Fractions Concept of a fraction Halving Objectives Day 1 Understand the concept of 1/2, 1/3 and 1/4 of shapes and numbers. Day 2 Find 1/2 of quantities, including odd numbers. Day 3 Find halves of quantities less than 100. Before teaching, be aware that: On Day 1 children will need ‘Strips of 6’ sheet, ‘Strips of 8’ sheet and ‘Strips of 9’ sheet (see resources), mini-whiteboards and pens. You will need one large paper rectangle and circle to demonstrate folding. Notes for the essential practical activities are in the notes under the respective slides. On Day 2 children will need ‘Strips of 7’ sheet and ‘Strips of 15’ sheet (see resources), Cubes, mini-whiteboards and pens. Notes for the essential practical activities are in the notes under the respective slides. On Day 3 children will need tens and ones Place Value cards. Year 3

Fractions Concept of a fraction Halving Starters Day 1 Count in steps of 1/2 along a number line (pre-requisite skills) Day 2 Doubles to double 15 (pre-requisite skills) Day 3 Sort odd and even numbers (simmering 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

Count in steps of 1/2 along a number line Fractions Concept of a fraction Halving Starter Count in steps of 1/2 along a number line Pre-requisite skills – to use this starter, drag this slide to the start of Day 1 Display a 0–10 number line, with whole numbers labelled. Point to halfway between 3 and 4 and ask what number you are pointing to (31/2). Repeat with other halfway points and then, all together, count up from 0 in steps of 1/2. When you click your fingers children should pause then change direction and count backwards from the number they paused on. Year 3

Fractions Concept of a fraction Halving Starter Doubles to double 15 Pre-requisite skills – to use this starter, drag this slide to the start of Day 2 Sit children in a circle. Each child has a card 1–15 or double. Show your card if you have an ‘r’ in your name. Look for your double or half. Swap places! Repeat. Year 3

Sort odd and even numbers Fractions Concept of a fraction Halving Starter Sort odd and even numbers Simmering skills – to use this starter, drag this slide to the start of Day 3 Ask children to Think, Pair, Share what an odd number is, and how they can recognise one. They should tell you that it is a number that can’t be divided exactly into two identical whole numbers, and which ends in 1, 3, 5, 7 or 9. Repeat with even numbers. Children should tell you that an even number can be divided exactly into two identical whole numbers and ends in 2, 4, 6, 8 or 0. Stand a child at the front of the class, holding a whiteboard saying ‘odd’. At the back, stand a child with a whiteboard saying ‘even’. Say 79 and tell the children to stand up and face the correct whiteboard. Repeat with other 2-digit and 3-digit odd and even numbers. Year 3

Fractions Concept of a fraction Halving Objectives Day 1 Understand the concept of 1/2, 1/3 and 1/4 of shapes and numbers. Year 3

Day 1: Understand the concept of 1/2, 1/3 and 1/4 of shapes and numbers. Watch carefully whilst I fold and cut this piece of paper in half. 1/2 Remember how we write half… Show a large rectangle of paper and fold it in half, open it up then rip it into two along the fold. Hold one half up. This is 1 out of 2. Remind children how this is written as 1/2. Year 3

Day 1: Understand the concept of 1/2, 1/3 and 1/4 of shapes and numbers. Now let’s try with a circle. How much of the whole circle is this piece? 1/2 Show a large circle, fold it in half, then open it again and rip it into two along the fold. Hold up one half and ask children how much you are holding. Encourage them to write 1/2. Clarify that you are holding 1 out of 2 pieces, which form the whole circle. That’s 1 out of 2 pieces! Year 3

How many stars on your strip? How many stars in each half? Day 1: Understand the concept of 1/2, 1/3 and 1/4 of shapes and numbers. How many stars on your strip? Now fold it in half. How many stars in each half? So what is 1/2 of 6? Give each child a strip of 6 shapes (see resources) and ask them to fold it in half. How many are in each half? Show that the six objects have been split into two equal groups, each with three in, so half of 6 is 3. Year 3

Day 1: Understand the concept of 1/2, 1/3 and 1/4 of shapes and numbers. This time I’m going to fold the paper then fold it again… This is 1 of the 4 parts. 1/4 Show a large rectangle of paper and fold it in half and half again, then open it and rip it into four equal pieces along the folds. Hold up one part and say that it is 1 out of 4. Remind children how this can be recorded as 1/4. Remember how we write a quarter… Year 3

How many circles on your strip? Now fold it into quarters. Day 1: Understand the concept of 1/2, 1/3 and 1/4 of shapes and numbers. How many circles on your strip? Now fold it into quarters. How many circles in each quarter? So what is 1/4 of 8? Give each child a strip of 8 shapes (see resources) and ask them to fold it into quarters (half and half again). Then ask them to tell you what 1/4 of 8 is. Use your strip of 8 shapes to show that if 8 is split into 4, each quarter has 2 objects in it. Year 3

Day 1: Understand the concept of 1/2, 1/3 and 1/4 of shapes and numbers. This time I’m going to fold the paper into thirds. This is 1 of the 3 parts. 1/3 Show a large rectangle and fold it into thirds, then open it up and rip into three equal pieces along the folds. Hold up one part and say that it is 1 out of 3. Show that this can be recorded as 1/3. Remember how we write one third… Year 3

How many shapes on your strip? Day 1: Understand the concept of 1/2, 1/3 and 1/4 of shapes and numbers. How many shapes on your strip? Now fold it into thirds. How many shapes in each third? So what is 1/3 of 9? Give each child a strip of 9 shapes (see resources) and ask them to fold it into thirds. What is 1/3 of 9? Use your strip to show that when 9 is split into 3 equal groups, each group has 3 objects in it, so 1/3 of 9 is 3. 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: Place counters on each half/third/quarter of strips of paper to find fractions of amounts. ARE/GD: Fold strips of 12 and 24 objects to find 1/2, 1/3 and 1/4 of 12 and 24. 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: Find 1/2, 1/3 and 1/4 of numbers Sheet 1, enlarge the sheet to A3 so that children could use cubes to represent the apples. ARE: Find 1/2, 1/3 and 1/4 of numbers Sheet 1. GD: Find 1/2, 1/3 and 1/4 of numbers Sheet 1 – should try Challenge. Challenge Year 3

Fractions Concept of a fraction Halving Objectives Day 2 Find 1/2 of quantities, including odd numbers. Year 3

Day 2: Find 1/2 of quantities, including odd numbers. How many shapes on your strip? Now fold it into half. There are three objects in each half and one split down the middle. 1/2 of 7 = 31/2 Children fold a strip of 7 objects (see resources) in half. There are three objects in each half and one split down the middle. Year 3

Day 2: Find 1/2 of quantities, including odd numbers. In pairs, make a row of 26 cubes. Now break it in half to find half of 26… Half of 26 What is half of 26? We can record it like this… What happens at each step? 20 6 Make towers with cubes. 10 3 …and check by doubling 13. 10 + 3 = 13 Year 3

What do you think half of 27 might be? Talk to your partner. Day 2: Find 1/2 of quantities, including odd numbers. What do you think half of 27 might be? Talk to your partner. There would be one more cube to half…so it should be 131/2 Half of 27 20 7 We can record it in the same way as we did for 26… 10 31/2 10 + 31/2 = 131/2 Year 3

Check if the pair next to you agrees… Day 2: Find 1/2 of quantities, including odd numbers. What do you think half of 15 might be? Work together to use cubes to help. Check if the pair next to you agrees… Let’s see… If you were to cut this strip of objects in half, where would you cut it? Year 3

Day 2: Find 1/2 of quantities, including odd numbers. Whole class investigation Make a stick of 16 cubes. Break the stick in half. Record: 1/2 of 16 is 8. Make a stick of 17 cubes. Break it in half. Discuss how this is difficult, as we can’t cut one of the cubes in half! But half of 16 is 8, and half of the extra cube is 1/2, so half of 17 is 81/2. Work in pairs to use cubes to help find half of each number from 20 to 30. Which of these numbers are even? Which are odd? What do you notice about halving odd and even numbers? Test out your theories with some more numbers. Today’s GROUP ACTIVITY is a whole class investigation. You can find more details in the unit’s TEACHING AND GROUP ACTIVITIES download. WT: Halve numbers from 10 to 16. GD: Halve numbers from 20 to 40. Year 3

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 halves of odd and even numbers Sheet 1. ARE: Finding halves of odd and even numbers Sheet 2. GD: Finding halves of odd and even numbers Sheet 2. Year 3

Fractions Concept of a fraction Halving Objectives Day 3 Find halves of quantities less than 100. Year 3

We can use Place Value cards to help finding half. Day 3: Find halves of quantities less than 100. Let’s try with 46. We can use Place Value cards to help finding half. 4 0 6 4 0 6 Partition 46. 2 0 3 Halve each number. 2 0 3 + = 2 0 3 Then recombine. Year 3

Day 3: Find halves of quantities less than 100. 5 0 8 Let’s try with 58. 5 0 8 Partition 58. 2 0 5 4 Halve each number. 2 5 4 + = 2 0 9 Then recombine. Half of 58 We can record it like this, doing the partitioning step mentally… We can check by doubling 29. 25 4 25 + 4 = 29 Year 3

We can record it like this… We can check by doubling 37. Day 3: Find halves of quantities less than 100. 7 0 4 Let’s try with 74. 7 0 4 Partition 74. 3 0 5 2 Halve each number. 3 5 2 + = 3 0 7 Then recombine. Half of 74 We can record it like this… We can check by doubling 37. 35 2 35 + 2 = 37 Year 3

Day 3: Find halves of quantities less than 100. Whole class investigation We are going to try to make the longest and shortest ‘halving chains’ that we can. To do this pick any 2-digit number to start with. If the number is even, halve it. If the number is odd, add 1. Keep going until you get to 1, e.g. Starting with 28, half is 14. Half of 14 is 7 which is odd so add 1. Half of 8 is 4. Half of 4 is 2. Half of 2 is 1. The chain looks like this: 28 – 14 – 7 – 8 – 4 – 2 – 1 Try another example, this time starting with an odd number. Try several different 2-digit numbers. Do larger starting numbers produce longer chains? Today’s GROUP ACTIVITY is a whole class investigation. You can find more details in the unit’s TEACHING AND GROUP ACTIVITIES download. 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: Find half of 2-digit numbers Sheet 1. ARE: Find half of 2-digit numbers Sheet 1. GD: Find half of 2-digit numbers Sheet 2. Challenge Year 3

Well Done! You’ve completed this unit. Fractions Concept of a fraction Halving Well Done! You’ve completed this unit. Objectives Day 1 Understand the concept of 1/2, 1/3 and 1/4 of shapes and numbers. Day 2 Find 1/2 of quantities, including odd numbers. Day 3 Find halves of quantities less than 100. 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 Draw a symmetrical shape. Draw a line dividing it into half. Are your two halves exactly the same? Draw a shape that you can divide into quarters using two straight lines. Match each number to its half: 12 14 7 32 16 64 32 24 17 102 51 34 What is half of 13? Of 33? Of 53? Of 73? Of 93? Explain the pattern… Year 3