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Thursday 29th January, 2015 90 minutes Helen, Jenni, Jill, Charlotte, Sandra and Aimee Warm Up – Odd One Out 6, 12, 5 Work in pairs for 1 minute Work out the odd one out Feed back to whole group Session Schedule Warm up - Odd One Out – Helen / Jill - 5 mins ROPS Mathematics Curriculum Document – Jenni 10 mins Modelling Books / Learning Wall – Sandra 10 mins Utilising Materials – ‘Idealness’ of Tools (BES paper) – Helen / Jill 5 mins The Number Framework – Number Fans Aimee / Jill 15 mins Teacher Boxes (15 mins) Charlotte Group Boxes and Strand Maintenance – Charlotte – 10 mins Plenaries – Helen – 5 mins The Curriculum Document Curriculum statements are recorded under subheadings (as they are in each area) - 'an essence statement', planning expectations, implementation, differentiation, assessment, student voice and eLearning. Overviews – Circles show the percentage of expected coverage . The linear overview at each level - Levels 1 / 2, Levels 3 /4, Levels 5/6 shows what is to be covered in an ODD /EVEN year cycle. Teachers may select what order they cover the work particularly considering how topics related to the class inquiries. Web tool links -http://nzmaths.co.nz/ Assessment overview has school wide testing and data input requirements / OTJ’s in mathematics are made based on evidence arising from learning conversation, observations and formal assessments. Classroom Implementation Think/Pair/Share What is the purpose of a modelling book? Modelling Books …. Evidence of teaching and learning A record of progress and coverage A working document for teacher ‘noticing’ Helps capture and share students’ thinking A way to track formative assessment Evidence for OTJ’s Used for goal setting and next learning steps Supports group discussions / anchor / focusses discussion Record – teacher/students can refer to at a later time Scaffolds transition between materials, imaging and number properties Modelling Books – key elements: Used regularly Can be pre-prepared / added to later / recap previous lesson Readily available (rich learning resource) Hard copy or e-book version (e.g Educreations) Records: Date LI (good to co-construct at the end of a lesson) Group Name Pictures/diagrams, words and symbols Students’ thinking (referenced) Modelling books may also include: Key ideas or knowledge Links to numeracy stages Page reference to NDP ‘pink book’ Strands other than ‘Number and Algebra’ Notes about misconceptions Written recording from students Mike Askew, King's College, University of London According to Askew (2004), "While a hundred square board could be a material presence for a two-year old, it would not have the 'ideal' dimension that it might for a ten-year old. We are interested in how pupils come to 'read into' artefacts the 'ideality' inscribed in the material." In pairs, discuss why you think a hundreds square might be more ideal for a ten-year old, than a two-year old. A hundreds board ... is organised in rows and columns deepens understanding of the base ten number system/place value rows increase in ones columns increase in tens adding/subtracting ones = move left or right adding/subtracting tens = move up or down introduces patterning and part-whole concepts diagonals, verticals, skip counting predict next number in a pattern identify strategies to solve multiplication and division problems discussion around how numbers are organised can be used to develop number vocabulary odd/even/less than/greater than/prime numbers etc ideal tool to unpack students' misconceptions through discussion Idealness of Materials to make meaning (Researcher: Mike Askew, King’s College, University of London, 2004) Tasks/Activities: set up and initiated by the teacher (driven from NZC and the Numeracy Maths Project) Artefacts/Tools: materials that allow students to make mathematical meaning Actions: how the artefacts/tools are acted upon to promote talk to solve the task Talk: problems how meaning is co-constructed using artefacts to solve So What …? If the artefact chosen doesn't create the 'talk', then choose another artefact/s Use the most meaningful tools at the most IDEAL age and stage the child is at Pink Books - guide you. What artefacts could you use before these? Hundreds board (more abstract) Arrow Cards (more abstract) The Number Framework Pink Book Number ??? Discuss with your neighbour ... How many knowledge domains are there in the number framework? Do you know what they are? The Knowledge Domains are: Number ID Number Sequence and Order Grouping /Place Value Basic Facts Written Recording WALT: understand how number fans can be used across a variety of knowledge stages (as an exemplar piece of equipment) Number Fans Think/Pair/Share: Come up with 3 advantages of using number fans: Number Fans - Advantages Quick diagnostic test Full participation Easy to use with whole class Quick to see if students are having trouble (slower or look around) Low stakes Scaffolding / reminders about strategies while they think Students check their own answers e.g 81 instead of 18 Open up Pink Book One Knowledge section and SECRETLY choose a domain / stage and think of a question you can ask where the answer can be shown on a number fan. If you are a chosen goose, call your question out (scriber to write up) Everyone hold up your answer on your number fan. Now, find where the goose got the question from in the Pink Book , ie what stage is it and what knowledge domain is it? Goose: was the answer correct? E.g What is the remainder for the number of three’s in 17? Everyone holds up number fan 2 Stage = Stage 6 Knowledge Domain = Grouping/Place Value Gooses’ Questions: 1. 2. 3. Small Group Task – Number Fans Now, working in year groups of 3 people in each group Year 1 and 2 Year 3 and 4 Year 5 and 6 Use the template provided and the Number Framework (Book 1 pages 18-22) , make up at least five questions at one chosen stage that you can use with your class. Small Group Task Template Number ID Stage: Stage: (optional) Nbr Seq. and Order Grouping/ PV Basic Facts Written Recording Some number fan activities … STAGE: up to Stage 3 Show me 4 the number that comes after seven Just before 13 Between 7 and 9 A number that is less than five A number greater than 6 Show me 19 The number that comes before 17 The number that comes after 11 The number of people that live in your house The date of your birthday The number of your street STAGE: 4 Hold up double 4 (doubles to 10) Half of 12 (halves to 20) Hold up a 2 digit number, a 3 digit number 20 plus 35 100 minus 60 Hold up 87, 125, 490 … Hold up a number greater than 25, less than 8 Hold up an odd number, even number What number plus this number (hold up) make 20? Hold up a multiple of 2, 5, 10 What is 6 + 7, 16 + 7, 26 + 7 etc? STAGE: 5 All of the previous, plus Make a number with 3 digits. Show your partner and read it to them. Make a number between 200 and 250. What does two stand for? A number greater than 175 A number between 420 and 450 A 3 digit number with two even and one odd digit Hold up near doubles e.g double 9 + 2 Hold up a number 100 more than 2345, 200 more than 2345 Hold up a number greater than …, less than … Hold up a factor of six Hold up a prime number Hold up a multiple of 3, of 4, of 11, of 9 If 5 x 4 is 20, what is 6 x 4 or 4 x 4? I have 24 and half again. What number do I get? Hold up 3 numbers that add to … STAGE: 6 All of the previous, plus A 4 digit number with a 3 in the hundreds place. A number that is a multiple of 5. A multiple of 7 that is more than 30. Hold up a quarter of 36, a third of 36 I divided 25 by a number to get 5. What is it? I multiply 3 by a number to get 12. What is it? Show me a number that goes exactly into 42. Show me 7 x 9 Hold up 6 squared Hold up the square root of 36 3 out of 50 get excellence in a test. What % is this? Show me 2.3 12.94 3.06 0.7 Show me a decimal greater than 3.5, less than 0.6 greater than 2.78 but less than 3 Show me a decimal with a 3 in the tenths column Show me a decimal between 1 and 2, 1.1 and 1.2 Which is smaller? Hold up 0.69 or 0.7 Hold up the difference between 12 and 20 Stage 7 All of the previous, plus What is 1 more than 12.54? One tenth more than … Hold up 2 cubed What is the cubed root of 8 (small numbers only) Hold up a number less than -2, between -2 and 1 What is 0.75 as a percentage? What is 75% as a decimal? What is one eighth as a decimal? What is 25% of 60? Round 36.44 to one decimal place. Hold up 1.2 plus 1.2 Hold up 3.4 minus 0.2 Subtract 1.3 from 3.5 What is the difference between 1.7 and 3.4? Show me a number between 0.2 and 0.3 A car is travelling at a speed of 50kph for half an hour. How far does it travel? Hold up the quotient of 20 and 4? Hold up the product of 3 and 7 Hold up 3 numbers that multiply to make 30, 12, 60 … Stage 8 All of the previous, plus A shop has a coat marked at $65. It is in a 20% discount sale. How much will you pay? -3 x -5, Estimate the answer to 32.6 x 0.19 Estimate one third of 200 Pink paint is mixed in a ratio of 1 red to 3 white.. If Anne makes up a batch of 12 litres of pink paint, how many litres of white did she use? What is 20% of $250? What is 3! Increase 0.7 by 10%. OTHER IDEAS: How many: blind mice? Hours in a day? Sides on an octagon? Holes on a golf course? Give out 3 to 4 digit cards: What is the largest number you can make? What is the smallest number you can make? How many different numbers can you make? Put the numbers in order of size – smallest to largest, largest to smallest A number that is half the number I am holding up A number that is greater than the one I am holding up Number Knowledge Stages Stage Number Sequence Place Value Number Facts 0-3 Numbers to 20 Know add/sub groupings to 5 4 Numbers to 100 Numbers to 100 Know groupings to 10, and with 10 5 Numbers to 1000 Numbers to 1000 Know all addition facts to 20, and subtraction facts to 10 Know 2, 5, 10 x tables 6 Numbers to 1,000,000 All whole numbers and tenths Recall all add/sub facts to 20 and all mult facts up to 10 x 10 7-8 Fractions, percentages and negative numbers Decimals, percentages and powers of 10 Recall all mult / div facts to 10 x 10 Other materials Explore numeracy teacher boxes and discuss in small groups how different materials might be used to support place value understanding. Demonstrate how a combination of materials can be used together to show a concept. Feedback from groups. Numeracy Teacher Boxes Key Understandings Consider the different ways that materials can be used across a variety of concepts and stages (covered today with Number Fans). Materials can be used in isolation, or in different combinations to demonstrate a concept. It is powerful for children to have the opportunity to show their understanding of a concept using a variety of equipment. One piece of equipment to show a concept for one child may not be as meaningful as it is for another child. Meaningful and Engaging Group Boxes Relevant and meaningful activities – what does this look like? Use to consolidate, maintain and revise knowledge Introducing activities as part of your tumble Keep it simple and varied – drip feed and rotate activities Examples... Strand Maintenance Strand maintenance activities included once a week per group as part of maths tumble. Important that strands are not taught in an isolated unit and then not revisited until the next year. Strand maintenance activities enable students to apply, practise and consolidate their learning over time. Strand box – introduce different strand maintenance activities as they are taught through the year. (Share examples) Figure it out resources www.nzmaths.co.nz https://www.tes.co.uk/ www.primaryresources.co.uk Plenaries End of session – 5 minutes ‘Wrap up’ learning - student reflection Students volunteer to share/explain findings Derive the LI at the end of the lesson Formative Assessment - where to next? Teacher Reflection How could I improve this lesson next time? OVERALL, DID THE CHILDREN LEARN WHAT I EXPECTED THEM TO LEARN? Spot the error Show a deliberate mistake with a similar calculation. In pairs: Spot the mistake Give the correct answer Suggest why the mistake may have been made and what could be done about it e.g Mary says that 46 + 37 = 73. What did she do wrong? Peer / Self Evaluation (DICE) How did you ...? What did you use to ...? What other materials could you have used? Why? Could you have worked it out another way? Which way was the best way? Why? Block It! (TPS) In Pairs: Students tell each other: 1 thing I learnt 1 thing I already knew 1 question I want to ask (Post-it note to record) Then feedback to class Milk Bottle Tops Place red card inside. Turn over. Traffic Lights After a group session, use wooden pegs with names OR Colour in the traffic light in exercise books I don’t get it. I understand most of it. I understand this. In groups of three (who you have not already worked with today), you have 10 seconds each to tell your group something that you will take away with you today. Future PD What future PD would YOU like? e.g how to teach a particular concept e.g how to use a certain piece of equipment e.g anything else you would like help with to assist your teaching practice Please record on the sheet provided