focus Education (UK) Ltd 2014 276 Year 5 Objectives : Number 4 ADDITION AND SUBTRACTION ADDITION AND SUBTRACTION Objective 9: Add and subtract numbers mentally with increasingly large numbers Objective 10: Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy Add together mentally any two 2-digit numbers *1 Subtract any 2-digit number from a 2 or 3-digit number Use rounding to add together mentally any two 2-digit numbers, eg. 29 + 39 = 30 + 40 – 2 = Add together mentally any 2-digit and any 3digit number Subtract any 2-digit number from a 3 or 4-digit number *2 Use rounding to subtract any 2-digit number from a 2 or 3-digit number, eg. 321 – 19 = 320 – 20 Add together mentally any two 3-digit numbers *3 Use rounding to add together mentally any two 3-digit numbers, eg. 398 + 449 = 400 + 450 – 3 = Use rounding to add together mentally any 1000s number and any 5-digit number, eg. 4203 + 58502 = 4200 + 58500 + 5 Subtract mentally any two 3-digit numbers Add together mentally any 1000s number and any 5-digit number Subtract any 1000s number from a 5-digit number *4 Objective 11: Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why Solve a range of addition and subtraction multistep problems involving numbers to at least 1, 000, 000 © Focus Education (UK) Ltd 2014 277 Year 5 Objectives : Number 5 MULTIPLICATION AND DIVISION Objective 12: Identify multiples and factors, including finding all factor pairs of a number and common factors of two numbers Identify all multiples of numbers up to 100 Know all factors that make up all numbers to 100 MULTIPLICATION AND DIVISION Objective 15: Multiply numbers up to 4-digits by a 1 or 2-digit number using a formal written method, including long multiplication for 2-digit numbers Multiply any number with 3-digits by a single digit number *1 Multiply any number with 4-digits by a single digit number *2 Multiply any number with 3-digits by a 2-digit number *3 Describe what a prime number is Recognise all prime numbers to 100 Multiply any number with 4-digits by a 2-digit number *4 Explain why a number is not a prime number Objective 16: Multiply and divide mentally, drawing upon known facts Objective 14: Establish whether a number up to 100 is a prime number and recall prime numbers to 19 Use mental applications to multiply and divide numbers making use of known number facts included in x table between x2 and x12 Objective 13: Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers Recognise all prime numbers to 100 Explain why a number is or is not a prime number © Focus Education (UK) Ltd 2014 278 Year 5 Objectives : Number 6 MULTIPLICATION AND DIVISION MULTIPLICATION AND DIVISION Objective 17: Divide numbers up to 4-digits by a 1-digit number using the formal written method of short division and interpret remainders appropriately for the context Divide any number with 3-digits by a single digit number *1 Divide any number with 4-digits by a single digit number Multiply any 2, 3, 4, 5 or 6-digit number by 10 *1 Divide any 2, 3, 4, 5 or 6-digit number by 10 *2 Multiply any 2, 3, 4, 5 or 6-digit number by 100 Divide any number with 3-digits by a single digit number with remainder *2 Divide any number with 4-digits by a single digit number with remainder *3 Divide any number with 3-digits by 10, showing remainder where appropriate Divide any number with 4-digits by 10, showing remainder where appropriate Objective 18: Multiply and divide numbers by 10, 100 and 1000 Divide any 3, 4, 5 or 6-digit number by 100 Multiply any 2, 3, 4, 5 or 6-digit number by 1000 *3 Divide any 4, 5 or 6-digit number by 1000 *4 *4 © Focus Education (UK) Ltd 2014 279 Year 5 Objectives : Number 7 MULTIPLICATION AND DIVISION MULTIPLICATION AND DIVISION Objective 21: Solve problems involving addition Objective 19: Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (3) and subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign Know the square of all numbers between 2 and 12 by heart *1 Solve problems involving subtraction with numbers up to 1,000,000 Use the symbols (²) and (√) accurately *2 Solve problems involving multiplication with numbers up to 1,000,000 Know the relationship between the square of a number and the square root of a number *3 Solve problems involving division with numbers up to 1,000,000 Solve problems involving a combination of the above with numbers up to 1,000,000 Know the cube of all numbers between 2 and 12 by heart *4 Use the symbol (3) accurately Objective 20: Solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes Solve problems involving multiplication and division, with numbers up to 1,000,000 Understand and use the equals sign to indicate equivalence, including in missing number problems, e.g. 13 + 24 = 12 + 25 Objective 22: Solve problems involving multiplication and division including scaling by simple fractions and problems involving simple rates Use multiplication and division as inverses, eg. multiply and divide by powers of 10 in scale drawings or multiplying and dividing by powers of a 1000 in converting between units such as kilometres and metres © Focus Education (UK) Ltd 2014 280 Year 5 Objectives : Number 8 FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES) Objective 23: Compare and order fractions whose denominations are all multiples of the same number Compare and order fractions with the same denominator Compare and order fractions with denominators of 2, 4 and 8 Compare and order fractions with denominators 5 and 10 Know how to convert fractions with different denominators into a common denominator Order 2 different fractions with different denominators that are multiples of the same number Order more than 2 different fractions with different denominators that are multiples of the same number Objective 24: Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths Identify equivalent fractions for 4/6, 5/10, 40/100 © Focus Education (UK) Ltd 2014 281 Year 5 Objectives : Number 9 FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES) Objective 25: Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements › 1 as a mixed number , e.g. ⅖ + ⅘ = 6/5 = 1 ⅕ Know that a whole number can be written as 2/2 or 4/4, etc. FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES) Objective 27: Multiply proper fractions and mixed fractions by whole numbers, supported by material and diagrams Know that 1and a half can be written as 3/2 Convert any improper fraction to a mixed fraction and vice versa Multiply a proper fraction by 10 *1 same denominator and denominators that are multiples of the same number Multiply a proper fraction by any whole number up to 10 *2 Add two fractions that have the same denominator with an answer of less than 1 Multiply a mixed fraction by 10 *3 Add two fractions that have the same denominator with an answer of more than 1, and then translate to a mixed number Multiply a mixed fraction by any number up to 10 *4 Objective 26: Add and subtract fractions with the Subtract two fractions with denominators that are multiples of the same number Subtract a fraction from a mixed number with denominators that are multiples of the same number © Focus Education (UK) Ltd 2014 282 Year 5 Objectives : Number 10 DECIMALS DECIMALS Objective 28: Read and write decimal numbers as fractions (e.g. 0.71 = 71/100) *1 Objective 30: Round decimals with 2 decimal places to the nearest whole number and to one decimal place Write any decimal with 1 decimal place as a fraction *2 Round any number to the nearest whole number, e.g. 18.23→ 18 *1 Write any decimal with 2 decimal places as a fraction *3 Round any number to one decimal place, eg. 17.91 → 17.9 *2 Write 0.5; 0.25; 0.1; as fractions Objective 29: Recognise and use thousandths and relate them to tenths, hundreds and decimal equivalents Objective 31: Read, write, order and compare numbers with up to 3 decimal places Order decimal fractions with 1 decimal place *1 Know that 10 thousandths are equivalent to one tenth Order decimal fractions with 2 decimal places *2 Work out how many thousandths there are in any given hundredth value Order decimal fractions with 3 decimal places *3 Work out how many thousandths there are in any given tenth value Order a set of decimal fractions with between 1 and 3 decimal places *4 Work out how many thousandths there are in any unit value Work out how many thousandths there are in any number to include u, t, h and th © Focus Education (UK) Ltd 2014 283 Year 5 Objectives : Number 11 DECIMALS PERCENTAGES Objective 32: Solve problems involving number up to three decimal places Objective 34: Write percentages as a fraction with denominator 100, and as a decimal percentages (eg ½ = 50% = 0.5) Add numbers with 1 decimal place Know that 50% is 50/100 = one half = ½ Add numbers with 2 and then 3 decimal places Know that 0.5 is 50% Subtract numbers with 1 decimal place Know that one quarter is 25% = 25/100 = ¼ Subtract numbers with 2 and then 3 decimal places Know that 0.25 is 25% = ¼ Solve a range of problems involving the above Know percentage value of all tenths; fifths; quarters and eighths Objective 33: Recognise the % symbol and understand that per cent relates to ‘a part of a hundred’ Objective 35: Solve problems which require knowing percentage and decimal equivalents of ½, ¼, ⅕, ⅖ ⅘ Know what the % symbol stands for Objective 36: Solve problems which require knowing those fractions with a denominator of a multiple of 10 or 25 Know that percentages deals with everything as part of 100 © Focus Education (UK) Ltd 2014 *1 *2 284 Focus on Mathematics Year 5 Pre-Learning Tasks Number Focus on Mathematics: Year 5 Name Objective 1 Date Number Read, write, order and compare numbers to at least 1,000,000 and determine the value of each digit Can you write these numbers in numerals? Two thousand, four hundred and fourteen *1 Can you write these numbers in words? 12,461 Thirteen thousand, three hundred and sixty-four 123,879 Two hundred and four thousand, one hundred and sixteen 15,247 Four hundred thousand, three hundred and eightythree 998,392 Sixty thousand, four hundred and five 719,709 © Focus Education (UK) Ltd 2014 *2 286 Focus on Mathematics: Year 5 Name Objective 2 Date Number Count forwards and backwards in steps of powers of 10 (100, 1000, 10,000) for any given number up to 1,000,000 Can you count on or back as required? 100 more than 237 100 more than 327 *1 100 less than 347 100 less than 672 1000 more than 257 1000 more than 4298 100,000 more than 135,478 100,000 more than 656,625 *2 1000 less than 3478 1000 less than 6625 10,000 more than 13478 10,000 more than 65625 10,000 less than 13978 10,000 less than 63628 100,000 less than 435,878 100,000 less than 856,925 1,000,000 more than 135,478 1,000,000 more than 1,656,625 *3 *4 *5 1,000,000 less than 4,935,878 1,000,000 less than 1,856,925 Starting Position: © Focus Education (UK) Ltd 2014 287 Name Objective 3 Focus on Mathematics: Year 5 Date Number Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero Can you respond to these problems? If Room A is 5⁰C and Room B is 7⁰C, which is warmer? *1 What comes next? -3, -4, -5, -6, … If Room A is -5⁰C and Room B is -7⁰C, which is warmer? 2, 1, 0, -1, … If Room A is 10⁰C and Room B is -7⁰C, which is colder? -4, -3, -2, -1, 0, …. If Room A is -6⁰C; Room B is 7⁰C and Room c is -3⁰C, which is warmer? -7, -6, -5, -4, -3, -2, -1, …. If Room A is -8⁰C; Room B is -9⁰C and Room c is -10⁰C, which is warmer? 3, 2, 1, 0, -1, -2, -3, … © Focus Education (UK) Ltd 2014 *2 288 Focus on Mathematics: Year 5 Name Objective 4 Date Number Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000 Can you round these numbers to the nearest 10, 100, 1000, 10,000 or 100,000? 1167 to the nearest 10 *1 77,771 to the nearest 1000 272 to the nearest 10 159,987 to the nearest 10,000 1145 to the nearest 100 918,756 to the nearest 10,000 5607 to the nearest 100 391,385 to the nearest 100,000 2134 to the nearest 1000 357,867 to the nearest 100,000 © Focus Education (UK) Ltd 2014 *2 289 Focus on Mathematics: Year 5 Name Date Objective 5 Number Estimate the answers to calculations involving addition, subtraction, multiplication and division Can you first estimate and then work out these calculations? Estimate estimate to nearest 10 18 + 35 Calculate Estimate *1 estimate to nearest 10 108 + 350 *2 estimate to nearest 10 472 - 158 estimate to nearest 100 123 x 13 estimate to nearest 100 672 - 158 108 + 650 *4 25 x 14 estimate to nearest 100 estimate to nearest 10 12 x 13 estimate to nearest 10 67 - 15 estimate to nearest 100 estimate to nearest 10 Calculate 250 x 14 *3 estimate to nearest 10 186 ÷ 8 estimate to nearest 10 122 ÷ 6 © Focus Education (UK) Ltd 2014 290 Focus on Mathematics: Year 5 Name Date Objective 7 Number Read Roman numerals to 1000 (M) and recognise years written in Roman numerals Can you write these numbers as Roman numerals? 5 *1 213 50 *2 199 100 *3 175 406 *4 925 604 288 © Focus Education (UK) Ltd 2014 291 Focus on Mathematics: Year 5 Name Date Objective 8 Number Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) Can you calculate these accurately? 13232 12334+ 11325 14123+ 10462 20257+ 11727 41231+ 12437 14659+ 16448 12255+ 27223 16465+ 11795 12836+ 34571 24259+ 23456 34862+ 12973 35686+ 32971 32519+ 56732 13545 14376+ 75682 23876 43975+ 89943 19243 45778+ 95832 73271 56659+ *1 32876 10323- 34599 12416- 15689 21643- 47787 15535- *3 *2 34450 11326- 78592 35869- 38419 27260- 42879 34588- *4 53653 24676- 62181 37336- 73581 56775- 84932 46737- © Focus Education (UK) Ltd 2014 292 Focus on Mathematics: Year 5 Name Objective 9 Date Number Add and subtract numbers mentally with increasingly large numbers Can you complete these very quickly? (2 minutes maximum) 23 + 37 *1 16 + 54 106 - 67 Can you complete these very quickly? (2 minutes maximum) 456 + 345 *3 235 + 765 *2 235 - 156 230 - 34 347 - 289 78 - 34 23,789 + 2,000 348 - 78 16, 987 + 6,000 345 - 67 56,732 - 8,000 1234 - 78 89,765 - 5,000 2346 - 98 72,367- 6,000 © Focus Education (UK) Ltd 2014 *4 293 Focus on Mathematics: Year 5 Name Date Objective 15 Number Multiply numbers up to 4-digits by a 1 or 2-digit number using a formal written method, including long multiplication for 2-digit numbers Can you multiply these accurately? 230 3x 405 5x 670 4x 302 8x 317 9x 448 5x 752 6x 785 8x 5231 9x 5645 7x 7223 6x 9541 5x 6723 6x 5662 7x 9413 8x 5532 9x *1 *2 902 x12 506 x26 607 x24 809 x32 126 x25 873 x45 847 x26 568 x34 3244 x34 7209 x24 8655 x45 6587 x34 © Focus Education (UK) Ltd 2014 *3 *4 294 Focus on Mathematics: Year 5 Name Date Objective 17 Number Divide numbers up to 4-digits by a 1-digit number using the formal written method of short division and interpret remainders appropriately for the context Can you divide these accurately? 235 ÷ 5 348 ÷ 6 248 ÷ 4 237 ÷ 3 3372÷ 6 2645÷5 1036÷7 5154÷6 566÷5 349÷6 247÷8 345÷7 873÷5 567÷9 239÷7 987÷4 *1 *2 9150 ÷ 9 5720 ÷ 7 6076 ÷ 3 1452 ÷ 7 8987 ÷ 6 8114 ÷ 7 3247 ÷ 10 7209 ÷ 10 8656 ÷ 10 © Focus Education (UK) Ltd 2014 *3 *4 295 Focus on Mathematics: Year 5 Name Objective 18 Date Number Multiply and divide numbers by 10, 100 and 1000 Can you multiply or divide as needed? 23 X 10 *1 45456 ÷ 100 345 x 10 25435 ÷ 100 94723 x 10 675345 ÷ 100 235 ÷ 10 *2 34987 x 1000 67543 ÷ 10 23789 x 1000 348761 ÷ 10 16,987 x 1000 3476 X100 562,732 ÷ 1000 123,454 x 100 189,765 ÷ 1000 213,496 x 100 72367÷ 1000 © Focus Education (UK) Ltd 2014 *3 *4 296 Focus on Mathematics: Year 5 Name Objective 19 Date Number Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (3) Can you write the square number; the square root of the number or the cube of the number as indicated? 5² *1 10² ²√100 If the square of a number is 64, what is its square root? *3 If the square of a number is 81, what is its square root? *2 3(3) ²√81 4(3) ²√64 5(3) © Focus Education (UK) Ltd 2014 *4 297 Focus on Mathematics: Year 5 Name Date Objective 26 Number Add and subtract 2 fractions with the same denominator Can you put these fractions in order (smallest first)? 2 4 1 4 3 4 1 6 5 6 4 6 3 4 1 2 3 8 1 5 3 10 6 10 1 2 4 5 *1 3 6 7 10 *2 Can you reorganise these fractions so that they have the same denominator? 2 3 5 6 7 8 1 2 1 2 *3 3 4 Can you reorganise these fractions so that they have the same denominator and then order them (smallest first)? 1 2 3 4 5 8 7 8 1 5 1 2 7 10 9 10 © Focus Education (UK) Ltd 2014 *4 3 5 298 Focus on Mathematics: Year 5 Name Date Objective 27 Number Multiply proper fractions and mixed fractions by whole numbers, supported by material and diagrams Can you work out the following calculations? ¾ x 10 *1 2¾ x 10 5/8 x 10 45/8 x 10 2/3 x 10 62/3 x 10 1/6 x 6 *2 71/6 x 6 2/5 x 8 82/5 x 8 ¾x7 7¾ x 7 3/5 x 9 53/5 x 9 1/8 x 9 91/8 x 9 © Focus Education (UK) Ltd 2014 *3 *4 299 Focus on Mathematics: Year 5 Name Date Objective 28 Number Read and write decimal numbers as fractions (e.g. 0.71 = 71/100) Can you write the following decimal numbers as fractions? 0.25 *1 0.15 0.5 2.5 0.1 1.25 0.3 3.75 4.1 *2 *3 6.83 7.3 9.45 6.9 10.75 8.5 3.78 © Focus Education (UK) Ltd 2014 300 Focus on Mathematics: Year 5 Name Date Objective 30 Number Round decimals with 2 decimal places to the nearest whole number and to one decimal place Can you round these decimal numbers to one whole number? 6.25 *1 Can you round these decimal numbers to one decimal place number? 0.15 7.5 2.58 8.1 1.25 9.3 3.75 11.1 6.83 9.3 9.45 6.9 10.75 8.5 3.78 © Focus Education (UK) Ltd 2014 *2 301 Focus on Mathematics: Year 5 Name Date Objective 31 Number Read, write, order and compare numbers with up to 3 decimal places Can you order these decimal numbers (smallest first)? 6.2; 7.3; 2.7 *1 0.153; 0.234; 0.765 7.5; 6.1; 4.6 2.584; 6.786; 2.345 8.1; 7.2; 7.7 1.254; 2.319; 1.255 9.3; 8.2; 6.5 3.753; 4.845; 2.735 11.12; 2.65; 7.12 *2 6.83; 1.2; 6.634 9.13; 6.98; 7.45 3.2; 9.45; 3.342 6.93; 5.23; 8.45 10.5; 10.75; 10.456 8.56; 6.78; 5.54 1.9; 3.78 1.659 © Focus Education (UK) Ltd 2014 *3 *4 302 Focus on Mathematics: Year 5 Name Date Objective 34 Number Write percentages as a fraction with denominator 100, and as a decimal (e.g. ½ = 50% = 0.5) Can you complete the missing values? Percentage (%) Decimal Fraction *1 Percentage (%) Decimal Fraction 50% 3/4 25% 5/6 33% 3/10 0.3 *2 0.6 1/4 2/9 0.75 0.2 © Focus Education (UK) Ltd 2014 303 Focus on Mathematics Year 5 Group Objectives Measurement, Geometry and Statistics Year 5 Objectives : Measurement MEASUREMENT MEASUREMENT Objective 1m: Convert between different units of metric measure, e.g. kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre Objective 3m: Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres Express a distance of more than 1Km in metres Express a distance of more than 1 cm in mm Express a weight of more than 1Kg in grams Express an amount of more than 1l in ml Objective 2m: Understand and use approximate equivalences between metric and common imperial units such as inches, pounds and pints Know the approximate number of metres in 1 mile Know the approximate relationship between inches and centimetres Know the approximate relationship between a pound and a gram Know that the perimeter of a composite rectilinear shape is measured by calculating the length of all the different sides Objective 4m: Calculate and compare the area of rectangles (including squares) and including using standard units, square centimetres (cm²) and square metres (m²) and estimate the area of irregular shapes Know that the area of a square or a rectangle is measured in cm² or m² Know that the area of a square is measured by multiplying the length of a side by itself Know that the area of a rectangle is measured by multiplying the length of the longer side by the shorter Use this information about calculating the area of a square or rectangle to work out the area of irregular shapes that can be divided up into squares and rectangles Know the approximate relationship between a pint and a litre © Focus Education (UK) Ltd 2014 305 Year 5 Objectives : Measurement 2 MEASUREMENT MEASUREMENT Objective 5m: Estimate volume, e.g. Using 1cm³ blocks to build cuboids (including cubes) and capacity, e.g. using water Know that volume is measured in cm³ or m³ Objective 7m: Use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation, including scaling Use cubes to work out volume of a given shape Carry out addition problems which relate to measurement as in money; length; weight; volume Use water to estimate and work out the capacity of a given container Objective 6m: Solve problems involving converting between units of time Carry out subtraction problems which relate to measurement as in money; length; weight; volume Carry out multiplication problems which relate to measurement as in money; length; weight; volume Carry out division problems which relate to measurement as in money; length; weight; volume Solve problems involving days and weeks, expressing the answer as weeks and days © Focus Education (UK) Ltd 2014 306 Year 5 Objectives : Geometry PROPERTIES of SHAPES PROPERTIES of SHAPES Objective 1g: Identify 3-D shapes, including cubes and other cuboids, from 2–D representations Objective 4g: Recognise and compare different triangles, including isosceles, equilateral and right angles triangles Understand relationship between square and cube; rectangle and cuboid; triangle and prism and triangle and square based pyramid Describe an equilateral triangle Objective 2g: Know angles are measured in degrees and identify right angles as ¼ turn (total 90˚); straight line as half turn = 180˚; whole turn = 360˚ Know that 90˚ is equivalent to quarter a turn Describe an isosceles triangle Describe a right angle triangle Objective 5g: Identify and name parallelogram; rhombus and trapezium Know what a parallelogram is and describe it in mathematical terms Know that 180˚ is equivalent to half a turn Know what a rhombus is and describe it in mathematical terms Know that 360˚ is equivalent to a full turn Objective 3g: Estimate and compare acute, obtuse and reflex angles Know what a trapezium is and describe it in mathematical terms * Objective 3g, 4g, and 5g are non statutory Estimate and compare acute, obtuse and reflex angles in a range of drawings © Focus Education (UK) Ltd 2014 307 Year 5 Objectives : Geometry 2 PROPERTIES of SHAPES Objective 6g: Draw given angles, and measure them in degrees (˚) Draw and be able to measure an angle of 90˚ Draw and be able to measure an angle of 45˚ Draw a given angle using a protractor and label it appropriately Objective 7g: Identify angles at a point and one whole turn (total 360˚) Objective 8g: Identify angles at a point on a straight line and ½ a turn (total 180˚) Identify other multiples of 90 ˚ Objective 9g: Distinguish between regular and irregular polygons based on reasoning about equal sides and angles Explain that a hexagon has more sides and smaller angles than a pentagon © Focus Education (UK) Ltd 2014 308 Year 5 Objectives : Geometry 3 PROPERTIES of SHAPES POSITION and DIRECTION Objective 10g; Use the properties of rectangles to deduce related facts and find missing lengths and angles Draw a square accurately having been given the length of the side Draw a rectangle accurately having been given the length and breadth Draw an equilateral triangle with a given length Draw an isosceles triangle accurately given the length of side and the base Draw a triangle to a given set of angles and sides Objective 11g: Identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language and know that the shape has not changed Use a 2-D grid and coordinates in the first quadrant to reflect and translate different shapes Use four quadrants to reflect and translate different shapes Reflect the shapes in lines that are parallel to the axes © Focus Education (UK) Ltd 2014 309 Year 5 Objectives : Statistics STATISTICS Objective 2s: Complete, read and interpret information in tables, including timetables STATISTICS Know how to construct a table from a set of given information Objective 1s: Solve comparison, sum and difference problems using information presented in a line graph Can read tables with given axes Can construct own table and make decisions about the axes Can compare information on line graphs to answer questions Know what a pie chart is Can solve sum problems using information on line graphs to answer questions Can read a simple pie chart with segments that are divisible by 10 Can solve difference problems using information on line graphs to answer questions Can interpret timetables to answer questions Know how to construct a bar graph from a set of given information Know how to apply scales on the axes of a bar graph Can read bar graphs with scales Can construct own bar graph and make decisions about the scales for the axes © Focus Education (UK) Ltd 2014 310 Focus on Mathematics Step up to the Challenge Year 5 Number Year 5: Can you challenge yourself to meet the Objective? Objective 1: Read, write, order and compare numbers to at least 1,000,000 determine the value of each digit Me My Teacher Can you partition any number up to 1,000,000 showing the value of each digit? Do you know and use terms: units; tens, hundreds, thousands, ten thousands, hundred thousands and one million correctly? Can you recognise the value of each digit up to 1,000,000? Can you read and write numbers to 1,000,000? Can you read and write number to 50,000? Can you remember how to read and write numbers to: 1000 and then to 10,000? © Focus Education (UK) Ltd 2014 312 Year 5: Can you challenge yourself to meet the Objective? Objective 2: Count forwards and backwards in steps of powers of 10 (100, 1000, 10,000 ) for any given number up to 1,000,000 Me My Teacher Me My Teacher Can you count onwards and backwards from a given number in steps of 1,000,000s? Can you count onwards and backwards from a given number in steps of 100,000s? Can you count onwards and backwards from a given number in steps of 10,000s? Can you count onwards and backwards from a given number in steps of 1000s? Can you count onwards and backwards from a given number in steps of 100s? Objective 3: Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero Can you count backwards from + 30 to -30? Can you count forwards from - 20 to + 20? Can you interpret temperatures at minus ⁰C on a thermometer? © Focus Education (UK) Ltd 2014 313 Year 5: Can you challenge yourself to meet the Objective? Objective 4: Round any number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000 Me My Teacher Can you round any number up to 1,000,000 to the nearest 100,000, 10,000, 1000, 100 or 10? Can you round any number up to 100,000 to the nearest 10,000, 1000, 100 or 10? Can you round any number up to 10,000 to the nearest 1,000, 100 or 10? Can you round any number up to 1000 to the nearest 100? Can you round any number up to 1000 to the nearest 10? Can you round any number up to 100 to the nearest 10? © Focus Education (UK) Ltd 2014 314 Year 5: Can you challenge yourself to meet the Objective? Objective 5: Estimate the answers to calculations involving addition, subtraction, multiplication and division Me My Teacher Can you estimate the answer to any given division involving a 3-digit number divided by a 1-digit to the nearest 10? Can you estimate the answer to any given division involving a 3-digit number divided by a 1-digit number to the nearest 100? Can you estimate the answer to any given division involving a 2-digit number divided by a 1-digit number to the nearest 10? Can you estimate the answer to any given multiplication involving two 3-digit numbers to the nearest 10? Can you estimate the answer to any given multiplication involving two 3-digit numbers to the nearest 100? Can you estimate the answer to any given multiplication involving two 2-digit numbers to the nearest 10? Can you estimate the answer to any given addition or subtraction involving two 3-digit numbers to the nearest 10? Can you estimate the answer to any given addition or subtraction involving two 3-digit numbers to the nearest 100? Can you estimate the answer to any given addition or subtraction involving two 2-digit numbers to the nearest 10? © Focus Education (UK) Ltd 2014 315 Year 5: Can you challenge yourself to meet the Objective? Objective 6: Solve number problems and practical problems that involve all of the above, including addition, subtraction, multiplication and division Me My Teacher Me My Teacher Can you calculate the answer to any given addition involving two 3-digit numbers to the nearest 10? Can you calculate the answer to any given addition involving two 3-digit numbers to the nearest 100? Can you calculate the answer to any given addition involving two 2-digit numbers to the nearest 10? Objective 7: Read Roman numerals to 1000 (M) and recognise years written in Roman numerals Do you know all the Roman numerals to 1000? Do you know the Roman numerals for 100? Do you know the Roman numerals for 50? Can you remember the Roman numerals from 1 to 10? © Focus Education (UK) Ltd 2014 316 Year 5: Can you challenge yourself to meet the Objective? Objective 8: Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction) Me My Teacher Can you subtract a 5-digit number from another using column subtraction which requires exchange between the units, tens, hundreds or thousands (or any two of these)? Can you subtract a 5-digit number from another using column subtraction which requires no exchange between the units, tens, hundreds or thousands? Can you add 3 numbers with 5-digits using column addition where the units, tens or hundreds make more than 10? Can you add 2 numbers with 5-digits together using column addition, where the units, tens or hundreds when added make more than 10.? Can you add 2 numbers with 5-digits together using column addition without exchange between units and tens? © Focus Education (UK) Ltd 2014 317 Year 5: Can you challenge yourself to meet the Objective? Objective 9: Add and subtract numbers mentally with increasingly large numbers Me My Teacher Can you subtract any 1000s number from a 5-digit number? Can you add together mentally any 1000s number and any 5-digit number? Can you subtract mentally any two 3-digit numbers? Can you add together mentally any two 3-digit numbers? Can you subtract any 2-digit number from a 3 or 4-digit number? Can you add together mentally any 2-digit and any 3-digit number? Can you subtract any 2-digit number from a 2 or 3-digit number? Can you add together mentally any two 2-digit numbers? © Focus Education (UK) Ltd 2014 318 Year 5: Can you challenge yourself to meet the Objective? Objective 10: Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy Me My Teacher Me My Teacher Can you use rounding to add together mentally any 1000s number and any 5-digit number, e.g. 4203 + 58502 = 4200 + 58500 + 5? Can you use rounding to add together mentally any two 3-digit numbers, e.g. 398 + 449 = 400 + 450 – 3 =? Can you use rounding to subtract any 2-digit number from a 2 or 3-digit number, e.g. 321 – 19 = 320 – 20? Can you use rounding to add together mentally any two 2-digit numbers, e.g. 29 + 39 = 30 + 40 – 2 = ? Objective 12 and 13: Identify multiples and factors, including finding all factor pairs of a number and common factors of two numbers; know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers Can you recognise all prime numbers to 100? Can you describe what a prime number is? Do you know all factors that make up all numbers to 100? Can you identify all multiples of numbers up to 100? © Focus Education (UK) Ltd 2014 319 Year 5: Can you challenge yourself to meet the Objective? Objective 15: Multiply numbers up to 4-digits by a 1 or 2-digit number using a formal written method, including long multiplication for 2digit numbers Me My Teacher Can you multiply any number with 3-digits by a single digit number? Can you multiply any number with 4-digits by a single digit number Can you multiply any number with 3-digits by a 2-digit number? Can you multiply any number with 4-digits by a 2-digit number? © Focus Education (UK) Ltd 2014 320 Year 5: Can you challenge yourself to meet the Objective? Objective 17: Divide numbers up to 4-digits by a 1-digit number using the formal written method of short division and interpret remainders appropriately for the context Me My Teacher Can you divide any number with 4-digits by 10, showing remainder where appropriate? Can you divide any number with 3-digits by 10, showing remainder where appropriate? Can you divide any number with 4-digits by a single digit number with remainder? Can you divide any number with 3-digits by a single digit number with remainder? Can you divide any number with 4-digits by a single digit number? Can you divide any number with 3-digits by a single digit number? © Focus Education (UK) Ltd 2014 321 Year 5: Can you challenge yourself to meet the Objective? Objective 18: Multiply and divide numbers by 10, 100 and 1000 Me My Teacher Can you divide any 4, 5 or 6-digit number by 1000? Can you multiply any 2, 3, 4, 5 or 6-digit number by 1000? Can you divide any 3, 4, 5 or 6-digit number by 100? Can you multiply any 2, 3, 4, 5 or 6-digit number by 100? Can you divide any 2, 3, 4, 5 or 6-digit number by 10? Can you multiply any 2, 3, 4, 5 or 6-digit number by 10? © Focus Education (UK) Ltd 2014 322 Year 5: Can you challenge yourself to meet the Objective? Objective 19: Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (3) Me My Teacher Can you use the symbols (3) (cubed) accurately? Do you know the cube of all numbers between 2 and 12 by heart? Do you know the relationship between the square of a number and the square root of a number? Can you use the symbols (²) and (√) accurately? Do you know the square of all numbers between 2 and 12 by heart? © Focus Education (UK) Ltd 2014 323 Year 5: Can you challenge yourself to meet the Objective? Objective 21: Solve problems involving addition and subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign Me My Teacher Can you understand and use the equals sign to indicate equivalence, including in missing number problems, e.g. 13 + 24 = 12 + 25; 33 = 5 x ? Can you solve problems involving a combination of the above with numbers up to 1,000,000? Can you solve problems involving division with numbers up to 1,000,000? Can you solve problems involving multiplication with numbers up to 1,000,000? Can you solve problems involving subtraction with numbers up to 1,000,000? © Focus Education (UK) Ltd 2014 324 Year 5: Can you challenge yourself to meet the Objective? Objective 23: Compare and order fractions whose denominations are all multiples of the same number Me My Teacher Can you order more than 2 different fractions with different denominators that are multiples of the same number? Can you order 2 different fractions with different denominators that are multiples of the same number? Do you know how to convert fractions with different denominators into a common denominator? Can you compare and order fractions with denominators of 5 and 10? Can you compare and order fractions with denominators of 2, 4 and 8? Can you compare and order fractions with the same denominator? © Focus Education (UK) Ltd 2014 325 Year 5: Can you challenge yourself to meet the Objective? Objective 25: Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements › 1 as a mixed number , e.g. ⅖ + ⅘ = 6/5 = 1 ⅕ Me My Teacher Me My Teacher Can you convert any improper fraction to a mixed fraction and vice versa? Do you know that 1and a half can be written as 3/2? Do you know that a whole number can be written as 2/2 or 4/4, etc.? Objective 26: Add and subtract fractions with the same denominator and denominators that are multiples of the same number Can you subtract a fraction from a mixed number with denominators that are multiples of the same number? Can you subtract two fractions with denominators that are multiples of the same number? Can you add two fractions that have the same denominator with an answer of more than 1, and then translate to a mixed number? Can you add two fractions that have the same denominator with an answer of less than 1? © Focus Education (UK) Ltd 2014 326 Year 5: Can you challenge yourself to meet the Objective? Objective 27: Multiply proper fractions and mixed fractions by whole numbers, supported by material and diagrams Me My Teacher Me My Teacher Can you multiply a mixed fraction by any number up to 10? Can you multiply a mixed fraction by 10? Can you multiply a proper fraction by any whole number up to 10? Can you multiply a proper fraction by 10? Objective 28: Read and write decimal numbers as fractions (e.g. 0.71 = 71/100) Can you write any decimal with 2 decimal places as a fraction? Can you write any decimal with 1 decimal place as a fraction? Can you write 0.5; 0.25; 0.1; as fractions? © Focus Education (UK) Ltd 2014 327 Year 5: Can you challenge yourself to meet the Objective? Objective 29: Recognise and use thousandths and relate them to tenths, hundreds and decimal equivalents Me My Teacher Me My Teacher Can you work out how many thousandths there are in any number to include u, t, h and th? Can you work out how many thousandths there are in any unit value? Can you work out how many thousandths there are in any given tenth value? Can you work out how many thousandths there are in any given hundredth value? Do you know that 10 thousandths are equivalent to one tenth? Objective 30: Round decimals with 2 decimal places to the nearest whole number and to one decimal place Can you round any number to one decimal place, e.g. 17.91 → 17.9? Can you round any number to the nearest whole number, eg. 18.23→ 18? © Focus Education (UK) Ltd 2014 328 Year 5: Can you challenge yourself to meet the Objective? Objective 31: Read, write, order and compare numbers with up to 3 decimal places Me My Teacher Me My Teacher Can you order a set of decimal numbers with between 1 and 3 decimal places? Can you order decimal numbers with 3 decimal places? Can you order decimal numbers with 2 decimal places? Can you order decimal numbers with 1 decimal place? Objective 32: Solve problems involving number up to three decimal places Can you solve a range of problems involving the above? Can you subtract numbers with 2 and then 3 decimal places? Can you subtract numbers with 1 decimal place? Can you add numbers with 2 and then 3 decimal places? Can you add numbers with 1 decimal place? © Focus Education (UK) Ltd 2014 329 Year 5: Can you challenge yourself to meet the Objective? Objective 34: Write percentages as a fraction with denominator 100, and as a decimal (e.g. ½ = 50% = 0.5) Me My Teacher Do you know percentage value of all tenths; fifths; quarters and eighths? Do you know that 0.25 is 25% = ¼? Do you know that one quarter is 25% = 25/100 = ¼ ? Do you know that 0.5 is 50%? Do you know that 50% is 50/100 = one half = ½? © Focus Education (UK) Ltd 2014 330 Making Mathematics Work Step up to the Challenge Year 5 Measurement, Geometry and Statistics Year 5: Can you challenge yourself to meet the Objective? Objective 1m: Convert between different units of metric measure, e.g. kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre Me My Teacher Me My Teacher Can you express an amount of more than 1l in ml? Can you express a weight of more than 1Kg in grams? Can you express a distance of more than 1 cm in mm? Can you express a distance of more than 1Km in metres? Objective 2m: Understand and use approximate equivalences between metric and common imperial units such as inches, pounds and pints Do you know the approximate relationship between a pint and a litre? Do you know the approximate relationship between a pound and a gram? Do you know the approximate relationship between inches and centimetres? Do you know the approximate number of metres in 1 mile? © Focus Education (UK) Ltd 2014 332 Year 5: Can you challenge yourself to meet the Objective? Objective 4m: Calculate and compare the area of rectangles (including squares) and including using standard units, square centimetres (cm²) and square metres (m²) and estimate the area of irregular shapes Me My Teacher Me My Teacher Can you use information about calculating the area of a square or rectangle to work out the area of irregular shapes that can be divided up into squares and rectangles? Do you know that the area of a rectangle is measured by multiplying the length of the longer side by the shorter? Do you know that the area of a square is measured by multiplying the length of a side by itself? Do you know that the area of a square or a rectangle is measured in cm² or m²? Objective 5m: Estimate volume, e.g. Using 1cm³ blocks to build cuboids (including cubes) and capacity, e.g. using water Can you use water to estimate and work out the capacity of a given container? Can you use cubes to work out volume of a given shape? Do you know that volume is measured in cm³ or m³? © Focus Education (UK) Ltd 2014 333 Year 5: Can you challenge yourself to meet the Objective? Objective 7m: Use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation, including scaling Me My Teacher Me My Teacher Can you carry out addition problems which relate to measurement as in money; length; weight; volume ? Can you carry out subtraction problems which relate to measurement as in money; length; weight; volume? Can you carry out multiplication problems which relate to measurement as in money; length; weight; volume? Can you carry out division problems which relate to measurement as in money; length; weight; volume? Objective 2g: Know angles are measured in degrees and identify right angles as ¼ turn (total 90˚); straight line as half turn = 180˚; whole turn = 360˚ Do you know that 360˚ is equivalent to a full turn? Do you know that 180˚ is equivalent to half a turn? Do you know that 90˚ is equivalent to quarter a turn? © Focus Education (UK) Ltd 2014 334 Year 5: Can you challenge yourself to meet the Objective? Objective 4g: Recognise and compare different triangles, including isosceles, equilateral and right angles triangles Me My Teacher Me My Teacher Can you describe a right angle triangle? Can you describe an isosceles triangle? Can you describe an equilateral triangle? Objective 5g: Identify and name parallelogram; rhombus and trapezium Do you know what a parallelogram is and can you describe it in mathematical terms? Do you know what a rhombus is and can you describe it in mathematical terms? Do you know what a trapezium is and describe it in mathematical terms? © Focus Education (UK) Ltd 2014 335 Year 5: Can you challenge yourself to meet the Objective? Objective 6g: Draw given angles, and measure them in degrees (˚) Me My Teacher Me My Teacher Can you draw a given angle using a protractor and label it appropriately? Can you draw and measure an angle of 45˚? Can you draw and measure an angle of 90˚? Objective 10g; Use the properties of rectangles to deduce related facts and find missing lengths and angles Can you draw a triangle to a given set of angles and sides? Can you draw an isosceles triangle accurately given the length of side and the base? Can you draw an equilateral triangle with a given length? Can you draw a rectangle accurately having been given the length and breadth? Can you draw a square accurately having been given the length of the side? © Focus Education (UK) Ltd 2014 336 Focus on Mathematics Non-Negotiables Year 5 Possible Planning Outline Year 5 Mathematics Non-Negotiables • The following areas of learning are known as the non-negotiables. They have a specific role in helping pupils meet the year group expectations. In a nutshell we are suggesting that if pupils are not confident in these areas then they will find the rest of the curriculum difficult to access. • The non-negotiables are designed to: 1. Identify the essential components that pupils need to become confident with, i.e. be able to demonstrate in independent tasks and be able to apply in other contexts. 2. Unblock learning, i.e. to keep teachers focused on the essential rather than coverage at the expense of progress. 3. Unlock learning and progress. • The non-negotiables are not designed to imply that the rest of the curriculum is an irrelevance – it clearly isn’t. But rather to give a structure for professionals to decide what the right curriculum is for their pupils. © Focus Education (UK) Ltd 2014 338 Year 5 Mathematics Non-Negotiables • Count forwards and backward with positive and negative numbers through zero. • Count forwards and backwards in steps of powers of 10 for any given number up to 1000000. • Compare and order numbers with 3 decimal places. • Read Roman numerals to 1000. • Identify all multiples and factors, including finding all factor pairs. • Use known tables to derive other number facts. • Recall prime numbers up to 19. • Recognise place value of any number up to 1,000,000. • Round any number to 1,000,000 to the nearest 10, 100, 1000, 10,000 or 100,000. • Round decimals with 2 decimal places to nearest whole number and 1decimal place. • Add and subtract: o Numbers with more than 4-digits using efficient written method (column). o Numbers with up to 2 decimal places. • Multiply: o 4-digits by 1-digit/ 2-digit • Divide: o 4-digits by 1-digit • Multiply and divide: o Whole numbers and decimals by 10, 100 & 1000 • Count up/down in thousandths. • Recognise mixed numbers and fractions and convert from one to another. • Multiply proper fractions by whole numbers. • Solve time problems using timetables and converting between different units of time. © Focus Education (UK) Ltd 2014 339 Planning to meet the requirement of the nonnegotiables The following 3 pages suggest a planning outline for delivering the non-negotiables in classrooms. There should some element of teaching of these each day. Autumn Term Ist Half Term • • • • • • • • • • • • 2nd Half Term Count on/back from a given number in steps of 100/1000/10,000 up to a 100,000 Read, write and order numbers to 100,000 Compare numbers to at least 100,000 Partition numbers to at least 100,000 Find powers of 10 more than a given number Multiply and divide numbers mentally drawing upon known facts Multiply and divide any whole number by 10 and 100 and multiply and divide any decimal number by 10 Count on/back with positive and negative numbers, including through zero Round any number up to 50,000 to the nearest 10, 100 and 1000 Add/subtract: 3-digit and 1-digit numbers, a 3-digit number and tens and a 3-digit number and hundreds, combinations of 2 and 3 digit numbers Find complements to 100 and 1000 and 10. 000 Find factors and factor pairs of each number up to 20 • • • • • • • • • • • • • • • • • Count on/back from a given number in steps of 100/1000/10,000 up to and beyond a 100,000 Read, write and order numbers to 100,000 and beyond Compare numbers to 100,000 and beyond Partition numbers to 100,000 and beyond Find powers of 10 more than a given number Read, write, order and compare decimal numbers up to 2dp Partition decimal numbers to 2dp Round decimals with 1dp to the nearest whole number Multiply and divide numbers mentally drawing upon known facts Multiply and divide any whole number by 10 and 100 and multiply and divide any decimal number by 10 and 100 Count on/back with positive and negative numbers, including through zero) Count on/back in fraction and decimal sequences (e.g. 2.5 or 1 ½ Round any number up to 100,000 to the nearest 10, 100 and 1000 Add/subtract: 4-digit and 1-digit numbers, a 4 digit and tens, a 4digit number and hundreds and a 4-digit number and thousands and combinations of pairs of 2,3 or 4 digit numbers Find factors and factor pairs of each number up to and beyond 20 Find complements to 1000 Convert units of measurement (km and m; cm and m; cm and mm; gram and km, ml and L) © Focus Education (UK) Ltd 2014 340 Planning to meet the requirement of the nonnegotiables Spring Term Ist Half Term • • • • • • • • • • • • • • • • • • 2nd Half Term Count on/back from a given number in steps of 100/1000/10,000/100.000 up to 500,000 Read, write and order numbers to 500,000 Compare numbers to at least 500,000 Partition numbers to at least 500,000 Find powers of 10 more than a given number Read, write, order and compare decimal numbers up to 3dp Partition decimal numbers to 3dp Round decimals with 1 and 2dp to the nearest whole number Multiply and divide numbers mentally drawing upon known facts Multiply and divide any whole number by 10, 100, 1000 and multiply and divide any decimal number by 10 and 100 Count on/back with positive and negative numbers, including through zero Count on/back in fraction and decimal sequences? (e.g. 2.5 or 1½ Round any number up to 500,000 to the nearest 10, 100, 1000, 10,000 and 100,000 Add/subtract: 4-digit and 1-digit numbers, a 4 digit and tens, a 4-digit number and hundreds and a 4-digit number and thousands and combinations of pairs of 2,3 or 4 digit numbers Mentally add and subtract tenths Find factors and factor pairs of each number up to 50 Find complements to 100 and 1000 and to £1.00 Convert units of measurement (km and m; cm and m; cm and mm; gram and km, ml and L) • • • • • • • • • • • • • • • • • • • Count on/back from a given number in steps of 100/1000/10,000/100,000 up to and beyond 500,000 Read, write and order numbers to 500,000 and beyond Compare numbers to 500,000 and beyond Partition numbers to 500,000 and beyond Find powers of 10 more than a given number Read, write, order and compare decimal numbers up to 3dp Partition decimal numbers to 3dp Round decimals with 1 and 2dp to the nearest whole number Multiply and divide numbers mentally drawing upon known facts Multiply and divide any whole number by 10, 100, 1000 and multiply and divide any decimal number by 10 and 100 Count on/back with positive and negative numbers, including through zero) Count on/back in fraction and decimal sequences (e.g. 2.5 or 1 ½ Round any number up to 500,000 and beyond to the nearest 10, 100, 1000, 10,000 and 100,000 Add mentally a 4 digit number and a 3 digit number (for example 8,345 + 230) Subtract mentally any 4-digit number from a 3-digit number (for example 8,345 – 230) Find factors and factor pairs of each number up to 50 and beyond Find complements to 100 and 1000; £1.00 and £5.00 and to 1 using 2dp Convert units of measurement (km and m; cm and m; cm and mm; gram and km, ml and L) Mentally add and subtract tenths © Focus Education (UK) Ltd 2014 341 Planning to meet the requirement of the nonnegotiables Summer Term Ist Half Term • • • • • • • • • • • • • • • • • • 2nd Half Term Count on/back from a given number in steps of 100/1000/10,000/100,000 up to a 1,000,000 Read, write and order numbers to 1,000,000 Compare numbers to at least 1,000,000 Partition numbers to at least 1,000,000 Find powers of 10 more than a given number Read, write, partition, order and compare decimal numbers up to 3dp Round decimals with 1 and 2dp to the nearest whole number and to 1dp Multiply and divide numbers mentally drawing upon known facts Multiply and divide any whole and decimal number by 10, 100, 1000 Count on/back with positive and negative numbers, including through zero Count on/back in fraction and decimal sequences (e.g. 2.5 or 1 ½ Round any number up to 1,000,000 to the nearest 10, 100, 1000, 10,000 and 100,000 Add mentally a 4 digit number and 3 digit numbers (for example 8,345 + 230) Subtract mentally any 4-digit number from a 3-digit number (e.g. 8,345 – 230) Mentally add and subtract tenths and one-digit whole numbers and tenths Find factors and factor pairs of each number up to 100 Find complements to 100 and 1000; £1.00 and £5.00 and to 1 using 2dp Convert units of measurement (km and m; cm and m; cm and mm; gram and km, ml and L) • • • • • • • • • • • • • • • • • Count on/back from a given number in steps of 100/1000/10,000/100,000 to a 1,000,000 and beyond Read, write, and order numbers to 1,000,000 and beyond Compare numbers to 100,000 and beyond Partition numbers to 1,000,000 and beyond Find powers of 10 more than a given number Read, write, partition, order and compare decimal numbers up to 3dp Round decimals with 1 and 2dp to the nearest whole number and to 1dp Multiply and divide numbers mentally drawing upon known facts Multiply and divide any whole and decimal number by 10, 100, 1000 Count on/back with positive and negative numbers, including through zero Count on/back in fraction and decimal sequences (e.g. 2.5 or 1 ½ Round any number to 1,000,000 and beyond to the nearest 10, 100, 1000, 10,000 and 100,000 Add mentally a 5-digit number and 4- digit numbers (e.g. 15,345 + 2300) Mentally add and subtract tenths and one-digit whole numbers and tenths Find complements to 100. 1000, 10,000; £1.00, £5.00 and £10.00; and to 1 using 3dp Find factors and factor pairs of each number to 100 Convert units of measurement (km and m; cm and m; cm and mm; gram and km, ml and L) © Focus Education (UK) Ltd 2014 342 Focus on Mathematics Year 5 Assessment Assessment: Meeting Year 5 Expectations The main focus on assessment will be measuring a pupil’s journey towards and beyond the Year 5 expectations. The Year 5 expectations for number are set out below on this page. To meet the Year 5 expectations a pupil must be able to meet all of the statements outlined in the table, plus the ones for measurement and geometry, shown later. If they have not met all the statements then they will be deemed to be emerging. If a pupil is meeting the expectations then an assessment needs to made as to whether a pupil is exceeding the expectations. The next page sets out how to assess whether a pupil is exceeding the expectations or whether a pupil is at the emerging stage. The next page also provides you with a 9-point scale for deeper analysis, if required. Year 5 Expectations: Number • Count forwards and backwards in steps of power 10 for any given number up to 1,000,000 • Recognise and use thousandths and relate them to tenths, hundreds and decimal equivalents • Recognise mixed numbers and improper fractions and convert from one to the other • Read and write decimal numbers as fractions, e.g. 0.47 = 47/100 • Recognise the per cent symbol (%) and understand per cent relates to number of parts per hundred • Write percentages as a fraction with denominator hundred, and as a decimal number • Compare and add fractions whose denominators are all multiples of the same number • Multiply and divide numbers mentally drawing upon known facts up to 12 x 12 • Round any number to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000 • Round decimals with 2dp to the nearest whole number and to 1decimal place • Recognise and use square numbers and cube numbers and the notation for squared (²) and cubed (³) • Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 • Multiply number up to 4-digit by a 1 or 2-digit number using formal written methods, including long multiplication for 2-digit numbers • Divide numbers up to 4-digits by 1-digit numbers • Solve problems involving multiplication and division where large numbers are used by decomposing them into factors • Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why; solve problems involving 3 decimal places and problems which require knowledge of percentages and decimal equivalents © Focus Education (UK) Ltd 2014 344 Assessment: Meeting Year 5 Expectations The 3 or 9-point scale Effectively, pupils will be assessed on a 3-point scale: that is, pupils will be judged as having met the expectations; emerging towards the expectations or exceeding the expectations. However, for many schools, this may not give them enough information when tracking pupils through the school. So, if schools desire, the following 9-point system is outlined for them to use. Assessed position Emerging Stage C Emerging Stage B Emerging Stage A Meeting Stage C Meeting Stage B Meeting Stage A Exceeding Stage C Exceeding Stage B Exceeding Stage A Points allocation 1 2 3 4 5 6 7 8 9 • • • • • As is illustrated, Point 4 is the point that indicates that a pupil has met the expectations. If we are to take account of the new Assessment arrangements then it is hoped that 85% of pupils will be at least at this stage by the end of the year. Points 1 to 3 are the ‘emerging’ stages; Points 4 to 6 are the ‘meeting’ expectations stages; and Points 7 to 9 are the ‘exceeding’ stages. The following page sets out what each point actually means and provides clarity about the allocation of the points. © Focus Education (UK) Ltd 2014 345 Assessment: Meeting Year 5 Expectations A pupil will be deemed to be meeting the expectations only if they can satisfy their teacher that they meet all the expectations for their age A pupil will be deemed to be emerging towards the expectations if they do not meet all of the statements outlined for that year group •Meeting the expectations (Stage C) – Point 4 •It is accepted that a pupil might make the occasional error if they are at this stage. However, despite that, the teacher needs to be satisfied that they understand the concept fully. •Meeting the expectations (Stage B) - Point 5 •At this stage a pupil will rarely make mistakes and is very confident at meeting the statements. •Meeting the expectation (Stage A)- Point 6 •At this stage, not only is the pupil confident at meeting the statements but works at a rapid rate. However, they are not yet meeting all the statements for exceeding. •If they meet more than 75% of the statements but not all then they will be described as: •Emerging towards the expectations (Stage C) – Point 3 •If they meet between 50% and 75% of the statements then they will be described as: •Emerging towards the expectations (Stage B) – Point 2 •However if they are not meeting 50% of the expectations they will be described as: •Emerging towards the expectations (Stage A) – Point 1 •There is, therefore, no requirement to write a set of emerging statements © Focus Education (UK) Ltd 2014 A pupil will be deemed to be exceeding the expectations when, in addition to the statements set out for meeting the expectation (Stage A)they meet one or more of three sets of further expectations •Pupils will be deemed to be exceeding expectations if, in addition to what is outlined as Point 6, they show evidence of: •Accessing some of the following year group’s objectives •Being able to use the year group’s expectation within context •Being able to consistently apply the year group objectives in a range of situations. •A set of exceeding statements are set out for you to feel secure about your judgements. •If a pupil is meeting the exceeding statements, they will be deemed to be at Point 7 (Stage C) •If they are very confident and rarely make a mistake in relation to the ‘exceeding’ statements then they will be judged at Point 8 (Stage B) •A few pupils will be judged at Point 9 (Stage A). These will be pupils who are exceptionally confident in handling the exceeding statements and show exceptional mathematical ability for their age 346 Assessment: Meeting Year 5 Expectations The 3 or 9-point scale Effectively pupils will be assessed on a 3-point scale: that is pupils will be judged as having met the expectations; emerging (or developing) towards the expectation or exceeding the expectations. However, for many schools, this may not give them enough information when tracking pupils through the school. So, if schools desire, the following 9-point system is outlined for them to use. Assessed position Emerging Stage A Emerging Stage B Emerging Stage C Meeting Meeting advanced Meeting higher Exceeding Exceeding advanced Exceeding higher Points allocation 1 2 3 4 5 6 7 8 9 • • • • • As is illustrated Point 4 is the point that indicates that a pupil has met the expectations. If we are to take account of the new Assessment arrangements then it is hoped that 85% of pupils will be at least at this stage by the end of the year. Points 1 to 3 are the ‘emerging’ stages; Points 4 to 6 are the ‘meeting expectation’ stages; and Points 7 to 9 are the ‘exceeding’ stages. The following page sets out what each point actually means and provides clarity about the allocation of the points. © Focus Education (UK) Ltd 2014 347 Assessment: Meeting Year 5 Expectations Year 5 Expectations: Number • Count forwards and backwards in steps of power 10 for any given number up to 1,000,000 • Recognise and use thousandths and relate them to tenths, hundreds and decimal equivalents • Recognise mixed numbers and improper fractions and convert from one to the other • • Year 5 Expectations: Measurement, Geometry and Statistics • Know angles are measured in degrees: estimate and compare acute; obtuse and reflex angles Read and write decimal numbers as fractions, e.g. 0.47 = 47/100 • Recognise the per cent symbol (%) and understand per cent relates to number of parts per hundred Draw given angles and measure them in degrees (º) • Convert between different units of metric measures and estimate volume and capacity • Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres • Calculate and compare the area of squares and rectangles including using standard units (cm² and m²) • Solve comparison, sum and difference problems using information presented in a line graph • Write percentages as a fraction with denominator hundred, and as a decimal number • Compare and add fractions whose denominators are all multiples of the same number • Multiply and divide numbers mentally drawing upon known facts up to 12 x 12 • Round any number to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000 • Round decimals with 2dp to the nearest whole number and to 1decimal place • Recognise and use square numbers and cube numbers and the notation for squared (²) and cubed (³) • Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 • Multiply number up to 4-digit by a 1 or 2-digit number using formal written methods, including long multiplication for 2-digit numbers • Divide numbers up to 4-digits by 1-digit numbers • Solve problems involving multiplication and division where large numbers are used by decomposing them into factors • Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why; solve problems involving 3-decimal places and problems which require knowledge of percentages and decimal equivalents © Focus Education (UK) Ltd 2014 348 Assessment: Exceeding Year 5 Expectations Year 5 Exceeding Expectations: Number • Have a concept of numbers well beyond 1,000,000 and their relative association to distances to planets; historical data and geographical aspects • Divide whole numbers (up to 4 digits) by 2-digit numbers, using preferred method • Use rounding as a strategy for quickly assessing what approximate answers ought to be before calculating • Link working across zero for positive and negative numbers to work time between BC and AD in history • Recognise the symbol for square root (√) and work out square roots for numbers up to 100 • Calculate number problems algebraically, e.g. 2x – 3 = 5 • Use knowledge of measurement to create plans of areas around school, such as classroom , field, outside play area, etc. • Relate imperial measures still used regularly in our society to their metric equivalents, eg, miles to Km and lbs to Kg • Use a range of timetables to work out journey times on a fictional journey around the world, eg, how long would it take to reach the rainforests in the Amazon • Collect own data on personal project and present information in formats of their choosing, charts, graphs and tables © Focus Education (UK) Ltd 2014 349 Focus on Mathematics Year 5 Parents’ Guide Parents’ Guide ‘Must Dos’ by the end of Year 5 Number • • • • • • • • Read, write and order numbers to 1,000,000 Count on and back in steps of 100,1,000, 10,000 up to 1,000,000 Round any number to the nearest 10, 100, 1,000, 10,000 or 100,000 Estimate and calculate additions involving 2, 3-digit numbers (to nearest 10) Estimate and calculate subtractions involving 2, 3-digit numbers (to nearest 10) Estimate and calculate multiplications involving a 2-digit and a 3-digit numbers (to nearest 10) Estimate and calculate divisions of a 3-digit number by a 1-digit number (to nearest 10) Add 3, 5-digit numbers using column addition • • • • • • • • • • Subtract one 5-digit number from another, using column subtraction Rapid Recall: Mentally add a 2-digit number to a 3-digit number Rapid Recall: Mentally add a 1000s number to a 5-digit number Rapid Recall: Mentally subtract a 2digit number from a 3 or 4-digit number Rapid Recall: Mentally subtract a 1000s number from a 5-digit number Know all factors that make up numbers to 100 Recognise all prime numbers to 100 Multiply a 4-digit number by a 2-digit number using formal methods Divide a 4-digit number by a 1-digit number (with remainders) Multiply numbers by 10, 100 and 1,000 © Focus Education (UK) Ltd 2014 351 Parents’ guide ‘Must Dos’ by the end of Year 5 Number • • • • • • • Number Divide number by 10, 100 and 1,000 Recognise and use square numbers and square roots Know and use the symbols (²),(3) and (√) accurately Fractions: Compare and order fractions whose denominators are multiples of the same number Convert mixed numbers to improper fractions and visa versa Add and subtract fractions with the same denominator Multiple proper fractions and mixed fractions by whole numbers • • • • • • Decimal Fractions: Read and write decimal numbers as fractions (up to hundredths) Round decimals with two decimal places to nearest whole number and one decimal place Read, write, order and compare decimal numbers with up to three decimal places Percentages: Recognise the % symbol Understand that percentage is measured as part of 100 Solve problems which require knowing percentage and decimal value of ½, ¼, ⅕, ⅖ and ⅘ © Focus Education (UK) Ltd 2014 352 Parents’ Guide ‘Must Dos’ by the end of Year 5 Shape and measures • • • • • • Shape and Measures Measure angles in degrees Draw a given angle accurately Know and use reflex angles Construct shapes from given dimensions Identify 3D shapes from 2D representations Identify, describe and represent the position of a shape following reflection and translation • • • • Add, subtract, multiply and divide units of measure (using decimal notation) Understand and use basic equivalence between metric and common imperial units Calculate, estimate and compare areas of squares and rectangles using cm squared (cm²) and metre squared (m²) Recognise volume in practical contexts © Focus Education (UK) Ltd 2014 353 Focus on Mathematics Year Group Objectives Year 6 Year 6 Objectives: Number NUMBER AND PLACE VALUE Objective 1: Read, write, order and compare numbers to 10,000,000 and determine the value of each digit Revise reading and writing numbers to: 1000 and then to 100,000 *1 Read and write numbers to 1,000,000 Read and write numbers to 10,000,000 *2 Recognise the value of each digit up to 10,000,000 Know and use terms: units; tens, hundreds, thousands, ten thousands, hundred thousands, one million and ten million correctly Partition any number up to 10,000,000 showing the value of each digit Objective 2: Round any whole number to a required degree of accuracy Round any 7-digit number to the nearest million *1 Round any 6-digit number to the nearest hundred thousand Round any 5-digit number to the nearest ten thousand *2 Round any 4-digit number to the nearest thousand Round any number to the nearest degree of accuracy © Focus Education (UK) Ltd 2014 355 Year 6 Objectives: Number 2 NUMBER AND PLACE VALUE Objective 3: Use negative numbers in context , and calculate intervals across zero Interpret temperatures at minus ⁰C on a thermometer *1 Calculate the interval from - 20 to + 100 Calculate the interval from + 30 to -30 *2 Objective 4: Solve number and practical problems that involve all of the above Calculate the answer to any given problem involving the above ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION Objective 5: Add and subtract negative integers (Non Statutory) Add any 2 negative numbers together Know what happens when subtracting a negative number form another negative number Objective 6: Multiply multi-digit numbers up to 4-digits by a 2-digit whole number using the formal written method of long multiplication Revise multiplication of HTU x U *1 Revise multiplication of ThHTU x U Multiply 4-digit numbers by a 2-digit number using grid method or another conventional method © Focus Education (UK) Ltd 2014 *2 356 Year 6 Objectives : Number 3 ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION Objective 7: Divide numbers up to 4-digits by a 2-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context Objective 8: Divide numbers up to 4-digits by a 2-digit number using the formal written method of short division where appropriate , interpreting remainders according to the context Revise division of numbers with up to 4-digits by a single-digit number with and without remainders *1 Divide numbers with up to 4-digits by a 2-digit number up to 20 without remainders *2 Divide numbers with up to 4-digits by a 2-digit number up to 20 with remainders *3 Divide numbers with up to 4-digits by a 2-digit number with remainders Objective 9: Perform mental calculations, including with mixed operations and large numbers Perform mental calculations with large numbers Express remainder as a fractional value of the number divided by Perform mental calculations which require at least two different operations, eg. addition and multiplication Divide numbers with up to 4-digits by any 2-digit number with and without remainders Use rounding up to express answers as a whole number Divide numbers with up to 4-digits by a 2-digit number without remainders *4 © Focus Education (UK) Ltd 2014 357 Year 6 Objectives : Number 4 ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION Objective 10: Identify common factors, common multiples and prime numbers Know the common factors of any 2 given numbers Know the common multiples of any 2 given numbers Know all prime numbers Objective 11: Use their knowledge of the order of operations to carry out calculations involving the four operations Objective 12: Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION Objective 13: Solve problems involving addition, subtraction, multiplication and division Solve word problems involving addition with numbers up to 10,000,000 *1 Solve word problems involving subtraction with numbers up to 10,000,000 *2 Solve word problems involving multiplication with numbers up to 10,000,000 *3 Solve word problems involving division with numbers up to 10,000,000 Solve word problems with mixed operations with numbers up to 10,000,000 *4 Objective 14: Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy Know when it is appropriate to represent an answer to a given problem as a fractional value rounded to the nearest whole number value Estimate the answer to a problem before working it out and use the estimation to check on accuracy of problem solving © Focus Education (UK) Ltd 2014 358 Year 6 Objectives : Number 5 FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES) FRACTIONS INCLUDING DECIMALS AND PERCENTAGES) Objective 15: Use common factors to simplify fractions; use common multiples to express fractions in the same denomination Objective 17: Divide proper fractions by whole numbers Find the greatest common factor to simplify fractions Divide a proper fraction by a whole number and give answer in its simplest form Know how to use common multiples to express fractions in the same denomination Objective 18: Associate a fraction with division to calculate decimal fraction equivalents, e.g. 0.375 for a simple fraction ⅜ Objective 16: Multiply simple unit fractions and pairs of proper fractions, writing the answer in its simplest form Multiply a whole number with a fraction *1 *2 Turn mixed fractions into an improper fraction Multiply 2 mixed fractions and write answer in its simplest form Know that 1/10 can be represented as 0.1 *1 Know that ¼ can be represented as 0.25 Multiply a whole number with a fraction and give answer in its simplest form Multiply 2 simple fractions together and give answer in its simplest form Divide a proper fraction by a whole number *3 Know that ¾ can be represented as 0.75 Know all the decimal fraction equivalents for fractional values where the denominator is 3, 4, 5, 6, 8 or 10 © Focus Education (UK) Ltd 2014 359 Year 6 Objectives : Number 6 FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES) FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES) Objective 19: Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions Objective 21: Recall and use equivalences between simple fractions, decimals and percentages including in different contexts Revise addition and subtraction of fractions with the same denominator *1 Work out common denominator for a pair of fractions with different denominators, e.g. ⅔ and ⅗ Revise that ¼ can be represented as 0.25 and use this to solve problems Add 2 fractions with different denominators *2 Add 2 mixed numbers where the fractional values have different denominators *3 Subtract 2 fractions with different denominators Subtract 2 mixed numbers where the fractional values have different denominators Revise that 1/10 can be represented as 0.1 and use this to solve problems Revise that ¾ can be represented as 0.75 and use this to solve problems Revise all the decimal fraction equivalents for fractional values where the denominator is 3, 4, 5, 6, 8 or 10 and use this to solve problems *4 Objective 20: Multiply simple pairs of proper fractions, writing the answer in its simplest form, e.g. ¼ x ½ = 1/8 Multiply 2 simple fractions together and give the answer in its simplest form © Focus Education (UK) Ltd 2014 360 Year 6 Objectives : Number 7 DECIMALS DECIMALS Objective 22: Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places Objective 23: Multiply one-digit numbers with up to two decimal places by whole numbers *1 Know the value of each digit in a decimal fraction which has up to 3 decimal places *1 Multiply a decimal fraction with up to 2 decimal places by a single-digit number *2 Know that when multiplying a decimal fraction by 10 the decimal point moves one place to the right, e.g. 3.457 x 10 = 34.57 *2 Multiply a decimal fraction with up to 2 decimal places by a 2-digit number Divide a decimal fraction with up to 2 decimal places by a single-digit number *3 Divide a decimal fraction with up to 2 decimal places by a 2-digit number *4 Know that when multiplying a decimal fraction by 100 the decimal point moves two places to the right, e.g. 3.457 x 100 = 345.7 Objective 24: Use written division methods in cases where the answer has up to two decimal places Know that when multiplying a decimal fraction by 1000 the decimal point moves three places to the right, e.g. 3.457 x 100 = 3457 Know that when dividing a decimal fraction by 10 the decimal point moves one place to the left, e.g. 567.234 ÷ 10 = 56.7234 Know that when dividing a decimal fraction by 100 the decimal point moves two places to the left, e.g. 567.234 ÷ 100 = 5.67234 *3 Objective 25: Solve problems which require answers to be rounded to specified degrees of accuracy Know that when dividing a decimal fraction by 1000 the decimal point moves three places to the left, e.g. 567.234 ÷ 1000 = 0.567234 © Focus Education (UK) Ltd 2014 361 Year 6 Objectives : Number 6 FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES) FRACTIONS (INCLUDING DECIMALS AND PERCENTAGES) Objective 19: Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions Objective 21: Recall and use equivalences between simple fractions, decimals and percentages including in different contexts Revise addition and subtraction of fractions with the same denominator *1 Work out common denominator for a pair of fractions with different denominators, e.g. ⅔ and ⅗ Revise that ¼ can be represented as 0.25 and use this to solve problems Add 2 fractions with different denominators *2 Add 2 mixed numbers where the fractional values have different denominators *3 Subtract 2 fractions with different denominators Subtract 2 mixed numbers where the fractional values have different denominators Revise that 1/10 can be represented as 0.1 and use this to solve problems Revise that ¾ can be represented as 0.75 and use this to solve problems Revise all the decimal fraction equivalents for fractional values where the denominator is 3, 4, 5, 6, 8 or 10 and use this to solve problems *4 Objective 20: Multiply simple pairs of proper fractions, writing the answer in its simplest form, e.g. ¼ x ½ = 1/8 Multiply 2 simple fractions together and give the answer in its simplest form © Focus Education (UK) Ltd 2014 362 Year 6 Objectives : Number 7 DECIMALS DECIMALS Objective 22: Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places Objective 23: Multiply one-digit numbers with up to two decimal places by whole numbers *1 Know the value of each digit in a decimal fraction which has up to 3 decimal places *1 Multiply a decimal fraction with up to 2 decimal places by a single-digit number *2 Know that when multiplying a decimal fraction by 10 the decimal point moves one place to the right, e.g. 3.457 x 10 = 34.57 *2 Multiply a decimal fraction with up to 2 decimal places by a 2-digit number Divide a decimal fraction with up to 2 decimal places by a single-digit number *3 Divide a decimal fraction with up to 2 decimal places by a 2-digit number *4 Know that when multiplying a decimal fraction by 100 the decimal point moves two places to the right, e.g. 3.457 x 100 = 345.7 Objective 24: Use written division methods in cases where the answer has up to two decimal places Know that when multiplying a decimal fraction by 1000 the decimal point moves three places to the right, e.g. 3.457 x 100 = 3457 Know that when dividing a decimal fraction by 10 the decimal point moves one place to the left, e.g. 567.234 ÷ 10 = 56.7234 Know that when dividing a decimal fraction by 100 the decimal point moves two places to the left, e.g. 567.234 ÷ 100 = 5.67234 *3 Objective 25: Solve problems which require answers to be rounded to specified degrees of accuracy Know that when dividing a decimal fraction by 1000 the decimal point moves three places to the left, e.g. 567.234 ÷ 1000 = 0.567234 © Focus Education (UK) Ltd 2014 363 Year 6 Objectives : Number 8 RATIO and PROPORTION RATIO AND PROPORTION Objective 26: Use percentages for comparison and calculate percentages of whole numbers or measures, .g. 15% of 360 Objective 27: Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts *1 Recognise 50% as being a half of the original value Solve problems involving similar shapes where the scale factor is known or can be found Objective 28: Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples. Recognise 25% as being a quarter of the original value Recognise 75% as being three quarters of the original value Recognise 10% as being a tenth of the original value Know that to find 1% of a value you divide by 100 Find 25%, 50% and 75% of any given value Find 10%, 20%, 30%, etc. of a given value Find any percentage of a given value, eg, 18% of 360 *2 © Focus Education (UK) Ltd 2014 364 Year 6 Objectives : Number 9 ALGEBRA Objective 29: Use simple formulae Write rules algebraically for known relationships like p = 4s for finding out the perimeter of a square Objective 30: Generate and describe linear number sequences Continue a linear number sequence involving positive and negative numbers *1 Continue a linear number sequence involving fractions *2 Continue a linear number sequence involving decimal fractions *3 Objective 31: Express missing number problems algebraically Write known rules algebraically, e.g. a + b = b + a *1 Work out equations involving missing amount, e.g. If 2x -1 = 9, what is x? Work out calculations when given value of 2 letters, e.g. What is 2a + 3b if a =2 and b = 5? *2 Objective 32: Find pairs of numbers that satisfy an equation with two unknowns Objective 33: Enumerate possibilities of combinations of two variables © Focus Education (UK) Ltd 2014 365 Focus on Mathematics Year 6 Pre-Learning Tasks Number Focus on Mathematics: Year 6 Name Objective 1 Date Number Read, write, order and compare numbers to 10,000,000 and determine the value of each digit Can you write these numbers in numerals? Two hundred thousand, four hundred and fourteen *1 Can you write these numbers in words? 1,122,461 One million, thirteen thousand, three hundred and sixtyfour 5,123,879 Five million, two hundred and four thousand, one hundred and sixteen 2,015,247 Six million, four hundred thousand, three hundred and eighty- three 1,998,392 Five million, sixty thousand, four hundred and five 9,719,709 © Focus Education (UK) Ltd 2014 *2 367 Focus on Mathematics: Year 6 Name Objective 2 Date Number Round any whole number to a required degree of accuracy Can you round these numbers to the nearest 10, 100, 1000, 10,000 or 100,000? 2,391,385 to the nearest 1,000,000 *1 2,134 to the nearest 1,000 918,765 to the nearest 100,000 *2 5,607 to the nearest 100 357,385 to the nearest 100,000 1145 to the nearest 100 5607 to the nearest 100 272 to the nearest 10 159,887 to the nearest 100,000 1167 to the nearest 10 © Focus Education (UK) Ltd 2014 368 Focus on Mathematics: Year 6 Name Objective 3 Date Number Use negative numbers in context , and calculate intervals across zero Can you respond to these problems? If Room A is -2⁰C and Room B is -3⁰C, which is warmer? *1 What is the difference between -3 and +6 If Room A is -5⁰C and Room B is -7⁰C, which is warmer? What is the difference between -13 and +62 If Room A is -10⁰C and Room B is -7⁰C, which is colder? What is the difference between -24 and +73 If Room A is -6⁰C; Room B is -7⁰C and Room c is -3⁰C, which is warmer? What is the difference between +28 and -28 If Room A is -8⁰C; Room B is -9⁰C and Room c is -10⁰C, which is warmer? What is the difference between +19 and -6 © Focus Education (UK) Ltd 2014 *2 369 Focus on Mathematics: Year 6 Name Date Objective 6 Number Multiply multi-digit numbers up to 4-digits by a 2-digit whole number using the formal written method of long multiplication Can you multiply these accurately? *1 902 x12 506 x26 607 x24 809 x32 230 3x 405 5x 670 4x 302 8x 317 9x 448 5x 752 6x 785 8x 1326 x25 8673 x45 8471 x26 5686 x34 5231 9x 5645 7x 7223 6x 9541 5x 3244 x34 7209 x24 8655 x45 6587 x34 6723 6x 5662 7x 9413 8x 5532 9x © Focus Education (UK) Ltd 2014 *2 370 Focus on Mathematics: Year 6 Name Date Objective 7 Number Divide numbers up to 4-digits by a 2-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context Can you divide these accurately? 285 ÷ 5 378 ÷ 6 252 ÷ 4 282 ÷ 3 *1 9150 ÷ 19 5720 ÷ 17 6076 ÷ 13 3360÷ 16 2640÷15 176÷11 6160÷14 *2 1452 ÷ 27 8987 ÷ 36 8114 ÷ 57 5655÷15 3424÷16 270÷18 3451÷17 3247 ÷ 13 7209 ÷ 35 8656 ÷ 33 8753÷15 5267÷19 239÷17 1987÷14 *3 *4 For *4 express remainder as a fraction or round answer to nearest whole number. © Focus Education (UK) Ltd 2014 371 Focus on Mathematics: Year 6 Name Objective 13 Date Number Solve problems involving addition, subtraction, multiplication and division (using numbers up to 10,000,000) Can you respond to these problems? Country A has a population of 1,234, 897; Country B a population of 2,786,123 and Country C has a population of 345,897. How many people live in the 3 countries altogether? *1 Voyager spacecraft made three journeys into space. The first journey was 1,567,987Km; the second 3,456, 094Km and the third 3,675,912. How far did Voyager travel altogether? During a civil war in an unknown country 1,267,894 people left to seek asylum elsewhere. The country originally had a population of 4,783,976. How many people were left? The total attendance at City’s matches this season was 4,986,012 and the total attendance at Rovers’ matches was 3,872,123. How many more attended City’s matches? Can you respond to these problems? At a factory 2,987,123 mints are produced each week. How many will be produced after 3 weeks? *3 If 9,768,234 leaflets are produced over 5 days at a printers, how many are produced each day? *2 A new style vehicle can travel for 3,985,123Km but has to change its electrical system 5 times during the journey. How far does it travel with each electrical system? *4 2,300,876 attended theatre productions in London last year. 123,457 were male. How many females attended? If each ticket cost an average of £4, how much money was taken altogether? © Focus Education (UK) Ltd 2014 372 Focus on Mathematics: Year 6 Name Objective 16 Date Number Multiply simple unit fractions and pairs of proper fractions, writing the answer in its simplest form Can you work out these fractions? 1 4 x 5 5 6 x 6 5 7 3 4 x 5 Turn these mixed fractions into improper fractions: *1 2 x 5 3 6 *2 x 3 4 5 2 7 4 1 5 x 8 6 1 4 4 5 x 10 8 3 8 6 5 x4 3 8 x © Focus Education (UK) Ltd 2014 6 9 4 *3 *4 4 5 373 Focus on Mathematics: Year 6 Name Date Objective 18 Number Associate a fraction with division to calculate decimal fraction equivalents, e.g. 0.375 for a simple fraction ⅜ Can you write the following fractions as decimal fractions? 1/10 *1 5/6 3/10 1/6 1/4 5/8 3/4 7/10 3/5 9/10 1/5 2/5 1/8 3/8 7/8 1/2 © Focus Education (UK) Ltd 2014 374 Focus on Mathematics: Year 6 Name Date Objective 19 Number Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions Can you add these fractions? Can you reorganise these fractions so that they have the same denominator? 3 4 + 1 4 *1 8 5 6 + 9 5 6 + 4 5 *2 7 1 4 + 3 4 + 1 8 1 5 + 3 10 3 4 - 5 8 4 5 + 7 10 9 10 - 3 8 © Focus Education (UK) Ltd 2014 9 1 2 *3 7 8 *4 375 Focus on Mathematics: Year 6 Name Date Objective 22 Number Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places Can you show the decimal value of each number? U t h th *1 Can you divide these decimal fractions by 10, 100 and 1000? 234.13÷10 5.389 239.1÷10 6.257 123.95÷100 Can you multiply these decimal numbers by 10? 437.26÷100 23.85 x 10 1.457 x 10 *2 *3 2398.12÷1000 178.952÷1000 3.67 x 10 123.89 x 10 © Focus Education (UK) Ltd 2014 376 Focus on Mathematics: Year 6 Name Objective 23 Date Number Multiply one-digit numbers with up to two decimal places by whole numbers Can you multiply or divide these decimal fractions? 23.85x 6 *1 28.67÷5 83.41x 8 82.54÷7 32.73x 9 63.23÷6 15.83x 7 76.34÷8 34.98x 13 *2 23.87÷12 93.25x 26 65.82÷19 92.82x 25 79.56÷17 72.85x 32 92.76÷21 © Focus Education (UK) Ltd 2014 *3 *4 377 Focus on Mathematics: Year 6 Name Objective 26 Date Number Use percentages for comparison and calculate percentages of whole numbers or measures, e.g. 15% of 360 Can you multiply or divide these decimal fractions? 50% of 268 *1 1% of 500 25% of 844 17% of 500 75% of 1500 23% of 600 50% of 238 95% of 1000 25% of 260 65% of 250 75% of 2375 80% of 2000 10% of 2580 70% of 3500 20% of 5160 95% of 2500 © Focus Education (UK) Ltd 2014 *2 378 Focus on Mathematics: Year 6 Name Date Objective 30 Number Generate and describe linear number sequences Can you work out what comes next in these sequences? -4, -2, 0, +2, +4 … *1 1.5, 1.25, 1.00, 0.75… 9, 7, 5, 3, 1, …. 7.5, 7.0, 6.5, 6.0, 5.5…. -10, -7, -4, -1, …. 0.11, 0.13, 0.15, 0.17… 15, 10, 5, 0, -5… 6.3, 5.9, 5.5, 5.1….. 1/8, ¼, 3/8, ½, …. *2 -4, -10, -16, -22…… 9/10, 4/5, 7/10, 3/5…. *3 -55, -35, -15…… 0.2, 0.3, 0.4, 0.5…. 17, 11, 5, …… 0.25, 0.29, 0.33, 0.37…. 89, 64, 39, 14….. © Focus Education (UK) Ltd 2014 379 Focus on Mathematics: Year 6 Name Date Objective 31 Number Express missing number problems algebraically Can you work out the missing values? 2x – 4 = 8 *1 If a = 4 and b = 3 and c = 2 work out the following 5x + 4 = 24 2a + 3b = 6x – 6 = 18 7b – 4a = 7x + 3 = 24 2a + 5b + 6c 9x – 5 = 58 9c + 2b + 3a 10x – 6 = 54 2c x 2b 9x + 3 = 57 5c + 4b + 6a 8x + 7 = 39 10a + 10b + 10c © Focus Education (UK) Ltd 2014 *2 380 Focus on Mathematics Year 5 Group Objectives Measurement, Geometry and Statistics Year 6 Objectives : Measurement MEASUREMENT Objective 1m: Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate MEASUREMENT Objective 4m: Recognise that shapes with the same areas can have different perimeters and vice versa Use decimal notation to three decimal places to solve calculations with measures Draw a number of rectangles with the same perimeter Use other compound units for speed such as miles per hour and apply their knowledge in science as appropriate Objective 5m: Recognise when it is possible to use formulae for area and volume of shapes Objective 2m: Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places Use, add and subtract positive and negative integers for measures such as temperature and money Know when to apply a given formula to find out the area of a shape Know when to apply a given formula to find out the volume of a shape Objective 6m: Calculate the area of parallelograms and triangles Know the formula associated with finding the area of triangles Convert large numbers of cm into metres; ml into l; grams into Kg; and, minutes into hours Know the formula associated with finding the area of parallelograms Objective 3m: Convert between miles and kilometres © Focus Education (UK) Ltd 2014 382 Year 6 Objectives : Geometry PROPERTIES OF SHAPES Objective 3g: Compare and classify geometrical shapes based on properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons PROPERTIES OF SHAPES Objective 1g: Draw 2-D shapes using given dimensions and angles Objective 2g: Recognise, describe and build simple 3D shapes, including making nets Know what a net for a square looks like Create a cube using knowledge of what the net looks like Know what a net for an oblong looks like Classify triangles in terms of their properties Know that an equilateral triangle has three angles of 60˚ and three equal sides Know that an isosceles triangle has two sides which are equal and two angles which are equal Describe a right angled triangle according to properties Describe a square and oblong in terms of their properties Know the properties of rectangles such as parallelogram; trapezium; rhombus Know that the total of the three angles of any triangle adds up to 180˚ Use a protractor to measure individual angles of a triangle Draw a triangle given size of sides and angle sizes Know that the four angles of any quadrilateral adds up to 360˚ Work out the size of an angle in a quadrilateral by using a protractor to measure it © Focus Education (UK) Ltd 2014 383 Year 6 Objectives : Geometry 2 PROPERTIES OF SHAPES Objective 4g: Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius PROPERTIES OF SHAPES (Non Statutory) Objective 6g: Describe properties of common 3D shapes and identify parallel planes and symmetry Know that the line across the centre of a circle is known as the diameter Describe the properties of a cube, cuboid, sphere, prism and pyramid Know that the distance from the centre to the arc of a circle is the radius Point out the parallel planes associated with any 3d shape Know that the distance around the outside of a circle is the circumference Identify lines of symmetry in 3D shapes Know that the diameter of a circle is twice its radius Objective 5g: Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles Objective 7g: Estimate size of angles Recognise 90˚ as a corner angle and know that there are many of them in the built environment Recognise that 45˚ is half of a 90˚ and can estimate if an angle is greater or smaller than 45˚ Given 2 angles of a triangle know what the value of the third angle is Given 3 angles of a quadrilateral know what the value of the fourth angle is Know missing angles in parallelogram; rhombus and trapezium from working out diagonally opposite angles, etc. © Focus Education (UK) Ltd 2014 384 Year 6 Objectives : Geometry 3 POSITION AND DIRECTION Objective 8g: Describe positions on the full coordinate grid (all four quadrants) Identify each position on four quadrants of a grid using numbers on the axes Create shapes within a grid by following pairs of numbers on the grid Objective 9g: Draw and translate simple shapes on the coordinate plane and reflect them in the axes Use four quadrants of the grid to draw different shapes in different quadrants Reflect a given shape from one grid to another Translate a given shape across different grids © Focus Education (UK) Ltd 2014 385 Year 6 Objectives : Statistics STATISTICS Objective 1s: Interpret and construct pie charts and line graphs and use these to solve problems Know how to interpret information from a pie chart to solve a problem Know how to construct a pie chart from a set of given information Know how to interpret information from a line graph to solve a problem Know how to construct a line graph from a set of given information Know how to apply scales on the axes of a line graph Can read line graphs with scales Can construct own line graph and make decisions about the scales for the axes Objective 2s: Calculate and interpret the mean as average Know the term ‘mean’ is the average Find the average of a given set of numbers © Focus Education (UK) Ltd 2014 386 Focus on Mathematics Step up to the Challenge Year 6 Number Year 6: Can you challenge yourself to meet the Objective? Objective 1: Read, write, order and compare numbers to 10,000,000 and determine the value of each digit Me My Teacher Can you partition any number up to 10,000,000 showing the value of each digit? Do you know and use terms: units; tens, hundreds, thousands, ten thousands, hundred thousands, one million and ten million correctly? Can you recognise the value of each digit up to 10,000,000? Can you read and write numbers to 10,000,000? Can you read and write numbers to 1,000,000? Can you remember how to read and write numbers to: 1000 and then to 100,000? © Focus Education (UK) Ltd 2014 388 Year 6: Can you challenge yourself to meet the Objective? Objective 2: Round any whole number to a required degree of accuracy Me My Teacher Me My Teacher Can you round any 7-digit number to the nearest million? Can you round any 6-digit number to the nearest hundred thousand? Can you round any 5-digit number to the nearest ten thousand? Can you round any 4-digit number to the nearest thousand? Can you round any number to the nearest degree of accuracy? Objective 3: Use negative numbers in context , and calculate intervals across zero Can you calculate the interval from + 30 to -30? Can you calculate the interval from - 20 to + 100? Can you interpret temperatures at minus ⁰C on a thermometer? © Focus Education (UK) Ltd 2014 389 Year 6: Can you challenge yourself to meet the Objective? Objective 5: Add and subtract negative integers (non Statutory) Me My Teacher Me My Teacher Do you know what happens when subtracting a negative number form another negative number? Can you add any 2 negative numbers together? Objective 6: Multiply multi-digit numbers up to 4-digits by a 2-digit whole number using the formal written method of long multiplication Can you multiply 4-digit numbers by a 2-digit number using grid method or another conventional method? Can you remember how to multiply ThHTU x U? Can you remember how to multiply HTU x U? © Focus Education (UK) Ltd 2014 390 Year 6: Can you challenge yourself to meet the Objective? Objective 7: Divide numbers up to 4-digits by a 2-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context Me My Teacher Can you use rounding up to express answers as a whole number? Can you divide numbers with up to 4-digits by any 2-digit number with and without remainder? Can you express remainder as a fractional value of the number divided by? Can you divide numbers with up to 4-digits by a 2-digit number up to 20 with remainder? Can you divide numbers with up to 4-digits by a 2-digit number up to 20 without remainder? Can you remember how to divide numbers with up to 4-digits by a single-digit number with and without remainders? © Focus Education (UK) Ltd 2014 391 Year 6: Can you challenge yourself to meet the Objective? Objective 8: Divide numbers up to 4-digits by a 2-digit number using the formal written method of short division where appropriate , interpreting remainders according to the context Me My Teacher Me My Teacher Can you divide numbers with up to 4-digits by a 2-digit number with remainder? Can you divide numbers with up to 4-digits by a 2-digit number without remainder? Objective 10: Identify common factors, common multiples and prime numbers Do you know all the prime numbers? Do you know the common multiples of any 2 given numbers? Do you know the common factors of any 2 given numbers? © Focus Education (UK) Ltd 2014 392 Year 6: Can you challenge yourself to meet the Objective? Objective 13: Solve problems involving addition, subtraction, multiplication and division Me My Teacher Can you solve word problems with mixed operations with numbers up to 10,000,000? Can you solve word problems involving division with numbers up to 10,000,000? Can you solve word problems involving multiplication with numbers up to 10,000,000? Can you solve word problems involving subtraction with numbers up to 10,000,000? Can you solve word problems involving addition with numbers up to 10,000,000? © Focus Education (UK) Ltd 2014 393 Year 6: Can you challenge yourself to meet the Objective? Objective 16: Multiply simple unit fractions and pairs of proper fractions, writing the answer in its simplest form Me My Teacher Can you multiply 2 mixed fractions and write answer in its simplest form? Can you turn mixed fractions into an improper fraction? Can you multiply 2 simple fractions together and give answer in its simplest form? Can you multiply a whole number with a fraction and give answer in its simplest form? Can you multiply a whole number with a fraction? © Focus Education (UK) Ltd 2014 394 Year 6: Can you challenge yourself to meet the Objective? Objective 18: Associate a fraction with division to calculate decimal fraction equivalents, e.g. 0.375 for a simple fraction ⅜ Me My Teacher Do you know all the decimal fraction equivalents for fractional values where the denominator is 3, 4, 5, 6, 8 or 10? Do you know that ¾ can be represented as 0.75? Do you know that ¼ can be represented as 0.25? Do you know that 1/10 can be represented as 0.1? © Focus Education (UK) Ltd 2014 395 Year 6: Can you challenge yourself to meet the Objective? Objective 19: Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions Me My Teacher Can you subtract 2 mixed numbers where the fractional values have different denominators? Can you subtract 2 fractions with different denominators? Can you add 2 mixed numbers where the fractional values have different denominators? Can you add 2 fractions with different denominators? Can you work out the common denominator for a pair of fractions with different denominators, e.g. ⅔ and ⅗ ? Can you remember how to complete addition and subtraction of fractions with the same denominator? © Focus Education (UK) Ltd 2014 396 Year 6: Can you challenge yourself to meet the Objective? Objective 21: Recall and use equivalences between simple fractions, decimals and percentages including in different contexts Me My Teacher Do you remember all the decimal fraction equivalents for fractional values where the denominator is 3, 4, 5, 6, 8 or 10 and use this to solve problem? Do you remember that ¾ can be represented as 0.75 and use this to solve problems? Do you remember that ¼ can be represented as 0.25 and use this to solve problems? Do you remember that 1/10 can be represented as 0.1 and use this to solve problems? © Focus Education (UK) Ltd 2014 397 Year 6: Can you challenge yourself to meet the Objective? Objective 22: Identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places Me My Teacher Do you know that when dividing a decimal fraction by 1000 the decimal point moves three places to the left, e.g. 567.234 ÷ 1000 = 0.567234? Do you know that when dividing a decimal fraction by 100 the decimal point moves two places to the left, e.g. 567.234 ÷ 100 = 5.67234? Do you know that when dividing a decimal fraction by 10 the decimal point moves one place to the left, e.g. 567.234 ÷ 10 = 56.7234? Do you know that when multiplying a decimal fraction by 1000 the decimal point moves three places to the right, e.g. 3.457 x 100 = 3457? Do you know that when multiplying a decimal fraction by 100 the decimal point moves two places to the right, e.g. 3.457 x 100 = 345.7? Do you know that when multiplying a decimal fraction by 10 the decimal point moves one place to the right, e.g. 3.457 x 10 = 34.57? Do you know the value of each digit in a decimal fraction which has up to 3 decimal places? © Focus Education (UK) Ltd 2014 398 Year 6: Can you challenge yourself to meet the Objective? Objective 23: Multiply one-digit numbers with up to two decimal places by whole numbers Me My Teacher Can you divide a decimal fraction with up to 2 decimal places by a 2-digit number? Can you divide a decimal fraction with up to 2 decimal places by a single-digit number? Can you multiply a decimal fraction with up to 2 decimal places by a 2-digit number? Can you multiply a decimal fraction with up to 2 decimal places by a single-digit number? © Focus Education (UK) Ltd 2014 399 Year 6: Can you challenge yourself to meet the Objective? Objective 26: Use percentages for comparison and calculate percentages of whole numbers or measures, e.g. 15% of 360 Me My Teacher Can you find any percentage of a given value, e.g. 18% of 360 Can you find 10%, 20%, 30%, etc. of a given value? Can you find 25%, 50% and 75% of any given value? Do you know that to find 1% of a value you divide by 100? Do you recognise 10% as being a tenth of the original value? Do you recognise 75% as being three quarters of the original value? Do you recognise 25% as being a quarter of the original value? Do you recognise 50% as being a half of the original value? © Focus Education (UK) Ltd 2014 400 Year 6: Can you challenge yourself to meet the Objective? Objective 27: Use ratio to show the relative sizes of two quantities (non Statutory) Me My Teacher Me My Teacher Can you use ratio in defining the sizes of various shapes? Do you know what is meant by the term ‘ratio of 1:2’? Do you recognise that the symbol associated with ratio is ‘:’? Do you understand the term ratio? Objective 30: Generate and describe linear number sequences Can you continue a linear number sequence involving decimal fractions? Can you continue a linear number sequence involving fractions? Can you continue a linear number sequence involving positive and negative numbers? © Focus Education (UK) Ltd 2014 401 Year 6: Can you challenge yourself to meet the Objective? Objective 31: Express missing number problems algebraically Me My Teacher Can you work out calculations when given value of 2 letters, e.g. What is 2a + 3b if a =2 and b = 5? Can you work out equations involving missing amount, e.g. If 2x -1 = 9, what is x? Can you write known rules algebraically, e.g. a + b = b + a? © Focus Education (UK) Ltd 2014 402 Making Mathematics Work Step up to the Challenge Year 6 Measurement, Geometry and Statistics Year 6: Can you challenge yourself to meet the Objective? Objective 1m: Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate Me My Teacher Me My Teacher Can you use other compound units for speed such as miles per hour and apply your knowledge in science as appropriate? Can you use decimal notation to three decimal places to solve calculations with measures? Objective 2g: Recognise, describe and build simple 3D shapes, including making nets Do you know what a net for an oblong looks like? Can you create a cube using knowledge of what the net looks like? Do you know what a net for a square looks like? © Focus Education (UK) Ltd 2014 404 Year 6: Can you challenge yourself to meet the Objective? Objective 3g: Compare and classify geometrical shapes based on properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons Me My Teacher Can you work out the size of an angle in a quadrilateral by using a protractor to measure it? Do you know that the four angles of any quadrilateral adds up to 360˚? Can you draw a triangle given size of sides and angle sizes? Can you use a protractor to measure individual angles of a triangle? Do you know that the total of the three angles of any triangle adds up to 180˚? Do you know the properties of rectangles such as parallelogram; trapezium; rhombus? Can you describe a square and oblong in terms of their properties? Can you describe a right angled triangle according to properties? Do you know that an isosceles triangle has two sides which are equal and two angles which are equal? Do you know that an equilateral triangle has three angles of 60˚ and three equal sides? Can you classify triangles in terms of their properties? © Focus Education (UK) Ltd 2014 405 Year 6: Can you challenge yourself to meet the Objective? Objective 4g: Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius Me My Teacher Do you know that the diameter of a circle is twice its radius? Do you know that the distance around the outside of a circle is the circumference? Do you know that the distance from the centre to the arc of a circle is the radius? Do you know that the line across the centre of a circle is known as the diameter? © Focus Education (UK) Ltd 2014 406 Year 6: Can you challenge yourself to meet the Objective? Objective 5g: Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles Me My Teacher Me My Teacher Can you work out the missing angles in parallelogram; rhombus and trapezium from working out diagonally opposite angles, etc.? Given 3 angles of a quadrilateral can you work out what the value of the fourth angle is? Given 2 angles of a triangle can you work out what the value of the third angle is? Objective 6g: Describe properties of common 3D shapes and identify parallel planes and symmetry Can you identify lines of symmetry in 3D shapes? Can you point out the parallel planes associated with any 3d shape? Can you describe the properties of a cube, cuboid, sphere, prism and pyramid? © Focus Education (UK) Ltd 2014 407 Year 6: Can you challenge yourself to meet the Objective? Objective 8g: Describe positions on the full coordinate grid (all four quadrants) Me My Teacher Me My Teacher Can you create shapes within a grid by following pairs of numbers on the grid? Can you identify each position on four quadrants of a grid using numbers on the axes? Objective 9g: Draw and translate simple shapes on the coordinate plane and reflect them in the axes Can you use four quadrants of the grid to draw different shapes in different quadrants? Can you reflect a given shape from one grid to another? Can you use four quadrants of the grid to draw different shapes in different quadrants? © Focus Education (UK) Ltd 2014 408 Year 6: Can you challenge yourself to meet the Objective? Objective 1s: Interpret and construct pie charts and line graphs and use these to solve problems Me My Teacher Me My Teacher Can you construct own line graph and make decisions about the scales for the axes? Can you read line graphs with scales? Do you know how to apply scales on the axes of a line graph? Do you know how to construct a line graph from a set of given information? Do you know how to interpret information from a line graph? Do you know how to construct a pie chart from a set of given information? Do you know how to interpret information from a pie chart? Objective 2s: Calculate and interpret the mean as average Can you find the average of a given set of numbers? Do you know the term ‘mean’ is the average? © Focus Education (UK) Ltd 2014 409 Focus on Mathematics Non-Negotiables Year 6 Possible Planning Outline Year 6 Mathematics Non-Negotiables • The following areas of learning are known as the non-negotiables. They have a specific role in helping pupils meet the year group expectations. In a nutshell we are suggesting that if pupils are not confident in these areas then they will find the rest of the curriculum difficult to access. • The non-negotiables are designed to: 1. Identify the essential components that pupils need to become confident with, i.e. be able to demonstrate in independent tasks and be able to apply in other contexts. 2. Unblock learning, i.e. to keep teachers focused on the essential rather than coverage at the expense of progress. 3. Unlock learning and progress. • The non-negotiables are not designed to imply that the rest of the curriculum is an irrelevance – it clearly isn’t. But rather to give a structure for professionals to decide what the right curriculum is for their pupils. © Focus Education (UK) Ltd 2014 411 Year 6 Mathematics Non-Negotiables • Compare and order numbers up to 10,000,000. • Identify common factors, common multiples and prime numbers. • Round any whole number to a required degree of accuracy. • Multiply: o 4-digit by 2-digit • Divide: o 4-digit by 2-digit • • • • Add and subtract fractions with different denominators and mixed numbers. Multiply simple pairs of proper fractions, writing the answer in the simplest form. Divide proper fractions by whole numbers. Calculate percentage of a whole number. © Focus Education (UK) Ltd 2014 412 Planning to meet the requirement of the non-negotiables The following 3 pages suggest a planning outline for delivering the non-negotiables in classrooms. There should be some element of teaching of these each day. Autumn Term Ist Half Term • • • • • • • • • • • • • • • • 2nd Half Term Count on/back from a given number in steps of 10/100/1000/10000 up to at least 1,000,000 Count on/back in whole numbers, fraction and decimal sequences through zero to include negative numbers (e.g. 2.5 or 1 ¼) Find 0.01, 0.1, 1, 10 and powers of 10 more or less than a given number Read, write, partition, order and compare numbers to at least 1,000,000 Round any number to 1,000,000 to the nearest 10, 100, 1000, 10,000 and 100,000 (e.g. round 5 digit number to the nearest 10.000) Order and compare numbers including integers, decimals and negative numbers Read, write, order, partition and compare decimal numbers up to 3dp Round decimals with 1 and 2dp to the nearest whole number and to 1dp Multiply and divide mentally drawing upon known facts and/or using place value Multiply and divide any whole and decimal number by 10, 100 and 1000 giving answers up to 2dp Mentally add and subtract tenths and one-digit whole numbers and tenths Add/subtract mentally a 5-digit number and 4- digit numbers (e.g. 15,345 + 2300 and 12,462 – 2300 ) Count on/back with positive and negative numbers, including through zero Count on/back in fraction and decimal sequences Find factors and factor pairs of each number to 100 Find complements to 100. 1000 ,10,000 and to £1.00, £5.00 and £10.00 • • • • • • • • • • • • • • • • Count on/back from a given number in steps of 10/100/1000/10000 to 1,000,000 and beyond Count on/back in whole numbers, fraction and decimal sequences through zero to include negative numbers? (e.g. 2.5 or 1 ¼) Find 0.01, 0.1, 1, 10 and powers of 10 more or less than a given number Read, write, partition, order and compare numbers to 1,000,000 and beyond? Round any number to 1,000,000 to the nearest 10, 100, 1000, 10,000 and 100,000 (e.g. round 5 digit number to the nearest 10.000; 6 digit number to the nearest 100,000) Order and compare numbers including integers, decimals and negative numbers Read, write, order, partition and compare decimal numbers up to 3dp Round decimals with 3dp to the nearest whole number or to one or two decimal places Multiply and divide drawing upon known facts and/or using place value Multiply and divide any whole and decimal number by 10, 100 and 1000 giving answers up to 2dp Mentally add and subtract tenths and one-digit whole numbers and tenths Add/subtract mentally a 5-digit number and 4- digit numbers (e.g. 15,345 + 2300 and 12,462 – 2300 ) Continue a linear number sequence with positive and negative numbers, decimal and proper fractions including through zero Find factors and factor pairs of each number to 100 Convert units of measurement (km and m; cm and m; cm and mm; gram and km, ml and l and time) Find complements to 100, 1000 ,10,000 and to £5.00, £10.00 and £20.00 © Focus Education (UK) Ltd 2014 413 Planning to meet the requirement of the non-negotiables Spring Term Ist Half Term • • • • • • • • • • • • • • • • • 2nd Half Term Count on/back from a given number in steps of 10/100/1000/10000 to 1,000,000 and beyond Count on/back in whole numbers, fraction and decimal sequences through zero to include negative numbers (e.g. 2.5 or 1 ¼ Find 0.001, 0.01, 0.1, 1, 10 and powers of 10 more or less than a given number Read, write, partition, order and compare numbers to 5,000,000 Round any number to 5,000,000 and beyond to the nearest 10, 100, 1000, 10,000 and 100,000 (e.g. round any 6 digit number to the nearest hundred thousand and 7-digit number to the nearest million) Order and compare numbers including integers, decimals and negative numbers Read, write, order, partition and compare decimal numbers up to 3dp Round decimals with 3dp to the nearest whole number or to one or two decimal places Multiply and divide drawing upon known facts and/or using place value Multiply and divide any whole and decimal number by 10, 100 and 1000 giving answers up to 3dp Add/subtract mentally a 5-digit number and 4-digit numbers (e.g. 15,345 + 2300 and 12,462 – 2300 ) Mentally add and subtract tenths and 1-digit whole numbers and tenths Perform mental calculations with larger numbers and mental calculations which include at least 2 different operations (e.g. addition and multiplication) Continue a linear number sequence with positive and negative numbers, decimal and proper fractions including through zero Find factors and factor pairs of each number to 100 Convert units of measurement (km and m; cm and m; cm and mm; gram and km, ml and L and time) Find complements to 100. 1000 ,10,000 and to £5.00, £10.00 and £20.00 • • • • • • • • • • • • • • • Count on/back from a given number in steps of 10/100/1000/10000 to 1,000,000 and beyond Count on/back in whole numbers, fraction and decimal sequences through zero to include negative numbers (e.g. 2.5 or 1 ¼) Find 0.001, 0.01, 0.1, 1, 10 and powers of 10 more or less than a given number Read, write, partition, order and compare numbers to 5,000,000 and beyond Round any number to 5,000,000 and beyond to the nearest 10, 100, 1000, 10,000 and 100,000 (e.g. round any 6 digit number to the nearest hundred thousand and 7-digit number to the nearest million) Order and compare numbers including integers, decimals and negative numbers Read, write, order, partition and compare decimal numbers up to 3dp Round decimals with 3dp to the nearest whole number or to one or two decimal places Multiply and divide drawing upon known facts and/or using place value Multiply and divide any whole and decimal number by 10, 100 and 1000 giving answers up to 3dp Perform mental calculations with larger numbers and mental calculations which include at least 2 different operations (e.g. addition and multiplication) Continue a linear number sequence with positive and negative numbers, decimal and proper fractions including through zero Find factors and factor pairs of each number to 100 Convert units of measurement using decimal notation up to 3dp (km and m; cm and m; cm and mm; gram and km, ml and l and time) Find complements to 1000, 10,000 and to £10.00, £20.00 and £50 © Focus Education (UK) Ltd 2014 414 Planning to meet the requirement of the non-negotiables Summer Term Ist Half Term • • • • • • • • • • • • • • • • 2nd Half Term Count on/back from a given number in steps of 10/100/1000/10000 to 1,000,000 and beyond Count on/back in whole numbers, fraction and decimal sequences through zero to include negative numbers (e.g. 2.5 or 1¼ Find 0.001, 0.01, 0.1, 1, 10 and powers of 10 more or less than a given number Read, write, partition, order and compare numbers to 10,000,000 Round any 6 digit number to the nearest hundred thousand and 7digit number to the nearest million. Round any number to 10,000,000 to the nearest 10, 100, 1000, 10,000 and 100,000 (e.g. round any 6 digit number to the nearest hundred thousand and 7-digit number to the nearest million) Order and compare numbers including integers, decimals and negative numbers Read, write, order, partition and compare decimal numbers up to 3dp Round decimals with 3dp to the nearest whole number or to one or two decimal places Multiply and divide any whole and decimal number by 10, 100 and 1000 giving answers up to 3dp Perform mental calculations with larger numbers and mental calculations which include at least 2 different operations (e.g. addition and multiplication) Continue a linear number sequence with positive and negative numbers, decimal and proper fractions including through zero Find factors and factor pairs of each number to 100 Convert units of measurement using decimal notation up to 3dp (km and m; cm and m; cm and mm; gram and km, ml and L and time) Find complements to 1000, 10,000 and to £10.00, £20.00 £50 and £100 • • • • • • • • • • • • • • Count on/back from a given number in steps of 10/100/1000/10000 to 1,000,000 and beyond Count on/back in whole numbers, fraction and decimal sequences through zero to include negative numbers (e.g. 2.5 or 1 ¼) Find 0.001, 0.01, 0.1, 1, 10 and powers of 10 more or less than a given number Read, write, partition, order and compare numbers to 10,000,000 Round any number to 10,000,000 to the nearest 10, 100, 1000, 10,000 and 100,000 (e.g. round any 6 digit number to the nearest hundred thousand and 7-digit number to the nearest million) Order and compare numbers including integers, decimals and negative numbers Read, write, order, partition and compare decimal numbers up to 3dp Round decimals with 3dp to the nearest whole number or to one or two decimal places Multiply and divide any whole and decimal number by 10, 100 and 1000 giving answers up to 3dp Perform mental calculations with larger numbers and mental calculations which include at least 2 different operations (e.g. addition and multiplication) Continue a linear number sequence with positive and negative numbers, decimal and proper fractions including through zero Find factors and factor pairs of numbers to 100 Convert units of measurement using decimal notation up to 3dp (km and m; cm and m; cm and mm; gram and km, ml and l and time) Find complements to 1000, 10,000 and to £10.00, £20.00 £50 and £100 © Focus Education (UK) Ltd 2014 415 Focus on Mathematics Year 6 Assessment Assessment: Meeting Year 6 Expectations The main focus on assessment will be measuring a pupil’s journey towards and beyond the Year 6 expectations. The Year 6 expectations for number are set out below on this page. To meet the Year 6 expectations a pupil must be able to meet all of the statements outlined in the table, plus the ones for measurement and geometry, shown later. If they have not met all the statements then they will be deemed to be emerging. If a pupil is meeting the expectations then an assessment needs to made as to whether a pupil is exceeding the expectations. The next page sets out how to assess whether a pupil is exceeding this expectation or whether a pupil is at the emerging stage. The next page also provides you with a 9-point scale for deeper analysis, if required. Year 6 Expectations: Number • Use negative numbers in context, and calculate intervals across zero • Round any whole number to a required degree of accuracy and solve problems which require answers to be rounded to a specific degree of accuracy • Solve problems involving the relative sizes of two quantities where the missing values can be found by using integer multiplication and division facts • Use common factors to simplify fractions; use common multiples to express fractions in the same denomination • Solve problems involving the calculation of percentages, (e.g. of measures) such as 20% of 440 and the use of percentages for comparison • Multiply 1-digit numbers with up to two decimal places by whole numbers • Perform mental calculations, including with mixed operations with large numbers • Divide numbers up to 4-digits by a 2-digit whole number using formal written methods of long division and interpret remainder in various ways • Use knowledge of order of operations to carry out calculations involving all four operations • Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions • Multiply simple pairs of proper fractions, writing the answer in its simplest form • Divide proper fractions by whole numbers (⅛ ÷ 2 = 1/16) • Associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375 for ⅜) • Express missing number problems algebraically • Find pairs of numbers that satisfy an equation with two unknowns © Focus Education (UK) Ltd 2014 417 Assessment: Meeting Year 6 Expectations The main focus on assessment will be measuring a pupil’s journey towards and beyond the Year 5 expectations. The Year 5 expectations for number are set out below on this page. To meet the Year 5 expectations a pupil must be able to meet all of the statements outlined in the table, plus the ones for measurement and geometry, shown later. If they have not met all the statements then they will be deemed to be emerging. If a pupil is meeting the expectations then an assessment needs to made as to whether a pupil is exceeding the expectations. The next page sets out how to assess whether a pupil is exceeding the expectations or whether a pupil is at the emerging stage. The next page also provides you with a 9-point scale for deeper analysis, if required. Year 5 Expectations: Number • Count forwards and backwards in steps of power 10 for any given number up to 1,000,000 • Recognise and use thousandths and relate them to tenths, hundreds and decimal equivalents • Recognise mixed numbers and improper fractions and convert from one to the other • Read and write decimal numbers as fractions, e.g. 0.47 = 47/100 • Recognise the per cent symbol (%) and understand per cent relates to number of parts per hundred • Write percentages as a fraction with denominator hundred, and as a decimal number • Compare and add fractions whose denominators are all multiples of the same number • Multiply and divide numbers mentally drawing upon known facts up to 12 x 12 • Round any number to 1,000,000 to the nearest 10, 100, 1,000, 10,000 and 100,000 • Round decimals with 2dp to the nearest whole number and to 1decimal place • Recognise and use square numbers and cube numbers and the notation for squared (²) and cubed (³) • Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 • Multiply number up to 4-digit by a 1 or 2-digit number using formal written methods, including long multiplication for 2-digit numbers • Divide numbers up to 4-digits by 1-digit numbers • Solve problems involving multiplication and division where large numbers are used by decomposing them into factors • Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why; solve problems involving 3 decimal places and problems which require knowledge of percentages and decimal equivalents © Focus Education (UK) Ltd 2014 418 Assessment: Meeting Year 6 Expectations The 3 or 9-point scale Effectively, pupils will be assessed on a 3-point scale: that is, pupils will be judged as having met the expectations; emerging towards the expectations or exceeding the expectations. However, for many schools, this may not give them enough information when tracking pupils through the school. So, if schools desire, the following 9-point system is outlined for them to use. Assessed position Emerging Stage C Emerging Stage B Emerging Stage A Meeting Stage C Meeting Stage B Meeting Stage A Exceeding Stage C Exceeding Stage B Exceeding Stage A Points allocation 1 2 3 4 5 6 7 8 9 • • • • • As is illustrated, Point 4 is the point that indicates that a pupil has met the expectations. If we are to take account of the new Assessment arrangements then it is hoped that 85% of pupils will be at least at this stage by the end of the year. Points 1 to 3 are the ‘emerging’ stages; Points 4 to 6 are the ‘meeting’ expectations stages; and Points 7 to 9 are the ‘exceeding’ stages. The following page sets out what each point actually means and provides clarity about the allocation of the points. © Focus Education (UK) Ltd 2014 419 Assessment: Meeting Year 6 Expectations Year 6 Expectations: Number Year 6 Expectations: Measurement, Geometry and Statistics • Use negative numbers in context, and calculate intervals across zero • Round any whole number to a required degree of accuracy and solve problems which require answers to be rounded to a specific degree of accuracy • Recognise, describe and build simple 3D shapes, including making nets • Solve problems involving the relative sizes of two quantities where the missing values can be found by using integer multiplication and division facts • • Use common factors to simplify fractions; use common multiples to express fractions in the same denomination Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangle, quadrilateral and regular polygons • Solve problems involving the calculation of percentages, (e.g. of measures) such as 20% of 440 and the use of percentages for comparison • • Multiply 1-digit numbers with up to two decimal places by whole numbers Illustrate and name parts of circles, including radius, diameter and circumference and know that the radius is half the diameter • Perform mental calculations, including with mixed operations with large numbers • • Divide numbers up to 4-digits by a 2-digit whole number using formal written methods of long division and interpret remainder in various ways • Use knowledge of order of operations to carry out calculations involving all four operations Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and visa versa, using decimal notation to up to 3 decimal places Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions • • • Multiply simple pairs of proper fractions, writing the answer in its simplest form Calculate the area of a parallelogram and triangles and calculate, estimate and compare volume of cubes and cuboids using standard units • Divide proper fractions by whole numbers (⅛ ÷ 2 = 1/16 • Interpret and construct pie charts and line graphs and use these to solve problems • Associate a fraction with division and calculate decimal fraction equivalents (eg, 0.375 for ⅜) • Express missing number problems algebraically • Find pairs of numbers that satisfy an equation with two unknowns © Focus Education (UK) Ltd 2014 420 Assessment: Exceeding Year 6 Expectations Year 6 Exceeding Expectations: Number • Compare, order and convert between fractions, decimals and percentages in contexts related to science, history or geography learning • Move beyond squared and cubed numbers to calculate problems such as X x 10n where n is positive • Use =, ≠, <, >, ≤, ≥ correctly • Multiply all integers, (using efficient written methods) including mixed numbers and negative numbers • Recognise an arithmetic progression, and find the nth term • Use formula for measuring area of shape, such as cuboid and triangle to work out area of irregular shape in the school environment • Use four operations with mass, length, time, money and other measures, including with decimal quantities • Create a scaled model of a historical or geographical structure showing an acceptable degree of accuracy using known measurements • Calculate costs and time involved to visit a destination in another part of the world relating to on-going learning in history or geography • Collect own data on personal project and present information in formats of their choosing, charts, graphs and tables and answer specific questions related to their research © Focus Education (UK) Ltd 2014 421 Focus on Mathematics Year 6 Parents’ Guide Parents’ Guide ‘Must Dos’ by the end of Year 6 Number • • • • • • • • • • Number Read, write and order numbers to 10,000,000 Round any number to any degree of accuracy Add and subtract negative numbers Multiply a 4-digit number by a 2-digit number Divide a 4-digit number by a 2-digit number, expressing remainder as a fraction, decimal fraction or by rounding to whole numbers Mental Agility: Calculations involving large numbers Mental Agility: Calculations involving two operations Use estimation to check answers Carry out problem solving calculations involving all 4 operations Add and subtract mixed numbers with fractions of different denominations • • • • • • • • • • • Fractions: Multiply simple fractions, writing answers in their simplest forms Divide proper fractions by whole numbers Identify value of each digit in a 3 decimal place number Multiply decimal fraction with 3 decimal places by 10, 100 and 1000 Multiply and divide a number with 2 decimal places by 1-digit and 2-digit numbers Percentages: Use percentages for comparisons Calculate percentage of whole numbers Recall and use equivalences between fractions, decimal fractions and percentages Ratio: Use ratio to show relative sizes of 2 quantities Algebra: Solve linear missing numbers Continue a linear number sequence involving positive and negative numbers © Focus Education (UK) Ltd 2014 423 Parents’ Guide ‘Must Dos’ by the end of Year 6 Shape and Measures • • • • • • • • • • Shape and Measures Compare and classify geometrical shapes based on properties and size Find unknown angles in a triangle, quadrilateral and regular polygon Illustrate and name parts of a circle, including radius, diameter and circumference Recognise, describe and build 3D shapes Create a cuboid from a net Describe properties of 3D shapes and identify parallel planes and symmetry Estimate size of angles Describe position on the full coordinate grid Draw, translate and reflect shapes Read, write and convert between standard units • Calculate area of parallelograms and triangles • Data: Draw, read and interpret graphs • Use and interpret mean as an average © Focus Education (UK) Ltd 2014 424