1. Doubling and Halving and the concept of a half
Fractions
Doubling and Halving and the concept of a half
Objectives
Day 1
Double 2-digit numbers up to 50.
Double and halve 2-digit numbers, including odd numbers
Day 2
Halve even 2-digit numbers.
Double and halve 3-digit numbers.
Day 3
Halve odd numbers with even tens digits, e.g. 25 and 65.
Halve odd numbers with odd tens digits, e.g. 35 and 75.
Before teaching, be aware that:
On Day 1 children will need mini-whiteboards and pens, Y3 will need sets of Place Value cards (2 sets per pair).
On Day 2 & 3 children will need mini-whiteboards and pens.
Year 3/4

2. Doubling and Halving and the concept of a half
Fractions
Doubling and Halving and the concept of a half
Short Mental Workouts
Day 1
Doubles to 20
Day 2
Halve multiples of 10
Day 3
Count in 5s and 10s
The short activities suggested here do not have to be done at the beginning of your maths lesson - they are suitable for doing at any time of the day to provide ongoing revision of important mental and oral skills.
While there probably isn’t time during your maths lesson for these activities, it is crucial to regularly revisit the skills used. If you decide to use them – perhaps at the beginning of the day for ‘morning maths’, as you line up for lunch, or as a ‘brain-break’ during the afternoon - it might be useful to drag and drop the relevant slide or slides below to that day’s teaching.
Year 3/4

3. Doubling and Halving and the concept of a half
Fractions
Doubling and Halving and the concept of a half
Short Mental Workout
Doubles to 20
You can choose to drag this slide to the start of Day 1
Doubles to double 20
Play ‘Ping Pong’. Say a number from 1 to 20 (Y3s to 15) as you throw a bean bag to a child. Children respond with double that number as they throw back the bean bag. Occasionally say ‘ping’, to which everyone responds ‘pong’.
Year 3/4

4. Doubling and Halving and the concept of a half
Fractions
Doubling and Halving and the concept of a half
Short Mental Workout
Halve multiples of 10
You can choose to drag this slide to the start of Day 2
Halve multiples of 10
Call out doubles of multiples of 10 from 20 to 200. Children use a number fan to show you half those numbers. Give Y3s the option to work with a partner. Check that children are applying number facts (halves of numbers of 20) to support these calculations, e.g. half of 16 is 8, so half of 160 is 80….
Year 3/4

5. Doubling and Halving and the concept of a half
Fractions
Doubling and Halving and the concept of a half
Short Mental Workout
Count in 5s and 10s
You can choose to drag this slide to the start of Day 3
Count in 5s and 10s
Sit children in a circle. Play Mexican wave counting. Count in 10s from 0 to at least 200, beginning with Y3 children. Children raise their hands as they say their number. Start at a different place in the circle, this time counting in 5s to at least 130.
Year 3/4

6. Doubling and Halving and the concept of a half
Fractions
Doubling and Halving and the concept of a half
Objectives
Day 1
Double 2-digit numbers up to 50.
Double and halve 2-digit numbers, including odd numbers.
Year 3/4

7. Let’s revise some doubles...
Day 1: Double 2-digit numbers up to 50; Double and halve 2-digit numbers, including odd numbers. 7 14 6 12 3 6
Let’s revise some doubles... 8 16 4 8 9 18 20 40 50
100 30 60 80
160
Year 3/4

8. Let’s see how we can double 26.
Day 1: Double 2-digit numbers up to 50; Double and halve 2-digit numbers, including odd numbers.
Let’s see how we can double 26. 26
First partition 26… 20 40
= 52
Then recombine.
Double each number...
Double 26 is 52.
Year 3/4

9. Let’s try doubling 35 together…
Day 1: Double 2-digit numbers up to 50; Double and halve 2-digit numbers, including odd numbers.
Let’s try doubling 35 together… 35
First partition 35… 30 60
= 70
Then recombine.
Double each number...
Double 35 is 70.
Year 3/4

10. Day 1: Double 2-digit numbers up to 50; Double and halve 2-digit numbers, including odd numbers.
Now let’s try 47… 47
First partition 47… 40 80
= 94
Then recombine.
Double each number…
Double 47 is 94.
Today would be a great day to use a problem-solving investigation – Doubling Forever – as the Y4 group activity, which you can find in this unit’s IN-DEPTH INVESTIGATION box on Hamilton’s website.
Alternatively, Y4 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.
Y4 WT: Double 2-digit numbers (with support).
Y4 ARE/GD: Double 2-digit numbers (randomly generated).
Year 3/4

11. The Practice Sheet on this slide is suitable for most Y4 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT: Use bar models to support doubling and halving numbers to 99 - Sheet 2
ARE: Use bar models to support doubling and halving numbers to 99 - Sheet 3
GD: Use bar models to support doubling and halving numbers to 99 - Sheet 4
Challenge
Year 3/4

12. Day 1: Double 2-digit numbers up to 50.
3 0 4
3 0 4
Now let’s find double 34 using place value cards.
Work in pairs: each of you make 34 with your cards…
3 0 4
Partition the numbers.
Remember:
partition 
double 10s and 1s
recombine
3 0 + =
6 0
Double 10s and 1s. 4 + = 8
Further teaching for Year 3
Then recombine.
6 0 8 + =
6 0 8
Year 3/4

13. Now let’s find double 46 using place value cards.
Day 1: Double 2-digit numbers up to 50.
4 0 6
4 0 6
Now let’s find double 46 using place value cards.
4 0 6
Partition the numbers.
4 0 + =
8 0
Double the 10s and 1s. 6 + =
1 0 2
Further teaching for Year 3
Then recombine.
8 0 + =
1 0 2
9 0 2
Year 3/4

14. Let’s check that with a jotting...
Day 1: Double 2-digit numbers up to 50.
Let’s check that with a jotting... 46
First partition 46… 40 80
= 92
Then recombine.
Double each number...
Double 46 is 92.
Year 3/4

15. Day 1: Double 2-digit numbers up to 50.
Now try 57. 57
First partition 57… 50
100
= 114
Then recombine.
Double each number...
Double 57 is 114.
Today would be a great day to use a problem-solving investigation – Doubling Forever– as the Y3 group activity, which you can find in this unit’s IN-DEPTH INVESTIGATION box on Hamilton’s website.
Alternatively, Y3 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.
Y3 WT/ARE: Double 2-digit numbers to 50 activity sheet.
Y3GD: Double 2-digit numbers to 50./Begin to double 2-digit numbers greater than 50.
Year 3/4

16. The Practice Sheet on this slide is suitable for most Y3 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Double 2-digit numbers – Sheet 1
Challenge
Year 3/4

17. Doubling and Halving and the concept of a half
Fractions
Doubling and Halving and the concept of a half
Objectives
Day 2
Halve even 2-digit numbers.
Double and halve 3-digit numbers.
Year 3/4

18. Day 2: Halve even 2-digit numbers; Double and halve 3-digit numbers.
The shop has a half price sale on today, so we need to work out how much the chocolates will cost!
Year 3/4

19. Let’s see how to find half of 54p.
Day 2: Halve even 2-digit numbers; Double and halve 3-digit numbers.
Let’s see how to find half of 54p.
54p
First partition 54… 50 25
= 27p
Then recombine.
Halve each number...
27p in the half price sale!
Year 3/4

20. Let’s see how to find half of 38p.
Day 2: Halve even 2-digit numbers; Double and halve 3-digit numbers.
Let’s see how to find half of 38p.
38p
First partition 38… 30 15
= 19p
Then recombine.
Halve each number...
19p in the half price sale!
Y3 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.
Y3 WT: Halving even 2-digit numbers.
Y3 ARE/GD: Find chocolate bar costs that have been halved in price. Check answers to halving questions by doubling.
Year 3/4

21. The Practice Sheet on this slide is suitable for most Y3 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT: Halve even numbers to 30 - Sheet 1
ARE/GD: Halve even numbers to Sheet 2
Challenge
Year 3/4

22. Let’s check through halves of 100s.
Day 2: Double and halve 3-digit numbers.
100 50
Let’s check through halves of 100s.
200
100
300
150
400
200
500
250
We can use these number facts to help us double and halve 3-digit numbers!
600
300
700
350
Further teaching for Year 4
800
400
900
450
Year 3/4

23. Partition and double each part.
Day 2: Double and halve 3-digit numbers.
Let’s try double 226.
226
Partition and double each part.
400 40 12
= 452
Double 200 is ?
Double 20 is ?
Now on your whiteboards find double 471 and double 638.
Double 6 is ?
Three numbers to add this time!
Year 3/4

24. Who can talk us through this one? Careful with the addition!
Day 2: Double and halve 3-digit numbers.
471
Who can talk us through this one?
800
140 2
= 942
And this one?
638
Careful with the addition!
1200 60 16
= 1276
Year 3/4

25. We can halve 3-digit numbers in the same way.
Day 2: Double and halve 3-digit numbers.
We can halve 3-digit numbers in the same way.
226
100 10 3
Half of 200 is ?
= 113
Half of 20 is ?
Half of 6 is ?
Now on your whiteboards find half of 576 and 357.
Half of 226 is ?
Year 3/4

26. Who can talk through halving 576? Careful halving odd numbers!
Day 2: Double and halve 3-digit numbers.
576
Who can talk through halving 576?
250 35 3
= 288
And half of 357?
357
150 25
31/2
Y4 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.
Y4 WT: Doubling and halving 3-digit numbers.
Y4 ARE/GD: Doubling and halving 3-digit numbers; reasoning about strategies.
Careful halving odd numbers!
/2 = 1781/2
Year 3/4

27. The Practice Sheet on this slide is suitable for most Y4 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Double and halve 3-digit numbers - Sheet 3
Challenge
Year 3/4

28. Doubling and Halving and the concept of a half
Fractions
Doubling and Halving and the concept of a half
Objectives
Day 3
Halve odd numbers with even tens digits, e.g. 25 and 65.
Halve odd numbers with odd tens digits, e.g. 35 and 75.
Year 3/4

29. Let’s halve multiples of 10, write them on your whiteboards…
Day 3: Halve odd numbers with even tens digits, e.g. 25 and 65; Halve odd numbers with odd tens digits, e.g. 35 and 75. 20 10 60 30
Let’s halve multiples of 10, write them on your whiteboards… 30 15 80 40 90 45 40 20 70 35 50 25
Year 3/4

30. … we can partition and halve, then add.
Day 3: Halve odd numbers with even tens digits, e.g. 25 and 65; Halve odd numbers with odd tens digits, e.g. 35 and 75.
… we can partition and halve, then add.
Let’s check those...
Talk to your partner. How can we find half of 48, 32 and 56? 48 32 56 20 4 15 1 25 3
=24
= 16
= 28
Year 3/4

31. Now let’s see what happens when the 1s digit is odd.
Day 3: Halve odd numbers with even tens digits, e.g. 25 and 65; Halve odd numbers with odd tens digits, e.g. 35 and 75.
Now let’s see what happens when the 1s digit is odd. 45 20
21/2
How can you halve the odd 1s digit?
/2 = 221/2
Now on your whiteboards find half of 37.
Year 3/4

32. Let’s check half of 37… Who can talk it through?
Day 3: Halve odd numbers with even tens digits, e.g. 25 and 65; Halve odd numbers with odd tens digits, e.g. 35 and 75.
Let’s check half of 37… Who can talk it through? 37 15
31/2
/2 = 181/2
Y4 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.
Mixed attainment groups - Find halves, describing patterns of halves in different number sequences: 2- and 3-digit numbers.
Year 4

33. The Practice Sheet on this slide is suitable for most Y4 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Halve odd 2- then 3-digit digit numbers – Sheet 2
Challenge
Year 3/4

34. Half of an odd number always ends in 1/2
Day 3: Halve odd numbers with even tens digits, e.g. 25 and 65.
Work in pairs to halve each of the single-digit odd numbers 3, 5, 7 and 9. What do you notice about this sequence?
Let’s check…
11/2
21/2
31/2
41/2
Half of an odd number always ends in 1/2
Further teaching for Year 3
Year 3/4

35. Day 3: Halve odd numbers with even tens digits, e.g. 25 and 65.
Work in pairs to halve each of 5, 25, 45 and 65. Can you describe any patterns you notice?
Let’s check…
21/2
121/2
221/2
321/2
What did you notice?
Y3 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: Halve odd numbers with even tens digits, e.g. 5 and 25, describing patterns of halves in different number sequences: 2-digit numbers.
ARE/GD: Halve odd numbers with both even and odd tens digits, describing patterns of halves in different number sequences: 2-digit numbers.
Year 3/4

36. The Practice Sheet on this slide is suitable for most Y3 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Halve odd 2-digit numbers – Sheet 1
Challenge
Year 3/4

37. Doubling and Halving and the concept of a half
Fractions
Doubling and Halving and the concept of a half
Well Done! You’ve completed this unit.
Objectives
Day 1
Double 2-digit numbers up to 50.
Double and halve 2-digit numbers, including odd numbers
Day 2
Halve even 2-digit numbers.
Double and halve 3-digit numbers.
Day 3
Halve odd numbers with even tens digits, e.g. 25 and 65.
Halve odd numbers with odd tens digits, e.g. 35 and 75.
You can now use the Mastery: Reasoning and Problem-Solving questions to assess children’s success across this unit. Go to the next slides.
Year 3/4

38. Problem solving and reasoning questions
Year 3
Start at 3 and keep doubling until your answer is close to 100 but NOT over. How many doubles did you write? Repeat, starting at 4. How many this time?
Write the missing number(s) in these bar diagrams:
Starting with 72, keep halving until you reach a 1-digit number. What is half of that number?   ? 36 52
Year 3/4

39. Problem solving and reasoning answers
Year 3
Start at 3 and keep doubling until your answer is close to 100 but NOT over. How many doubles did you write? 5 – the sequence is 6, 12, 24, 48, 96
Repeat, starting at 4. How many this time? 8, 16, 32, 64.
Write the missing number(s) in these bar diagrams:
Mistakes may be due to not partitioning correctly to double and halve 2-digit numbers, for example giving an answer of 66 for the first of these or 21 for the second
Starting with 72, keep halving until you reach a 1-digit number. What is half of that number? 41/2
The sequence is 36, 18, 9 then 41/2. Not all children may be confident halving an odd number.   72 36 52 26
Year 3/4

40. Problem solving and reasoning questions
Year 4
Write two sentences to relate these three numbers: 37, 74 and 148.
Use a jotting to double these numbers:
i) ii) iii) 438
Describe any pattern in the answers
Starting with 576, keep halving until you reach a 1-digit number.
What is half of that number?
Year 3/4

41. Problem solving and reasoning answers
Year 4
Write two sentences to relate these three numbers: 37, 74 and 148.
2 x 37 = 74 and 2 x 74 = 148
Use a jotting to double these numbers:
i) ii) iii)
Describe any pattern in the answers. The differences between the initial numbers is 111, the answers have a difference of 222.
Where children have made errors with doubling 3-digit number it is often the result of treating digits of the number as a single digit, ignoring place value. This would produce an answer of 18 or 34 for (a). It is useful to get children to estimate first.
Starting with 576, keep halving until you reach a 1-digit number.
What is half of that number? 41/2 
The sequence is 288, 144, 72, 36, 18, 9 then 41/2.
Year 3/4