Use understanding of fractions to find fractions of amounts Objectives Day 1 Revise finding unit fractions of quantities using division facts. Day 2 Revise finding non-unit fractions of quantities using division and multiplication. Before teaching, be aware that: On Day 1 children will need cubes. On Day 2 children will need mini-whiteboards and pens. Year 3

Use understanding of fractions to find fractions of amounts Starters Day 1 Division facts for 5 times table (pre-requisite skills) Day 2 Division facts for 3 times table (pre-requisite skills) Choose starters that suit your class by dragging and dropping the relevant slide or slides below to the start of the teaching for each day. Year 3

Fractions Use understanding of fractions to find fractions of amounts Starter Division facts for 5 times table Pre-requisite skills – to use this starter, drag this slide to the start of Day 1 On a 3 by 3 grid, children write nine different numbers 1 to 12. Ask 5 times table division questions, e.g. what is 35 ÷ 5? If children have the answer on their grid, they tick it. Winner is first to tick all six of their answers. Year 3

Fractions Use understanding of fractions to find fractions of amounts Starter Division facts for 3 times table Pre-requisite skills – to use this starter, drag this slide to the start of Day 2 Ask children to write the sequence of number sentences for dividing by 3. Provide the following two facts to help them start: 3 ÷ 3 = 1 6 ÷ 3 = 2 … 36 ÷ 3 = 12 Call out division questions for the 3x table, e.g. How many 3s in 27? What is 21 divided by three? Children answer using number fans. Year 3

Use understanding of fractions to find fractions of amounts Objectives Day 1 Revise finding unit fractions of quantities using division facts. Year 3

Take 12 cubes with your partner and use them to find half of 12. Day 1: Revise finding unit fractions of quantities using division facts. Take 12 cubes with your partner and use them to find half of 12. What is 1/2 of 12? How do you know? 12 ÷ 2 = 6 Year 3

How could you find 1/3 of 12? Or 1/4 ? Day 1: Revise finding unit fractions of quantities using division facts. How could you find 1/3 of 12? Or 1/4 ? Or 1/6? Or 1/12? What division facts do they link to? Let’s check… 1/3 of 12 = 4; 12 ÷ 3 = 4 1/4 of 12 = 3; 12 ÷ 4 = 3 1/6 of 12 = 2; 12 ÷ 6 = 2 Now try to find 1/5 of 12? What happens? Check with the cubes. 1/12 of 12 = 1; 12 ÷ 12 = 1 Year 3

Day 1: Revise finding unit fractions of quantities using division facts. Now try with 16 cubes. What is 1/2 of 16? What other fractions of 16 can you find? Which divisions leave a remainder? Let’s check… 1/2 of 16 = 4; 16 ÷ 2 = 8 1/4 of 16 = 4; 16 ÷ 4 = 4 1/8 of 16 = 2; 16 ÷ 8 = 2 Who got all those? Dividing 16 by 3, 5, 6, 7, 9 or 10 all left a remainder! 1/16 of 16 = 1; 16 ÷ 16 = 1 Children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download. WT: Investigating fractions of 20 using cubes. ARE: Investigating fractions of 24 and then further numbers using cubes to check. GD: Investigating fractions of 24 and then further numbers using number facts. Year 3

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT: Finding unit fractions Sheet 1. ARE/GD: Finding unit fractions Sheet 2. Challenge Year 3

Use understanding of fractions to find fractions of amounts Objectives Day 2 Revise finding non-unit fractions of quantities using division and multiplication. Year 3

Day 2: Revise finding non-unit fractions of quantities using division and multiplication. 25 5 25 5 25 5 25 5 25 25 5 We can use a bar model to help us find fractional amounts. What is 1/5 of 25? There are 5 smaller boxes, how many should go in each? What is 25 ÷ 5? So what is 2/5 of 25? Once we know 1/5 we can use times tables facts to find the others! 3/5 of 25? 4/5 of 25? Year 3

On your whiteboards draw a bar model to represent 24 ÷ 6. Day 2: Revise finding non-unit fractions of quantities using division and multiplication. Let’s check… On your whiteboards draw a bar model to represent 24 ÷ 6. 24 4 24 4 24 4 24 4 24 4 24 4 24 6 sections. How many smaller sections? What number goes in each? 4 in each. What is 1/6 of 24? We could count on in 4s: 4, 8, 12… but it is quicker to multiply 4 by 5! So what is 5/6 of 24? Year 3

Now on your whiteboards draw a bar model to represent Day 2: Revise finding non-unit fractions of quantities using division and multiplication. Let’s check… 24 3 24 3 24 3 24 3 24 3 24 3 24 3 24 3 24 Now on your whiteboards draw a bar model to represent 24 ÷ 8. 8 sections. How many smaller sections? What number goes in each? 3 in each, since 24 ÷ 8 = 3 1/8 of 24 = 3 Use this to find 3/8 of 24, 5/8 of 24, 2/8 of 24 and 6/8 of 24, in each case by multiplying 3 by the numerator of the fraction. Year 3

Day 2: Revise finding non-unit fractions of quantities using division and multiplication. Now try 3/4 of 20 and 2/3 of 15. Can you find these without drawing the bar model? What calculations will you do? …then multiplying by the numerator (top number of the fraction). Try dividing the number by the denominator (bottom) of the fraction… Today would be a great day to use a problem-solving investigation – Does it or not? – as the group activity, which you can find in this unit’s IN-DEPTH INVESTIGATION box on Hamilton’s website. Alternatively, children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download. WT: Solve non-unit fraction questions by playing a card game, using bar models to solve. ARE/GD: Solve non-unit fraction questions by playing a card game OR Create and play non-unit fraction bingo. 1/3 of 15 = 5, so 2/3 = 10. Can you see why? 1/4 of 20 = 5, so 3/4 = 15. Can you see why? Year 3

The Practice Sheet on this slide is suitable for most children. Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box. WT: Finding non-unit fractions Sheet 1, use bar models to support. ARE: Finding non-unit fractions Sheet 1. GD: Finding non-unit fractions Sheet 2. Challenge Year 3

Use understanding of fractions to find fractions of amounts Well Done! You’ve completed this unit. Objectives Day 1 Revise finding unit fractions of quantities using division facts. Day 2 Revise finding non-unit fractions of quantities using division and multiplication. You can now use the Mastery: Reasoning and Problem-Solving questions to assess children’s success across this unit. Go to the next slide. Year 3

Problem solving and reasoning questions True or false? • A piece of paper folded equally in 3, then folded in half is divided into sixths when you open it out. • 1/3 of a piece of paper is larger than 2/6 of the same piece. • Two eighths make a quarter. • 2/5 of 5 is 2. • 3/8 of 16 is 5. Draw a bar model to represent each question: 3/8 of 32? 4/5 of 40? 5/6 of 42? Write the answers. Write < or > or = between these fractions of amounts: 3/5 of 40 2/3 of 30 Year 3

Problem solving and reasoning: Answers True or false? • A piece of paper folded equally in 3, then folded in half is divided into sixths when you open it out. True. • 1/3 of a piece of paper is larger than 2/6 of the same piece. False, they are the same since 1/3 and 2/6 are equivalent fractions. • Two eighths make a quarter. True. • 2/5 of 5 is 2. True. • 3/8 of 16 is 5. False it is 6. Draw a bar model to represent each question: 3/8 of 32? 12 4/5 of 40? 32 5/6 of 42? 35 Write the answers. Write < or > or = between these fractions of amounts: 3/5 of 40 > 2/3 of 30 3/5 of 40 = 24 and 2/3 of 30 = 20, so 3/5 of 40 is the greater. Year 3