1. Order fractions; fractions of amounts
Objectives
Day 1
Find equivalent fractions; simplify fractions using multiples and factors
Day 2
Compare fractions with related denominators
Compare and order fractions with unrelated denominators.
Day 3
Find unit and non-unit fractions of amounts.
Before teaching, be aware that:
On Day 1-3 children will need mini-whiteboards and pens.
Year 5/6

2. Order fractions; fractions of amounts
Short Mental Workouts
Day 1
Count in 1/4s and 1/8s along a number line
Day 2
Common multiples
Day 3
Mental division
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 5/6

3. Fractions Order fractions; fractions of amounts Short Mental Workout
Count in 1/4s and 1/8s along a number line
To use this activity, drag this and the following slide to the start of Day 1
Count in quarters and eighths along a number line
Children count in steps of quarters or eighths. Point to the relevant place on the line (see next slide) BUT they try to say the simplest fraction possible, e.g. 1/4, not 2/8.
Year 5/6

4. Year 5/6

5. Order fractions; fractions of amounts
Short Mental Workout
Common multiples
To use this activity, drag this and the following slide to the start of Day 2
Common multiples
Playing as a whole class, highlight a number on the 100-square (see next slide) e.g. 32. Children talk to a partner about what pair(s) of numbers the highlighted number could be a common multiple of, e.g. 32 is a common multiple of 1 and 32, 2 and 16, 4 and 8. Repeat, highlighting different numbers.
Year 5/6

6. Year 5/6

7. Order fractions; fractions of amounts
Short Mental Workout
Mental division
To use this activity, drag this slide to the start of Day 3
Mental division
Remind children that they can divide by 4 by halving twice. Your challenge is to divide as many numbers as you can - between 50 and by 4 before time is up! Allow 2 minutes, then discuss which numbers children found quick to divide by 4 in this way and which were not so straightforward.
Year 5/6

8. Order fractions; fractions of amounts
Objectives
Day 1
Find equivalent fractions; simplify fractions using multiples and factors
Year 5/6

9. What do you notice about your list of fractions?
Day 1: Find equivalent fractions; simplify fractions using multiples and factors; Find equivalent fractions; simplify fractions using multiples and factors
Work with a partner to find as many fractions equivalent to 1/4 as you can on this fraction wall.
Write them on a whiteboard.
What do you notice about your list of fractions?
CHALLENGE!
Work in pairs to write fractions equivalent to ¹/4 which are NOT on the fraction wall…
If we multiply both the numerator and denominator by the same number we’ll get an equivalent fraction!
Year 5/6

10. Day 1: Find equivalent fractions; simplify fractions using multiples and factors; Find equivalent fractions; simplify fractions using multiples and factors
3/12
We can write this more simply as ¹/4.
This is called writing the fraction in its simplest form.
3 is the highest common factor of 3 and 12 so we can divide both the numerator and denominator of 3/12 by 3 to give ¹/4.
Year 5/6

11. Day 1: Find equivalent fractions; simplify fractions using multiples and factors; Find equivalent fractions; simplify fractions using multiples and factors
9/₁₂
How can we simplify this fraction? Use the fraction wall to check.
Work with a partner to simplify these fractions: 6/8 4/6 4/10
Use the fraction wall to check.
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.
Y5/6 WT/ARE/GD: Use two cards (1-12) to make a fraction and simplify it, if possible.
Y5 WT use fraction wall to support.
Y5/6 GD Use extended set of cards (1-24).
Year 5/6

12. Challenge
The Practice Sheets on this and the next slide are suitable for most Y5 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Find equivalent fractions - Sheet 1 (2 pages)
Year 5/6

13. The Practice Sheets on this and the previous slide are suitable for most Y5 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Find equivalent fractions - Sheet 1 (2 pages)
Year 5/6

14. Challenge
The Practice Sheet on this slide is suitable for most Y6 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Find equivalent fractions - Sheet 2
Year 5/6

15. Order fractions; fractions of amounts
Objectives
Day 2
Compare fractions with related denominators
Compare and order fractions with unrelated denominators.
Year 5/6

16. Which do you think is greater? Explain to your partner how you know.
Day 2: Compare fractions with related denominators; Compare and order fractions with unrelated denominators.
Which do you think is greater? Explain to your partner how you know.
3/5 7/10
How many 1/10s are the same as 1/5? How many 1/10s are the same as 2/5? And 3/5? We can use equivalence between 1/5s and 1/10s to help us to compare them…
Year 5/6

17. Which do you think is greater? Explain to your partner how you know.
Day 2: Compare fractions with related denominators; Compare and order fractions with unrelated denominators.
Which do you think is greater? Explain to your partner how you know.
2/5 3/10
Year 5/6

18. See how 1/6 is half the size of 1/3.
Day 2: Compare fractions with related denominators; Compare and order fractions with unrelated denominators.
See how 1/6 is half the size of 1/3.
How many 1/6s are the same as 2/3?
Which is greater 5/6 or 2/3?
Year 5/6

19. See how 1/8 is half the size of 1/4.
Day 2: Compare fractions with related denominators; Compare and order fractions with unrelated denominators.
See how 1/8 is half the size of 1/4.
Which is greater, 7/8 or 3/4?
5/8 or 1/2? How can you be sure?
Today would be a great day to use a problem-solving investigation – Fraction Pictures – as the Y5 group activity, which you can find in this unit’s IN-DEPTH INVESTIGATION box on Hamilton’s website.
Alternatively, Y5 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.
Y5 WT/ARE/GD: Write lots of fractions equivalent to 1/2, then say whether fractions are < or > 1/2, then < or > 1/3.
Year 5/6

20. The Practice Sheet on this slide is suitable for most Y5 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Compare fractions - Sheet 1
Challenge
Year 5/6

21. Which fraction is bigger? Try to convince your partner.
Day 2: Compare and order fractions with unrelated denominators.
2/3 3/4
You could divide a strip into 1/3s and the same length strip into 1/4s and show 2/3 is less than 3/4.
Which fraction is bigger?
Try to convince your partner.
We can’t write 1/3s as 1/4s or vice versa BUT we can write both 2/3 and 3/4 as the same sort of fraction. What sort of fraction might that be?
HINT! 3 and 4 are both factors of…
Now we can write both
fractions as 1/12s.
12!
8/12 < 9/12
We proved it!
2/3 < 3/4.
Further teaching for Year 6
2 3
8 12
? 12
3 4
? 12
9 12 = =
Year 5/6

22. Day 2: Compare and order fractions with unrelated denominators.
What would be a good denominator to use for both the fractions?
HINT! 2 and 5 are both factors of…
1/2 3/5
Which fraction is bigger?
Write both fractions as tenths.
5/10 6/10
Which is bigger: 1/2 or 3/5? Can you explain why?
Year 5/6

23. Day 2: Compare and order fractions with unrelated denominators.
What would be a good denominator to use?
6 and 9 are both factors of…
1/6 2/9
Which fraction is bigger?
Write both fractions as eighteenths.
3/18 4/18
Which is bigger: 1/6 or 2/9? Can you explain why?
Today would be a great day to use a problem-solving investigation – Fraction Pictures – as the Y6 group activity, which you can find in this unit’s IN-DEPTH INVESTIGATION box on Hamilton’s website.
Alternatively, Y6 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.
Y6 WT: Look for pairs of fractions that can written with the same denominator; confirm with a fraction wall, then compare.
Y6 ARE/GD: Use equivalence to sort fractions into three groups: < 1/3, = 1/3, > 1/3.
Year 5/6

24. The Practice Sheet on this slide is suitable for most Y6 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Write and compare pairs and trios of fractions with unrelated denominators - Sheet 2
Year 5/6

25. Order fractions; fractions of amounts
Objectives
Day 3
Find unit and non-unit fractions of amounts.
Year 5/6

26. 28 children in Reception, can you see why?
Day 3: Find unit and non-unit fractions of amounts; Find unit and non-unit fractions of amounts.
In a school of 196 children, 1/7 are in reception. 2/7 are in KS1 and 4/7 are in KS2.
How can we find how many children are in reception?
196
We can use the vertical layout or ‘chunking! Who from Y6 can talk us through this?
× 7 = 196
20 × 7 = 140 56
8 × 7 = 56
28 children in Reception, can you see why?
Year 5/6

27. Work with a partner to find how many children are in KS2.
Day 3: Find unit and non-unit fractions of amounts; Find unit and non-unit fractions of amounts.
In a school of 196 children, 1/7 are in reception. 2/7 are in KS1 and 4/7 are in KS2.
How can we find how many children are in KS1?
196 28
Work with a partner to find how many children are in KS2.
Year 5/6

28. Day 3: Find unit and non-unit fractions of amounts; Find unit and non-unit fractions of amounts.
In a school of 182, the same fractions are in each key stage.
Work in threes:
one to find 1/7 of 182
the next finds 2/7
the third finds 4/7 of 182.
How could you check your answers?
182
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.
Y5 WT/ARE/GD: Draw bar models to find unit, then non-unit fractions of amounts.
Y6 WT: Play fractions of amounts bingo.
Y6 ARE/GD: Use the bar model to help solve word problems which involve finding non-unit fractions of amounts.
Year 5/6

29. The Practice Sheet on this slide is suitable for most Y5 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Find unit and non-unit fractions of amounts - Sheet 1
Year 5/6

30. The Practice Sheet on this slide is suitable for most Y6 children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Find non-unit fractions of amounts and calculate fractions of numbers, e.g. ☐/3 of 81 is 54 - Sheet 2
Challenge
Year 5/6

31. Order fractions; fractions of amounts
Well Done! You’ve completed this unit.
Objectives
Day 1
Find equivalent fractions; simplify fractions using multiples and factors
Day 2
Compare fractions with related denominators
Compare and order fractions with unrelated denominators.
Day 3
Find unit and non-unit fractions of amounts.
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 5/6

32. Problem solving and reasoning questions
Year 5
Write three fractions equivalent to 20/25.
Describe any pattern in the denominators.
Write the missing numbers to make each sentence true.
☐/6 = 5/☐
4/☐ < 5/☐
☐/6 > 7/10
Find 3/4 of 148:
Find 5/8 of 256:
148
256
Year 5/6

33. Problem solving and reasoning answers
Year 5
Write three fractions equivalent to 20/25. 40/ /5 8/ /15 etc.
Describe any pattern in the denominators. The denominators are all multiples of 5.
Write the missing numbers to make each sentence true.
2/6 = 8/24
4/☐ < 5/☐ Various answers possible, e.g. 4/9 < 5/6
5/6 > 7/10
Find 3/4 of 148: 1/4 of 148 = 37; 3/4 of 148 = 3 x 37 = 111
Find 5/8 of 256: 1/8 of 256 = 32; 5/8 of 256 = 5 x 32 = 160
148
 37 37
256
 32 32
Year 5/6

34. Problem solving and reasoning questions
Year 6
Ben simplified three fractions. They all came out at 3/4. Suggest what they could have been.
True or false?
- Any fraction which is simplified to give 1/3 has a numerator which is 3× the denominator.
- 36/64 cannot be simplified to 4/9.
Write the missing numbers:
☐/6 = 4/☐
6/☐ = ☐/20
☐/10 > 1/☐
☐/32 > ☐/8
Find 3/4 of 202:
3/8 of 344 biscuits are wafers, 5/8 are chocolate. How many of each?
202
Year 5/6

35. Problem solving and reasoning answers
Year 6
Ben simplified three fractions. They all came out at 3/4. Suggest what they could have been. Examples of fractions equivalent to 3/4 include: 6/8, 9/12, 12/16, 15/20.
Can children explain how they have found these? i.e. by multiplying the numerator and denominator by the same number.
True or false?
- Any fraction which is simplified to give 1/3 has a numerator which is 3× the denominator. False, the denominator would be 3 x the numerator, e.g. 2/6, 4/12
- 36/64 cannot be simplified to 4/9. True, it is equivalent to 9/16 in its simplest form
Write the missing numbers:
2/6 = 4/ /10 = 12/20
☐/10 > 1/☐ e.g. 6/10 > 1/2, 4/10 > 1/3 ☐/32 > ☐/ e.g. 20/32 > 1/8, 5/32 > 1/8
Find 3/4 of 202: 1/4 of 202 = 50.5 or 501/2 so 3/4 of 202 = or 1511/2
3/8 of 344 biscuits are wafers, 5/8 are chocolate. How many of each? 129 are wafers, 215 chocolate
202
 50.5
50.5
Year 5/6