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Fractions Workshop How the teaching of fractions progresses throughout the school Children come from Year 2 being able to recognise simple fractions and find halves and quarters of sets of objects and small numbers. Fractions work in Year 2 is often very practical based. Teachers make use of lots of resources. Moving in to Years 3 and 4, the practical element is still very important. Teachers still make use of lots of resources. Fractions of shapes: Year 3 I can find 12 and 14 of different shapes: Complete the shading on this diagram so that one half of the shape is shaded. Is this shape divided into quarters? Explain how you know. I can say what fraction of a shape is shaded: What fraction of this shape is shaded? Can you say this fraction in another way? Roughly how much of this cake has been eaten? I can find a fraction of a shape drawn on squared paper Is there more than one way to shade 2/3 of a 2 by 6 grid? Why? Finding fractions of a number by using division: I can find fractions of numbers by using division: 50 ÷ 5 = 10. Now complete: 1 of 50 = 10 Would you rather have 1/3 of 30 sweets or 1/5 of 40 sweets? Year 3 Why? I can find a fraction of a number of cubes by sharing them in equal groups How can you find 1/3 of 27? Year 3 I can find one fifth of a number by dividing it by 5 Year 3/4 What numbers/shapes are easy to find one third, one quarter, one fifth, one tenth of? Why? Tell me how to find one sixth of 42. Would you rather have 1/5 of 30 sweets or 3/4 of 12 sweets? Why? I can find the fraction of an amount, such as 2/5 of £10 Which would you rather have: 1/3 of £30 or 1/5 of £60? Why? Which would you prefer to receive as pocket money: 5/6 of £24 or 3/7 of £49? Why? Fractions to describe part of a whole: I can use a fraction to describe a part of a whole: What fraction of these tiles is circled? The pizza was sliced into six equal slices. I ate two of the slices. What fraction of the pizza did I eat? Using diagrams, I can find pairs of fractions that make 1 whole Use this 3 by 4 rectangle to find two fractions that add up to 1. Can you find a pair of fractions that together make less than one whole? Year 3 Equivalent fractions: Year 3 I can show you on a diagram of a rectangle made from eight squares that one half is the same as two quarters or four eighths: What fraction of the square is shaded? Tell me some fractions that are equivalent to 1/2. How do you know? Are there any others? Year 3/4 I can find fractions that are equivalent to 1/4 What fraction of these rabbits is grey? How do you know when a fraction is equivalent to 1/2? Tell me some fractions that are equivalent to 1/4. How do you know? Are there any others? What about 3/4? I can use a 2 by 5 rectangle to show you that one fifth is the same as two tenths Tell me some fractions that are equivalent to 1/3. How do you know? Are there any others? What about 2/3? Two of these shapes have three quarters shaded. Point to them. Explain how you know. I can use diagrams to check that two fractions are equivalent Show me on the number line that four eighths are equivalent to one half. Year 3/4 Use this fraction wall to find a fraction equivalent to 3/4 . I can explain how I know that two fractions, such as 7/10 and 14/20 , are equivalent Tell me some fractions that are equivalent to one quarter. How do you know? Are there others? What about two thirds? What is the missing number? How do you know? Find the missing number Ordering fractions and mixed numbers on a number line: Year 4 I can order mixed numbers and put them on a number line Draw an arrow on the number line to show 1 3/4. Write the two missing numbers in this sequence. Tell me a fraction that is bigger than 3. I can place mixed numbers in the correct place on a number line I ate more than 1/2 a pizza but less than 3/4. What fraction could I have eaten? What would you prefer: 3 pizzas shared between 4 people or 6 pizzas shared between 10 people? Explain why. Decimal and fraction equivalents: Year 4 I can recognise decimals and fractions that are equivalent Tell me two fractions that are the same as 0.5. Are there any other possibilities? You have been using your calculator to find an answer. The answer on the display reads 8.5. What could this mean? Which of these is the same as 0.4? A four B four tenths C four hundredths D one fourth Write down a number lying between 7 and 8. Write it as a fraction and then as a decimal. I can give the decimal equivalent of a simple fraction such as 3/10 and explain how I know Tell me two fractions that are the same as 0.2. I know that 1/2 can also be written as 0.5, 1/4 as 0.25 and 3/4 as 0.75 Year 5/6 Knowing that ¼ is half of ½ and that by adding ¼ and ½ together they can find ¾ I know that one tenth can be written as 1/10 or as 0.1 and that one hundredth can be written as 1/100 or 0.01 Which of these decimals means 7/10? A 70 B 7 C 0.7 D 0.07 I know that 25/100 is the same as 0.25. It is also the same as 1/4 Which of these fractions is the same as nought point four (0.4)? 1/ , 1/ , 1/ 4 4 4 40 400, /10, /100 I can use a calculator to find the decimal equivalent of a fraction What calculation would you key into a calculator to find 3/20 as a decimal? Use a calculator to establish whether 27/40 is bigger or smaller than 0.75. Simplifying fractions or using the same common denominator: Year 5 I can write a large whole number as a fraction of a smaller one, simplify fractions and put them in order of size Karen makes a fraction using two number cards. She says, 'My fraction is equivalent to 1/2. One of the number cards is 6' What could Karen's fraction be? Give both possible answers. What fraction of 9 is 6? What fraction of 90 is 60? Which is larger: 1/3 or 2/5? Explain how you know. Arrange these numbers in order: 1 3/4, 15/8, 1.6 Changing mixed numbers to improper fractions (and vice verse): Year 5 I can explain how to turn a mixed number such as 23/4 into an improper fraction. What mixed number is equivalent to 13/4? How do you know? Find an improper fraction that lies between 3 and 4. Know what ‘per cent’ means and to know the percentage equivalents of fractions: Year 5 I know that 'per cent' means 'parts in every 100', so 1% = 1/100. I can give a simple fraction such as 1/10 as a percentage Shade 10% of this grid. What percentage is the same as 7/10? Explain how you know. Which is a better mark in a test: 61% , or 30 out of 50? How do you know? 40% of a class of children are boys. What percentage are girls? Find a fraction or a percentage of a quantity (including using a calculator): Year 6 I can tell you what calculations I will do to find a fraction of a quantity. What is one fifth of 20? What fraction of £1 is 30p? Explain how you know. One third of a number is 7. What is the number? Complete this statement in different ways: ☐ is 1/4 of ☐ I can tell you what calculations I will do to find a percentage of a quantity. Kate says: 'To find 10% of an amount, you divide it by 10. So to find 20% of an amount, you divide it by 20.' Is Kate correct? How do you know? What calculations would you do to find 15% of £150? I can find fractions and percentages of whole numbers Year 6 Harry said: 'To calculate 10% of a quantity you divide it by 10, so to find 20% of a quantity you must divide by 20.' What is wrong with Harry's statement? What is 1/3 of 9, 12, 15, …? How did you work it out? What is fifty per cent of £20? What is two thirds of 66? What is three quarters of 500? I know what to enter into a calculator to find a fraction of an amount, for example to find 3/4 of 150g What two steps are involved in finding 3/4 of a number? I divide a number by 5, then multiply the answer by 4. What fraction of the number have I found? Explain the steps you would take to find 35% of an amount without a calculator. How would you find 35% of an amount using a calculator? Fraction/decimal/percentage equivalents: Year 6 I can work out a quantity as a percentage of another and find equivalent percentages, decimals and fractions What is twenty out of forty as a percentage? Put a ring around the fraction which is equivalent to forty per cent. Write in the missing numbers. 30% of 60 is ☐. 30% of ☐ is 60. What percentage of £8 is £2? How you can help at home… • Help your child to learn their times tables and become confident with using them (to be able to say that a child knows their times tables, they must also be able to recall the division problem with speed and accuracy) • Help your child to learn the vocabulary; numerator and denominator. • Use fractions, decimals and percentages when out shopping (e.g.if there is a sale on, can they calculate the discount?) • Be practical - cut up fruit/pizza/cake in to different fractions; share ¼ of the toys etc - use egg cartons to demonstrate fractions How you can help at home… Websites such as: •http://www.mathszone.co.uk/ •http://www.coolmath4kids.com/ •http://www.gamequarium.com/fractions.html •http://www.bgfl.org/bgfl/custom/resources_ftp/client_ftp/ks2/maths/fr actions/index.htm •http://www.funbrain.com/fract/index.html •http://www.woodlands-junior.kent.sch.uk/maths/fractions/ •http://www.primarygames.com/fractions/start.htm