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© Hamilton Trust
Year 5: Week 2, Day 3 Use equivalence to compare and order fractions
Each day covers one maths topic. It should take you about 1 hour or just a little more.
1. Start by reading through the Learning Reminders.
They come from our PowerPoint slides.
2. Tackle the questions on the Practice Sheet.
There might be a choice of either Mild (easier) or Hot (harder)! Check the answers.
3. Finding it tricky? That’s OK… have a go with a
grown-up at A Bit Stuck?
4. Have I mastered the topic? A few questions to Check your understanding. Fold the page to hide the answers!
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Learning Reminders
© Hamilton Trust
Learning Reminders
© Hamilton Trust
Learning Reminders
© Hamilton Trust
Learning Reminders
© Hamilton Trust
Challenge
Challenge copy here...
Working towards ARE© Hamilton Trust
Practice Sheet MildEquivalent fractions
Use the fraction wall to help you join each fraction on the left to the equivalent fraction in its simplest form.
Challenge
Write some fractions which are equivalent to 1/4 but not on the fraction wall.
2/8
3/6
3/9
3/12
4/12
5/10
4/8
6/8
2/6
4/6
8/12
9/12
1/2
1/3
2/3
1/4
3/4
© Hamilton Trust
© Hamilton Trust
Body copy here
Challenge
Working at ARE
Challenge copy here...
© Hamilton Trust
© Hamilton Trust
Practice Sheet MildOrdering fractions
Write these fractions as 1/6s. Then write them in order, starting with the smallest first.
2/3 1/2 1/3
Write these fractions as 1/10s. Then write them in order, starting with the smallest first.
1/2 2/5 3/5
Write these fractions as 1/12s. Then write them in order, starting with the smallest first.
2/3 3/4 1/4 1/3 1/6 5/6 1/2
© Hamilton Trust
Challenge
Challenge copy here...
Working towards ARE© Hamilton Trust
Practice Sheet HotEquivalent fractions
Ring all the fractions that are equivalent to 1/4
Challenge 2
Write at least 5 fractions which are equivalent to 2/5 .
2/8 2/7 3/12 4/20 5/20 1/ 0/30 1/ 0/40 4/16 4/100
Ring all the fractions that are equivalent to 1/3
3/12 3/6 2/6 4/12 4/9 1/ 0/30 3/9 5/15 6/15
Ring all the fractions that are equivalent to 1/5
5/15 2/10 3/15 4/20 5/20 5/100 2/ 0/100 1/ 0/50 4/25
Complete this list of fractions equivalent to 3/4
4 8 12 16 20
60 100
3 30 21
Challenge 1
Ava says that she can write 1/2, 3/4 , 2/5 and 2/3 as an equivalent number of fiftieths.Do you agree with her?
© Hamilton Trust
© Hamilton Trust
Practice Sheet HotComparing and ordering fractions
Compare these pairs of fractions. Write them as the same ‘sort’ of fractions (with the same denominator), then write > or < in between.
Challenge
Create a group of four fractions with different denominators that can be re-written as the same ‘sort’. Order them using > or < symbols.
1. 2/3 3/6 2. 2/3 2/9 3. 3/10 1/5 4. 3/4 7/8
5. 5/6 1/ 1/12 6. 7/10 3/5 7. 1/3 5/12 8. 2/5 7/15
9. 7/10 1/ 3/20 10. 1/3 4/15 11. 1/2 2/5 12. 2/3 4/5
Write these groups of fractions as the same ‘sort’ of fractions. Then write each group in order from least to greatest.
13. 1/2 3/4 5/8 14. 1/2 3/5 7/10
15. 1/3 4/15 2/5 16. 1/ 7/20 4/5 7/10
© Hamilton Trust
Challenge
Challenge copy here...
Working towards ARE© Hamilton Trust
Practice Sheets Answers
Equivalent fractions (mild)
2/8 3/6
3/9
3/12
4/12
5/10
4/8 6/8 2/6 4/6
8/12 9/12
1/2
1/3
2/3
1/4
3/4
Equivalent fractions (hot)The fractions equivalent to 1/4 are: 2/8 3/12 5/20 1/ 0/40 4/16
The fractions equivalent to 1/3 are: 2/6 4/12 1/ 0/30 3/9 5/15
The fractions equivalent to 1/5 are: 2/10 3/15 4/20 2/ 0/100 1/ 0/503/4 6/8 9/12 1/ 2/16 1/ 5/20 3/ 0/40 4/ 5/60 7/ 5/100 2/ 1/28 The final fraction in this list can be any that is equivalent to 3/4.
Fractions equivalent to 2/5 could include: 4/10 6/15 8/20 1/ 0/25 1/ 2/30 and so on
Challenge 2
Ava is partly correct: 1/2 = 2/ 5/50 and 2/5 = 2/ 0/50. but 2/3 and 3/4 cannot be writen as fiftieths, because thedenominators are not factors of 50.
Challenge 1
Ordering fractions (mild)
2/3 = 4/61/2 = 3/61/3 = 2/6
Order smallest first: 1/3 1/2 2/3
1/2 = 5/102/5 = 4/103/5 = 6/10
Order smallest first: 2/5 1/2 3/5
2/3 = 8/123/4 = 9/121/4 = 3/121/3 = 4/121/6 = 2/125/6 = 1/ 0/121/2 = 6/12
Order smallest first: 1/6 1/4 1/3 1/2 2/3 9/12
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Comparing and ordering fractions (hot)
1. 2/3 = 4/6, so 2/3 > 3/6 2. 2/3 = 6/9, so 2/3 > 2/9
3. 1/5 = 2/10, so 3/10 > 1/5 4. 3/4 = 6/8, so 3/4 < 7/8
5. 5/6 = 1/ 0/12, so 5/6 < 1/ 1/12 6. 3/5 = 6/10, so 7/10 > 3/5
7. 1/3 = 4/12, so 1/3 < 5/12 8. 2/5 = 6/15, so 2/5 < 7/15
9. 7/10 = 1/ 4/20, so 7/10 > 1/ 3/20 10. 1/3 = 3/15, so 1/3 > 4/15
11. 1/2 = 5/10 and 2/5 = 4/10, so 1/2 > 2/5 12. 2/3 = 1/ 0/15 and 4/5 = 1/ 2/15, so 2/3 < 4/5
13. 1/2 = 4/8 3/4 = 6/8, so 1/2 < 5/8 < 3/4 14. 1/2 = 5/10 3/5 = 6/10, so 1/2 < 3/5 < 7/10
15. 1/3 = 5/15 2/5 = 6/15, so 4/15 < 1/3 < 2/5 16. 7/10 = 1/ 4/20 4/5 = 1/ 6/20, so 7/10 < 4/5 < 1/ 7/20
¼ = 2⁄8¾ =
What to do:
1. Label the quarters above this line. Label the eighthsbelow it.
Now write as many pairs of equivalent fractions as you can.
2. Label the fifths above this line. Label the tenths below it.
Now write as many pairs of equivalent fractions as you can.
3. Label the sixths above this line. Label the twelfths below it.
Now write as many pairs of equivalent fractions as you can.
© Hamilton Trust
A Bit Stuck?Fraction families
Things you will need:• A pencil
0 1
0 1
0 1
Learning outcomes:• I can identify pairs of equivalent fractions on a fraction line.• I am beginning to identify fractions which are equivalent to ½, ¼ and ⅓, without thehelp of fraction line.
S-t-r-e-t-c-h:Write as many fractions as you can which are equivalent to ½, ¼ and ⅓.
© Hamilton Trust
© Hamilton Trust
Body copy here
Challenge
Working at ARE
Challenge copy here...
© Hamilton Trust
© Hamilton Trust
Resource Sheet Fraction Wall
1
1 _2
1 _2
1 _3
1 _3
1 _3
1 _4
1 _4
1 _4
1 _4
1 _5
1 _5
1 _5
1 _5
1 _5
1 _6
1 _6
1 _6
1 _6
1 _6
1 _6
1 _7
1 _7
1 _7
1 _7
1 _7
1 _7
1 _7
1 _8
1 _8
1 _8
1 _8
1 _8
1 _8
1 _8
1 _8
1 _9
1 _9
1 _9
1 _9
1 _9
1 _9
1 _9
1 _9
1 _9
1 _10
1 _10
1 _10
1 _10
1 _10
1 _10
1 _10
1 _10
1 _10
1 _10
1 _11
1 _11
1 _11
1 _11
1 _11
1 _11
1 _11
1 _11
1 _11
1 _11
1 _11
1 _12
1 _12
1 _12
1 _12
1 _12
1 _12
1 _12
1 _12
1 _12
1 _12
1 _12
1 _12
© Hamilton Trust
Check your understanding Questions
• Write three fractions equivalent to 3/5. • Make an observation about the pattern in the denominators. • Then write three fractions equivalent to 2/3 and do the same.
What can you predict about the pattern in the denominators of fractions equivalent to 5/6?
Write the missing numbers to make each number sentence true.
?/6 > 7/12 ?/6 = 5/? 4/? < 5/?
Fold here to hide answers:
Check your understanding Answers
• Write three fractions equivalent to 3/5. e.g. 6/10 9/15 12/20 • Make an observation about the pattern in the denominators. They are all multiples of 5. • Then write three fractions equivalent to 2/3 and do the same. E.g. 4/6 6/9 8/12 Denominators
are multiples of 3. • What can you predict about the pattern in the denominators of fractions equivalent to 5/6?
They will be multiples of 6, e.g. 10/12 15/18 20/24
Write the missing numbers to make each number sentence true.
?/6 > 7/12 1, 2 or 3 sixths ?/6 = 5/? 1/6 = 5/30 4/? < 5/? Many possibilities, some that can be checked on a fraction wall, e.g. 4/7 < 5/6
.