Halves and quarters
By the end of this chapter you will be able to
- Say when parts are equal and when they are not
- Find and name one half as one of two equal parts of a shape
- Find one half of a group by sharing it into two equal groups
- Find and name one quarter as one of four equal parts of a shape
- Find one quarter of a group by sharing it into four equal groups
- Say which is bigger, one half or one quarter
You should already know
- Counting objects to 20 (Chapters 1 and 4)
- Making equal groups and sharing (Chapter 9)
- Naming 2-D shapes (Chapter 3)
Where this leads
- Money: halves and quarters of a pound (Chapter 12)
- Half past the hour on a clock (Chapter 13)
National Curriculum for England, Key Stage 1 mathematics, Year 1. Content: Recognise, find and name a half as one of two equal parts of an object, shape or quantity, Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity, Recognise equal and not equal parts.
- 10.1 Equal and not equal parts: Worksheet (PDF) · Answers (PDF) · lesson page
- 10.2 One half of a shape: Worksheet (PDF) · Answers (PDF) · lesson page
- 10.3 One half of a group: Worksheet (PDF) · Answers (PDF) · lesson page
- 10.4 One quarter of a shape: Worksheet (PDF) · Answers (PDF) · lesson page
- 10.5 One quarter of a group: Worksheet (PDF) · Answers (PDF) · lesson page
- 10.6 Halves and quarters together: Worksheet (PDF) · Answers (PDF) · lesson page
- Check-up and end-of-chapter quiz: Worksheet (PDF) · Answers (PDF) · lesson page
Exercise P Do you remember?
Non-calculatorMethod. Touch each one once and say one number each. The last number is how many there are.
- Count each one and say its number. Each one gets one number, in order.1, 2, 3, 4, 5, 6, 7, 8, 9
- Look at the last number. The last number tells us how many there are.The last number is 9.
- Write the answer. 9
Check. Count again from the other side. You get 9 again. ✓
Watch out. Move each one to one side as you count it, so you do not lose your place.
Method. Count on from the bigger number.
- Start at 5. Start with the bigger number.5
- Count on 3. Say the next three numbers: 6, 7, 8.6, 7, 8
- Write the answer. 8
Check. Count back from 8 to check: 8 − 3 = 5. ✓
Watch out. Do not count the 5 again. Start by saying the next number after 5.
Method. Go round the outside of the shape and count each side once.
- Look at a triangle. A triangle has straight sides and three corners.Three corners
- Count the sides. Touch each side once as you go round.1, 2, 3
- Write the answer. 3
Check. Count the corners as well: 3 corners and 3 sides. ✓
Watch out. The corners are not sides. Count only the straight edges.
Method. The bigger number is the one that comes later when we count.
- Find 14 and 11 on the number line. Look at where each number sits.11 comes before 14
- Say which is further along. The number further along is bigger.14 is further along
- Write the answer. 14
Check. Count on from 11 to 14: 12, 13, 14. ✓
Watch out. Look at the tens: 14 has one ten, 11 has one ten too, so count the ones.
Method. Double means two of the same number added together.
- Write the number twice. Double 4 means 4 and 4.4 + 4
- Add them together. Count on from 4 with 4 more.4 + 4 = 8
- Write the answer. 8
Check. Halve it to check: half of 8 is 4. ✓
Watch out. Double means add the same number to itself.
Equal and not equal parts
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
Some shapes are cut into parts. When all the parts are the same size, they are equal parts. When one part is bigger or smaller than another, the parts are not equal.
The left rectangle has equal parts. The right rectangle does not, because one part is bigger.
Key ideas
- Equal parts are the same size.
- Parts that are not equal are different sizes.
- Check by comparing the parts side by side.
Method. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.2 parts
- Compare the sizes. Equal parts are the same size.The parts are the same size.
- Decide. Yes. The parts are equal.
Check. Measure the parts with a ruler or a strip of paper. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.2 parts
- Compare the sizes. Equal parts are the same size.One or more parts is a different size.
- Decide. No. The parts are not equal.
Check. Measure the parts with a ruler or a strip of paper. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.4 parts
- Compare the sizes. Equal parts are the same size.The parts are the same size.
- Decide. Yes. The parts are equal.
Check. Measure the parts with a ruler or a strip of paper. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Watch out
Watch out: a line can look as if it is in the middle when it is not. Check the size of each part before you decide.
Exam tip
Grown-up tip. Fold a piece of paper, a sandwich or a strip of card in two. Ask: “Are both parts the same size?” Then fold it again to make four.
Exercise 10A Equal and not equal parts
Non-calculatorMethod. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.2 parts
- Compare the sizes. Equal parts are the same size.The parts are the same size.
- Decide. Yes. The parts are equal.
Check. Measure the parts with a ruler or a strip of paper. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.2 parts
- Compare the sizes. Equal parts are the same size.One or more parts is a different size.
- Decide. No. The parts are not equal.
Check. Measure the parts with a ruler or a strip of paper. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.2 parts
- Compare the sizes. Equal parts are the same size.One or more parts is a different size.
- Decide. No. The parts are not equal.
Check. Measure the parts with a ruler or a strip of paper. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.4 parts
- Compare the sizes. Equal parts are the same size.The parts are the same size.
- Decide. Yes. The parts are equal.
Check. Measure the parts with a ruler or a strip of paper. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.4 parts
- Compare the sizes. Equal parts are the same size.One or more parts is a different size.
- Decide. No. The parts are not equal.
Check. Measure the parts with a ruler or a strip of paper. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Look at each picture and find the one with equal parts.
- Look at A. Count the equal parts and the shaded parts.A: 2 parts, not equal, 0 shaded
- Look at B. Count the equal parts and the shaded parts.B: 4 parts, equal, 0 shaded
- Look at C. Count the equal parts and the shaded parts.C: 3 parts, not equal, 0 shaded
- Find the picture that matches. We want the picture with equal parts.Matches: B
- Write the answer. B
Check. A and C do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Method. Look at each picture and find the one with equal parts.
- Look at A. Count the equal parts and the shaded parts.A: 2 parts, equal, 0 shaded
- Look at B. Count the equal parts and the shaded parts.B: 2 parts, not equal, 0 shaded
- Find the picture that matches. We want the picture with equal parts.Matches: A
- Write the answer. A
Check. B do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Method. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.3 parts
- Compare the sizes. Equal parts are the same size.One or more parts is a different size.
- Decide. No. The parts are not equal.
Check. Measure the parts with a ruler or a strip of paper. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.2 parts
- Compare the sizes. Equal parts are the same size.One or more parts is a different size.
- Decide. No. The parts are not equal.
Check. Measure the parts with a ruler or a strip of paper. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Look at each picture and find the one with equal parts.
- Look at A. Count the equal parts and the shaded parts.A: 2 parts, equal, 0 shaded
- Look at B. Count the equal parts and the shaded parts.B: 2 parts, not equal, 0 shaded
- Look at C. Count the equal parts and the shaded parts.C: 4 parts, equal, 0 shaded
- Look at D. Count the equal parts and the shaded parts.D: 2 parts, not equal, 0 shaded
- Find the picture that matches. We want the picture with equal parts.Matches: A and C
- Write the answer. A and C
Check. B and D do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
One half of a shape
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A half is one of two equal parts. If you share a shape into two equal parts, each part is one half. We say “one half”.
Two halves make one whole. A shape can be cut across the top and bottom, or down the middle.
Key ideas
- A half is one of two equal parts.
- Two halves make one whole.
- The parts must be the same size to be halves.
Method. One half is one of 2 equal parts. Check the parts and the shading.
- Count the parts. One half needs 2 equal parts.2 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one half.1 shaded
- Decide. Yes. The shaded part is one half.
Check. Say it in words: the shaded part is one half. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. One half is one of 2 equal parts. Check the parts and the shading.
- Count the parts. One half needs 2 equal parts.2 parts
- Check the parts are the same size. Equal parts are the same size.The parts are not the same size.
- Count the shaded parts. We need exactly one shaded part for one half.1 shaded
- Decide. No. The parts are not the same size, so the shaded part is not one half.
Check. Say it in words: the shaded part is not one half. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. Look at each picture and find the one with one half shaded.
- Look at A. Count the equal parts and the shaded parts.A: 4 parts, equal, 1 shaded
- Look at B. Count the equal parts and the shaded parts.B: 2 parts, equal, 1 shaded
- Look at C. Count the equal parts and the shaded parts.C: 2 parts, not equal, 1 shaded
- Find the picture that matches. We want the picture with one half shaded.Matches: B
- Write the answer. B
Check. A and C do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Watch out
Watch out: if you shade both parts, you have shaded the whole shape, not one half.
Exam tip
Grown-up tip. Cut a square of paper or a biscuit into two halves. Ask: “Are they the same size?” Then ask your child to point to one half.
Exercise 10B One half of a shape
Non-calculatorMethod. One half is one of 2 equal parts. Check the parts and the shading.
- Count the parts. One half needs 2 equal parts.2 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one half.1 shaded
- Decide. Yes. The shaded part is one half.
Check. Say it in words: the shaded part is one half. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. One half is one of 2 equal parts. Check the parts and the shading.
- Count the parts. One half needs 2 equal parts.2 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one half.1 shaded
- Decide. Yes. The shaded part is one half.
Check. Say it in words: the shaded part is one half. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. One half is one of 2 equal parts. Check the parts and the shading.
- Count the parts. One half needs 2 equal parts.2 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one half.1 shaded
- Decide. Yes. The shaded part is one half.
Check. Say it in words: the shaded part is one half. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. One half is one of 2 equal parts. Check the parts and the shading.
- Count the parts. One half needs 2 equal parts.2 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one half.2 shaded
- Decide. No. All the parts are shaded, so this is the whole shape.
Check. Say it in words: the shaded part is not one half. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. One half is one of 2 equal parts. Check the parts and the shading.
- Count the parts. One half needs 2 equal parts.4 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one half.1 shaded
- Decide. No. The shape has 4 equal parts, not 2, so the shaded part is not one half.
Check. Say it in words: the shaded part is not one half. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. One half is one of 2 equal parts. Check the parts and the shading.
- Count the parts. One half needs 2 equal parts.2 parts
- Check the parts are the same size. Equal parts are the same size.The parts are not the same size.
- Count the shaded parts. We need exactly one shaded part for one half.1 shaded
- Decide. No. The parts are not the same size, so the shaded part is not one half.
Check. Say it in words: the shaded part is not one half. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. Look at each picture and find the one with one half shaded.
- Look at A. Count the equal parts and the shaded parts.A: 2 parts, equal, 2 shaded
- Look at B. Count the equal parts and the shaded parts.B: 2 parts, equal, 1 shaded
- Look at C. Count the equal parts and the shaded parts.C: 4 parts, equal, 1 shaded
- Find the picture that matches. We want the picture with one half shaded.Matches: B
- Write the answer. B
Check. A and C do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Method. Each half is one of two equal parts. Two halves make one whole.
- Count the equal parts in the whole circle. Each half is one of the two equal parts.2 halves
- Think about how many make a whole. Two halves put together make the whole circle.1 half + 1 half = 1 whole
- Write the answer. 2
Check. Put two halves together: they make one whole circle. ✓
Watch out. Two halves make one whole. Do not say three.
Method. One part of two equal parts is one half.
- Count the equal parts. The cake is cut into two equal parts.2 equal parts
- Look at the part Sam ate. It is one of the two equal parts.One of 2 equal parts
- Write the answer. one half
Check. Two halves make the whole cake: one half and one half. ✓
Watch out. Use the words “one half” when you name one of two equal parts.
Method. Halves must be equal parts.
- Look at the two parts. The two parts here are not the same size.One part is bigger.
- Think about halves. A half is one of two equal parts.The parts must be equal.
- Write the answer. No. The two parts must be equal to be halves.
Check. Cutting in two does not always give halves. ✓
Watch out. Check the sizes before you say halves.
Method. Both rectangles are the same size. Each shaded part is one half of its rectangle.
- Look at rectangle A. One of the two equal parts is shaded.A: one half shaded
- Look at rectangle B. One of the two equal parts is shaded too.B: one half shaded
- Compare the two shaded parts. Both rectangles are the same size, so the halves are the same size.Same size
- Write the answer. Yes. Both shaded parts are one half of the same size rectangle.
Check. The shapes look different, but each shaded part is one of two equal parts. ✓
Watch out. The way a shape is cut does not change the size of a half.
One half of a group
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
We can find a half of a group too. Share the group into two equal groups. The number in one group is the half.
Here are 6 apples. Share them into two equal groups. Each group has 3 apples, so half of 6 is 3.
Key ideas
- Half of a group means two equal groups.
- Count the number in one group.
- Check: the two groups put together make the whole.
Key words. A half is one of two equal parts.
Method. Share 6 apples into 2 equal groups, so every group has the same number.
- Share the apples into 2 equal groups. Every group must have the same number, so give out one at a time.6 apples into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.3 in each group
- Write the answer. 3
Check. Add the groups back together: 3 + 3 = 6. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A half is one of two equal parts.
Method. Share 10 stars into 2 equal groups, so every group has the same number.
- Share the stars into 2 equal groups. Every group must have the same number, so give out one at a time.10 stars into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.5 in each group
- Write the answer. 5
Check. Add the groups back together: 5 + 5 = 10. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A half is one of two equal parts.
Method. Share 14 counters into 2 equal groups, so every group has the same number.
- Share the counters into 2 equal groups. Every group must have the same number, so give out one at a time.14 counters into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.7 in each group
- Write the answer. 7
Check. Add the groups back together: 7 + 7 = 14. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Watch out
Watch out: count the things in one group, not the number of groups. Half of 6 is 3, not 2.
Exam tip
Grown-up tip. Use two bowls and some buttons or pasta shapes. Share them out one at a time, into each bowl in turn. Ask: “How many are in one bowl?”
Exercise 10C One half of a group
Non-calculatorKey words. A half is one of two equal parts.
Method. Share 8 cubes into 2 equal groups, so every group has the same number.
- Share the cubes into 2 equal groups. Every group must have the same number, so give out one at a time.8 cubes into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.4 in each group
- Write the answer. 4
Check. Add the groups back together: 4 + 4 = 8. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A half is one of two equal parts.
Method. Share 4 balls into 2 equal groups, so every group has the same number.
- Share the balls into 2 equal groups. Every group must have the same number, so give out one at a time.4 balls into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.2 in each group
- Write the answer. 2
Check. Add the groups back together: 2 + 2 = 4. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A half is one of two equal parts.
Method. Share 12 things into 2 equal groups, so every group has the same number.
- Share the things into 2 equal groups. Every group must have the same number, so give out one at a time.12 things into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.6 in each group
- Write the answer. 6
Check. Add the groups back together: 6 + 6 = 12. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A half is one of two equal parts.
Method. Share 14 things into 2 equal groups, so every group has the same number.
- Share the things into 2 equal groups. Every group must have the same number, so give out one at a time.14 things into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.7 in each group
- Write the answer. 7
Check. Add the groups back together: 7 + 7 = 14. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A half is one of two equal parts.
Method. Share 16 things into 2 equal groups, so every group has the same number.
- Share the things into 2 equal groups. Every group must have the same number, so give out one at a time.16 things into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.8 in each group
- Write the answer. 8
Check. Add the groups back together: 8 + 8 = 16. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A half is one of two equal parts.
Method. Share 18 things into 2 equal groups, so every group has the same number.
- Share the things into 2 equal groups. Every group must have the same number, so give out one at a time.18 things into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.9 in each group
- Write the answer. 9
Check. Add the groups back together: 9 + 9 = 18. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A half is one of two equal parts.
Method. Share 20 stars into 2 equal groups, so every group has the same number.
- Share the stars into 2 equal groups. Every group must have the same number, so give out one at a time.20 stars into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.10 in each group
- Write the answer. 10
Check. Add the groups back together: 10 + 10 = 20. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A half is one of two equal parts.
Method. Share 16 stickers into 2 equal groups, so every group has the same number.
- Share the stickers into 2 equal groups. Every group must have the same number, so give out one at a time.16 stickers into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.8 in each group
- Write the answer. 8
Check. Add the groups back together: 8 + 8 = 16. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Method. Share the 12 counters first. Then find half of one pot.
- Share 12 counters into 2 pots. Each pot must have the same number.6 in each pot
- Find half of the 6 in one pot. Share the 6 counters into 2 equal groups.3 + 3 = 6
- Write the answer. 3
Check. Two pots of 3 make 6, and 6 + 6 = 12. ✓
Watch out. Read the question carefully. Share first, then find half of one pot.
Method. Equal shares have the same number of things on every plate.
- Count the things on each plate. We need to know how many are on each plate.6, 4
- Compare the numbers. Equal shares have the same number on every plate.The numbers are not the same.
- Decide. No. Each plate should have 5, but the plates have 6, 4.
Check. Add the plates together: 6 + 4 = 10. ✓
Watch out. Equal shares must have the same number on every plate.
Method. Share 6 into two equal groups to find half of 6.
- Share the 6 apples into 2 equal groups. Every group must have the same number.3 + 3 = 6
- Count how many are in one group. One group is one half of the apples.3 in one group
- Compare with what Mei said. Mei said 2, but each group has 3.Mei said 2, but half is 3
- Write the answer. No. Half of 6 is 3.
Check. Put the two groups back together: 3 + 3 = 6. ✓
Watch out. Count the apples in one group. Do not count the number of groups.
Method. If one half is 7, then the whole is two of those.
- Think of the two halves. Two equal halves make the whole.7 + 7
- Add the two halves together. The whole is the two halves put together.7 + 7 = 14
- Write the answer. 14
Check. Check: half of 14 is 7, because 7 + 7 = 14. ✓
Watch out. Do not just write 7. The whole is bigger than one half.
One quarter of a shape
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A quarter is one of four equal parts. If you share a shape into four equal parts, each part is one quarter.
Four quarters make one whole. Two quarters make one half.
Key ideas
- A quarter is one of four equal parts.
- Four quarters make one whole.
- Two quarters make one half.
Method. One quarter is one of 4 equal parts. Check the parts and the shading.
- Count the parts. One quarter needs 4 equal parts.4 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one quarter.1 shaded
- Decide. Yes. The shaded part is one quarter.
Check. Say it in words: the shaded part is one quarter. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. One quarter is one of 4 equal parts. Check the parts and the shading.
- Count the parts. One quarter needs 4 equal parts.4 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one quarter.2 shaded
- Decide. No. 2 parts are shaded, not one, so it is not one quarter.
Check. Say it in words: the shaded part is not one quarter. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. Look at each picture and find the one with 4 equal parts.
- Look at A. Count the equal parts and the shaded parts.A: 4 parts, equal, 0 shaded
- Look at B. Count the equal parts and the shaded parts.B: 3 parts, equal, 0 shaded
- Look at C. Count the equal parts and the shaded parts.C: 3 parts, not equal, 0 shaded
- Find the picture that matches. We want the picture with 4 equal parts.Matches: A
- Write the answer. A
Check. B and C do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Watch out
Watch out: a quarter needs four equal parts. Parts that are not the same size are not quarters.
Exam tip
Grown-up tip. Fold a square of paper in half, then in half again. Open it up and count the four parts. Each part is one quarter.
Exercise 10D One quarter of a shape
Non-calculatorMethod. One quarter is one of 4 equal parts. Check the parts and the shading.
- Count the parts. One quarter needs 4 equal parts.4 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one quarter.1 shaded
- Decide. Yes. The shaded part is one quarter.
Check. Say it in words: the shaded part is one quarter. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. One quarter is one of 4 equal parts. Check the parts and the shading.
- Count the parts. One quarter needs 4 equal parts.4 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one quarter.1 shaded
- Decide. Yes. The shaded part is one quarter.
Check. Say it in words: the shaded part is one quarter. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. One quarter is one of 4 equal parts. Check the parts and the shading.
- Count the parts. One quarter needs 4 equal parts.4 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one quarter.3 shaded
- Decide. No. 3 parts are shaded, not one, so it is not one quarter.
Check. Say it in words: the shaded part is not one quarter. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. One quarter is one of 4 equal parts. Check the parts and the shading.
- Count the parts. One quarter needs 4 equal parts.4 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one quarter.1 shaded
- Decide. Yes. The shaded part is one quarter.
Check. Say it in words: the shaded part is one quarter. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. One quarter is one of 4 equal parts. Check the parts and the shading.
- Count the parts. One quarter needs 4 equal parts.2 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one quarter.1 shaded
- Decide. No. The shape has 2 equal parts, not 4, so the shaded part is not one quarter.
Check. Say it in words: the shaded part is not one quarter. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Method. Four equal quarters make one whole shape.
- Count the equal parts in the whole shape. Each part is one quarter.4 quarters
- Think about how many make a whole. All four quarters together make the whole shape.1 + 1 + 1 + 1 = 4 quarters
- Write the answer. 4
Check. Count the quarters again: 1, 2, 3, 4. ✓
Watch out. Four quarters make one whole. Do not count only the shaded parts.
Method. Touch each one once and say one number each. The last number is how many there are.
- Count each one and say its number. Each one gets one number, in order.1, 2
- Look at the last number. The last number tells us how many there are.The last number is 2.
- Write the answer. 2
Check. Count again from the other side. You get 2 again. ✓
Watch out. Move each one to one side as you count it, so you do not lose your place.
Method. Count how many quarters fit into one half.
- Start with one half. One half is shared into equal quarters.One half
- Count the quarters that fit. Each quarter is one of the equal parts.2 quarters fit into one half
- Write the answer. 2
Check. Put them together: one quarter + one quarter = one half. ✓
Watch out. Check the size. More quarters make one half because each quarter is smaller.
Method. Look at each picture and find the one with 4 equal parts.
- Look at A. Count the equal parts and the shaded parts.A: 3 parts, not equal, 0 shaded
- Look at B. Count the equal parts and the shaded parts.B: 5 parts, equal, 0 shaded
- Look at C. Count the equal parts and the shaded parts.C: 4 parts, equal, 0 shaded
- Find the picture that matches. We want the picture with 4 equal parts.Matches: C
- Write the answer. C
Check. A and B do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Method. Look at each picture and find the one with one quarter shaded.
- Look at A. Count the equal parts and the shaded parts.A: 2 parts, equal, 1 shaded
- Look at B. Count the equal parts and the shaded parts.B: 4 parts, equal, 1 shaded
- Look at C. Count the equal parts and the shaded parts.C: 4 parts, equal, 3 shaded
- Find the picture that matches. We want the picture with one quarter shaded.Matches: B
- Write the answer. B
Check. A and C do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Method. A quarter is one of four equal parts. A half is one of two equal parts.
- Look at one quarter. A quarter is smaller, because it is one of four parts.Four parts
- Look at one half. A half is one of two parts, so each part is bigger.Two parts
- Compare them. The part with more parts is smaller.A quarter is smaller than a half.
- Write the answer. No. A quarter is smaller than a half.
Check. Two quarters make one half, so one half must be bigger than one quarter. ✓
Watch out. More equal parts means each part is smaller.
Method. Four equal slices make the whole pizza. One slice is one quarter.
- Count the equal slices. The pizza is cut into four equal slices.4 slices
- Look at the slice Ravi ate. It is one of the four equal slices.One of 4 equal slices
- Write the answer. one quarter
Check. Four quarter slices would make the whole pizza. ✓
Watch out. Use the words “one quarter” for one of four equal parts.
Method. Count the shaded quarters in each picture, then pick the biggest number.
- Look at A. Count the shaded quarters.A: 2 of 4 quarters shaded
- Look at B. Count the shaded quarters.B: 1 of 4 quarters shaded
- Look at C. Count the shaded quarters.C: 3 of 4 quarters shaded
- Find the most shaded. The picture with the most shaded quarters is the answer.C has the most shaded
- Write the answer. C
Check. The others have fewer shaded quarters. ✓
Watch out. Count the shaded parts. Do not choose the picture that just looks the most coloured.
One quarter of a group
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A quarter of a group is one of four equal groups. Share the group into four equal groups. The number in one group is the quarter.
Here are 8 stars in four equal groups. Each group has 2 stars, so a quarter of 8 is 2.
Key ideas
- A quarter of a group means four equal groups.
- Count the number in one group.
- Check: four equal groups put together make the whole.
Key words. A quarter is one of four equal parts.
Method. Share 8 stars into 4 equal groups, so every group has the same number.
- Share the stars into 4 equal groups. Every group must have the same number, so give out one at a time.8 stars into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.2 in each group
- Write the answer. 2
Check. Add the groups back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A quarter is one of four equal parts.
Method. Share 12 cubes into 4 equal groups, so every group has the same number.
- Share the cubes into 4 equal groups. Every group must have the same number, so give out one at a time.12 cubes into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.3 in each group
- Write the answer. 3
Check. Add the groups back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A quarter is one of four equal parts.
Method. Share 16 balls into 4 equal groups, so every group has the same number.
- Share the balls into 4 equal groups. Every group must have the same number, so give out one at a time.16 balls into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.4 in each group
- Write the answer. 4
Check. Add the groups back together: 4 + 4 + 4 + 4 = 16. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Watch out
Watch out: a quarter needs four equal groups, not two. Half of 8 is 4, but a quarter of 8 is 2.
Exam tip
Grown-up tip. Use four plates or cups. Share the things out one at a time, going round the plates. Ask: “How many on each plate?”
Exercise 10E One quarter of a group
Non-calculatorKey words. A quarter is one of four equal parts.
Method. Share 4 apples into 4 equal groups, so every group has the same number.
- Share the apples into 4 equal groups. Every group must have the same number, so give out one at a time.4 apples into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.1 in each group
- Write the answer. 1
Check. Add the groups back together: 1 + 1 + 1 + 1 = 4. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A quarter is one of four equal parts.
Method. Share 20 sweets into 4 equal groups, so every group has the same number.
- Share the sweets into 4 equal groups. Every group must have the same number, so give out one at a time.20 sweets into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.5 in each group
- Write the answer. 5
Check. Add the groups back together: 5 + 5 + 5 + 5 = 20. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A quarter is one of four equal parts.
Method. Share 12 balls into 4 equal groups, so every group has the same number.
- Share the balls into 4 equal groups. Every group must have the same number, so give out one at a time.12 balls into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.3 in each group
- Write the answer. 3
Check. Add the groups back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A quarter is one of four equal parts.
Method. Share 24 things into 4 equal groups, so every group has the same number.
- Share the things into 4 equal groups. Every group must have the same number, so give out one at a time.24 things into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.6 in each group
- Write the answer. 6
Check. Add the groups back together: 6 + 6 + 6 + 6 = 24. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A quarter is one of four equal parts.
Method. Share 28 things into 4 equal groups, so every group has the same number.
- Share the things into 4 equal groups. Every group must have the same number, so give out one at a time.28 things into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.7 in each group
- Write the answer. 7
Check. Add the groups back together: 7 + 7 + 7 + 7 = 28. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A quarter is one of four equal parts.
Method. Share 40 things into 4 equal groups, so every group has the same number.
- Share the things into 4 equal groups. Every group must have the same number, so give out one at a time.40 things into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.10 in each group
- Write the answer. 10
Check. Add the groups back together: 10 + 10 + 10 + 10 = 40. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A quarter is one of four equal parts.
Method. Share 44 things into 4 equal groups, so every group has the same number.
- Share the things into 4 equal groups. Every group must have the same number, so give out one at a time.44 things into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.11 in each group
- Write the answer. 11
Check. Add the groups back together: 11 + 11 + 11 + 11 = 44. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A quarter is one of four equal parts.
Method. Share 36 grapes into 4 equal groups, so every group has the same number.
- Share the grapes into 4 equal groups. Every group must have the same number, so give out one at a time.36 grapes into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.9 in each group
- Write the answer. 9
Check. Add the groups back together: 9 + 9 + 9 + 9 = 36. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A quarter is one of four equal parts.
Method. Share 8 beads into 4 equal groups, so every group has the same number.
- Share the beads into 4 equal groups. Every group must have the same number, so give out one at a time.8 beads into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.2 in each group
- Write the answer. 2
Check. Add the groups back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Method. Find half of 8 and a quarter of 8, then compare them.
- Find half of 8. Share 8 into two equal groups.4 + 4 = 8
- Find a quarter of 8. Share 8 into four equal groups.2 + 2 + 2 + 2 = 8
- Compare the two numbers. The bigger number is the bigger share.4 is more than 2
- Write the answer. Half of 8 is more.
Check. Half of 8 is 4 and a quarter of 8 is 2, so half is the bigger share. ✓
Watch out. The bigger the number of equal parts, the smaller each part is.
Method. Equal shares have the same number of things on every plate.
- Count the things on each plate. We need to know how many are on each plate.3, 3, 3, 4
- Compare the numbers. Equal shares have the same number on every plate.The numbers are not the same.
- Decide. No. 13 things cannot be shared into 4 equal plates.
Check. Add the plates together: 3 + 3 + 3 + 4 = 13. ✓
Watch out. Equal shares must have the same number on every plate.
Method. Find a quarter of 8, and half of 4, then compare them.
- Find a quarter of 8. Share 8 into four equal groups.2 in each group
- Find half of 4. Share 4 into two equal groups.2 in each group
- Compare the two answers. Both answers are the same.2 = 2
- Write the answer. Yes. Both are 2.
Check. Two groups of 2 make 4, and four groups of 2 make 8. ✓
Watch out. Check the groups, not just the numbers.
Halves and quarters together
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
Some things are shared into two parts, and some into four parts. More parts means smaller parts. So one quarter is smaller than one half.
Look at the bars below. Two halves make one whole. Four quarters make one whole.
Key ideas
- Two halves make one whole.
- Four quarters make one whole.
- Two quarters make one half.
- A quarter is smaller than a half.
Method. Compare the two shares. The bigger share has more.
- Find the share for one half. Each share is a part of the same whole.one half: one half
- Find the share for one quarter. Compare it with the other share.one quarter: one quarter
- Decide which is bigger. The share with the bigger size has more.one half > one quarter
- Write the answer. one half has more, because the share is bigger.
Check. Put the two shares side by side to compare them. ✓
Watch out. Two halves make the whole, so a half is a big share. Do not think a bigger number always means a bigger share.
Method. Put the quarters together and see what they make.
- Put the 2 quarters together. Each quarter is one of the equal parts.one quarter + one quarter
- Compare with a whole. Find which share of the whole these make.= one half
- Write the answer. one half
Check. Draw the 2 quarters and fit them side by side. ✓
Watch out. Two quarters make one half. Four quarters make one whole.
Method. Compare the two shares. The bigger share has more.
- Find the share for Ravi. Each share is a part of the same whole.Ravi: one half
- Find the share for Aisha. Compare it with the other share.Aisha: one quarter
- Decide which is bigger. The share with the bigger size has more.Ravi > Aisha
- Write the answer. Ravi has more, because the share is bigger.
Check. Put the two shares side by side to compare them. ✓
Watch out. Two halves make the whole, so a half is a big share. Do not think a bigger number always means a bigger share.
Watch out
Watch out: a quarter is not bigger than a half, even though 4 is bigger than 2. More parts means smaller parts.
Exam tip
Grown-up tip. Cut a sandwich in half, then cut one half in half again. Ask: “Which piece is bigger?” and “How many of the small pieces make the big piece?”
Exercise 10F Halves and quarters together
Non-calculatorMethod. Compare the two shares. The bigger share has more.
- Find the share for one whole. Each share is a part of the same whole.one whole: one whole
- Find the share for one half. Compare it with the other share.one half: one half
- Decide which is bigger. The share with the bigger size has more.one whole > one half
- Write the answer. one whole has more, because the share is bigger.
Check. Put the two shares side by side to compare them. ✓
Watch out. Two halves make the whole, so a half is a big share. Do not think a bigger number always means a bigger share.
Method. Put the quarters together and see what they make.
- Put the 4 quarters together. Each quarter is one of the equal parts.one quarter + one quarter + one quarter + one quarter
- Compare with a whole. Find which share of the whole these make.= one whole
- Write the answer. one whole
Check. Draw the 4 quarters and fit them side by side. ✓
Watch out. Two quarters make one half. Four quarters make one whole.
Method. Look at each picture and find the one with one half shaded.
- Look at A. Count the equal parts and the shaded parts.A: 4 parts, equal, 1 shaded
- Look at B. Count the equal parts and the shaded parts.B: 2 parts, equal, 1 shaded
- Find the picture that matches. We want the picture with one half shaded.Matches: B
- Write the answer. B
Check. A do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Method. Put the halves together and see what they make.
- Put the 2 halves together. Each half is one of the equal parts.one half + one half
- Compare with a whole. Find which share of the whole these make.= one whole
- Write the answer. one whole
Check. Draw the 2 halves and fit them side by side. ✓
Watch out. Two quarters make one half. Four quarters make one whole.
Method. Put the quarters together and see what they make.
- Put the 2 quarters together. Each quarter is one of the equal parts.one quarter + one quarter
- Compare with a whole. Find which share of the whole these make.= one half
- Write the answer. one half
Check. Draw the 2 quarters and fit them side by side. ✓
Watch out. Two quarters make one half. Four quarters make one whole.
Method. Compare the two shares. The bigger share has more.
- Find the share for Mei. Each share is a part of the same whole.Mei: one half
- Find the share for Tom. Compare it with the other share.Tom: one quarter
- Decide which is bigger. The share with the bigger size has more.Mei > Tom
- Write the answer. Mei has more, because the share is bigger.
Check. Put the two shares side by side to compare them. ✓
Watch out. Two halves make the whole, so a half is a big share. Do not think a bigger number always means a bigger share.
Method. Compare the two shares. The bigger share has more.
- Find the share for Lena. Each share is a part of the same whole.Lena: one half
- Find the share for Tom. Compare it with the other share.Tom: one half
- Decide which is bigger. The share with the bigger size has more.Lena = Tom
- Write the answer. They have the same amount.
Check. Put the two shares side by side to compare them. ✓
Watch out. Two halves make the whole, so a half is a big share. Do not think a bigger number always means a bigger share.
Method. Compare the number of equal parts, not just the numbers.
- Look at a quarter. A quarter is one of four equal parts.Four parts
- Look at a half. A half is one of two equal parts.Two parts
- Compare the sizes. More equal parts means each part is smaller.A quarter is smaller than a half.
- Write the answer. No. A quarter is smaller than a half.
Check. Two quarters make one half, so a half is bigger than a quarter. ✓
Watch out. Four is a bigger number than two, but a quarter is the smaller share.
Method. The smallest share has the most equal parts. A whole is the biggest.
- Find the size of each share. A quarter is smallest. A whole is biggest.one whole, one quarter, one half
- Put them in order, smallest first. Start with the smallest share.one quarter, one half, one whole
- Write the answer. one quarter, one half, one whole
Check. Check: a quarter is smaller than a half, and a half is smaller than a whole. ✓
Watch out. The more equal parts a shape is cut into, the smaller each part is.
Method. Compare the two shaded parts. Then find how much more one of them is.
- Look at Ravi. Ravi shades one of four equal parts.Ravi: one quarter
- Look at Tom. Tom shades one of two equal parts.Tom: one half
- Find the difference. Take the smaller share away from the bigger one.one half − one quarter = one quarter
- Write the answer. Tom. He shades one quarter more.
Check. A half is two quarters, so Tom has one more quarter than Ravi. ✓
Watch out. Compare the shares of the same size shape.
Chapter summary
| Skill | Method |
|---|---|
| Equal parts | The parts are the same size. Check by comparing them side by side. |
| One half | Share a shape or a group into two equal parts. Each part is one half. |
| Half of a group | Share the group into two equal groups. Count the number in one group. |
| One quarter | Share a shape or a group into four equal parts. Each part is one quarter. |
| Quarter of a group | Share the group into four equal groups. Count the number in one group. |
| Compare | Two halves make one whole. Four quarters make one whole. A quarter is smaller than a half. |
Can you…?
- I can say when parts are equal and when they are not
- I can find one half of a shape and say that it is one of two equal parts
- I can find half of a group by sharing it into two equal groups
- I can find one quarter of a shape and say that it is one of four equal parts
- I can find a quarter of a group by sharing it into four equal groups
- I can say which is bigger, one half or one quarter
Key terms
- equal parts
- parts that are the same size
- not equal
- parts that are different sizes
- half
- one of two equal parts; two halves make one whole
- quarter
- one of four equal parts; four quarters make one whole
- whole
- the whole shape or the whole group, before it is shared
- share
- to give out things so that every group or part is the same
Exercise 10Z Check-up
Non-calculatorMethod. One half is one of 2 equal parts. Check the parts and the shading.
- Count the parts. One half needs 2 equal parts.4 parts
- Check the parts are the same size. Equal parts are the same size.The parts are the same size.
- Count the shaded parts. We need exactly one shaded part for one half.1 shaded
- Decide. No. The shape has 4 equal parts, not 2, so the shaded part is not one half.
Check. Say it in words: the shaded part is not one half. ✓
Watch out. Parts must be the same size before you can call them halves or quarters.
Key words. A half is one of two equal parts.
Method. Share 14 stars into 2 equal groups, so every group has the same number.
- Share the stars into 2 equal groups. Every group must have the same number, so give out one at a time.14 stars into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.7 in each group
- Write the answer. 7
Check. Add the groups back together: 7 + 7 = 14. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Method. Look at each picture and find the one with one quarter shaded.
- Look at A. Count the equal parts and the shaded parts.A: 2 parts, equal, 1 shaded
- Look at B. Count the equal parts and the shaded parts.B: 4 parts, equal, 1 shaded
- Look at C. Count the equal parts and the shaded parts.C: 4 parts, equal, 2 shaded
- Find the picture that matches. We want the picture with one quarter shaded.Matches: B
- Write the answer. B
Check. A and C do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Key words. A quarter is one of four equal parts.
Method. Share 12 things into 4 equal groups, so every group has the same number.
- Share the things into 4 equal groups. Every group must have the same number, so give out one at a time.12 things into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.3 in each group
- Write the answer. 3
Check. Add the groups back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Method. Look at each picture and find the one with 4 equal parts.
- Look at A. Count the equal parts and the shaded parts.A: 4 parts, equal, 0 shaded
- Look at B. Count the equal parts and the shaded parts.B: 3 parts, not equal, 0 shaded
- Find the picture that matches. We want the picture with 4 equal parts.Matches: A
- Write the answer. A
Check. B do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Method. Count how many quarters fit into one half.
- Start with one half. One half is shared into equal quarters.One half
- Count the quarters that fit. Each quarter is one of the equal parts.2 quarters fit into one half
- Write the answer. 2
Check. Put them together: one quarter + one quarter = one half. ✓
Watch out. Check the size. More quarters make one half because each quarter is smaller.
Method. Find half of 12 and a quarter of 12, then compare them.
- Find half of 12. Share 12 into two equal groups.6 in each group
- Find a quarter of 12. Share 12 into four equal groups.3 in each group
- Compare the two answers. The bigger share has more.6 is more than 3
- Write the answer. Half of 12 is bigger.
Check. Half of 12 is 6 and a quarter of 12 is 3. ✓
Watch out. Half is the bigger share of the same amount.
Key words. A quarter is one of four equal parts.
Method. Share 20 cubes into 4 equal groups, so every group has the same number.
- Share the cubes into 4 equal groups. Every group must have the same number, so give out one at a time.20 cubes into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.5 in each group
- Write the answer. 5
Check. Add the groups back together: 5 + 5 + 5 + 5 = 20. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Method. The smallest share has the most equal parts. A whole is the biggest.
- Find the size of each share. A quarter is smallest. A whole is biggest.one whole, one half, one quarter
- Put them in order, smallest first. Start with the smallest share.one quarter, one half, one whole
- Write the answer. one quarter, one half, one whole
Check. Check: a quarter is smaller than a half, and a half is smaller than a whole. ✓
Watch out. The more equal parts a shape is cut into, the smaller each part is.
Method. Share 8 into two equal groups to find half of 8.
- Share the 8 things into 2 equal groups. Every group must have the same number.4 + 4 = 8
- Count how many are in one group. One group is one half.4 in one group
- Compare with what Mei said. Mei said 2, but each group has 4.Mei said 2, but half is 4
- Write the answer. No. Half of 8 is 4.
Check. Put the two groups back together: 4 + 4 = 8. ✓
Watch out. Count the things in one group. Do not count the number of groups.
Total 15 marks. Allow about 15 minutes.
Exercise 10X End-of-chapter quiz
Non-calculatorMethod. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.2 parts
- Compare the sizes. Equal parts are the same size.One or more parts is a different size.
- Decide. No. The parts are not equal.
Check. Measure the parts with a ruler or a strip of paper. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Look at each picture and find the one with one half shaded.
- Look at A. Count the equal parts and the shaded parts.A: 4 parts, equal, 1 shaded
- Look at B. Count the equal parts and the shaded parts.B: 2 parts, equal, 1 shaded
- Find the picture that matches. We want the picture with one half shaded.Matches: B
- Write the answer. B
Check. A do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Method. Look at each picture and find the one with one quarter shaded.
- Look at A. Count the equal parts and the shaded parts.A: 2 parts, equal, 1 shaded
- Look at B. Count the equal parts and the shaded parts.B: 4 parts, equal, 1 shaded
- Find the picture that matches. We want the picture with one quarter shaded.Matches: B
- Write the answer. B
Check. A do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Key words. A half is one of two equal parts.
Method. Share 18 things into 2 equal groups, so every group has the same number.
- Share the things into 2 equal groups. Every group must have the same number, so give out one at a time.18 things into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.9 in each group
- Write the answer. 9
Check. Add the groups back together: 9 + 9 = 18. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A quarter is one of four equal parts.
Method. Share 16 things into 4 equal groups, so every group has the same number.
- Share the things into 4 equal groups. Every group must have the same number, so give out one at a time.16 things into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.4 in each group
- Write the answer. 4
Check. Add the groups back together: 4 + 4 + 4 + 4 = 16. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A half is one of two equal parts.
Method. Share 14 counters into 2 equal groups, so every group has the same number.
- Share the counters into 2 equal groups. Every group must have the same number, so give out one at a time.14 counters into 2 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.7 in each group
- Write the answer. 7
Check. Add the groups back together: 7 + 7 = 14. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Key words. A quarter is one of four equal parts.
Method. Share 12 pencils into 4 equal groups, so every group has the same number.
- Share the pencils into 4 equal groups. Every group must have the same number, so give out one at a time.12 pencils into 4 groups
- Count how many are in one group. All the groups are the same, so one group gives the answer.3 in each group
- Write the answer. 3
Check. Add the groups back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Every group needs the same number. Do not give one group more than the others.
Method. Share 8 into four equal groups to find a quarter of 8.
- Share the 8 things into 4 equal groups. Every group must have the same number.2 + 2 + 2 + 2 = 8
- Count how many are in one group. One group is one quarter.2 in one group
- Compare with what Ravi said. Ravi said 4, but each group has 2.Ravi said 4, but a quarter is 2
- Write the answer. No. A quarter of 8 is 2.
Check. Put the four groups back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Four equal groups are needed for a quarter, not two.
Method. Find half of 20 and a quarter of 20, then compare them.
- Find half of 20. Share 20 into two equal groups.10 in each group
- Find a quarter of 20. Share 20 into four equal groups.5 in each group
- Compare the two answers. The bigger share has more.10 is more than 5
- Write the answer. Half of 20 is more.
Check. Half of 20 is 10 and a quarter of 20 is 5. ✓
Watch out. Half is the bigger share of the same amount.
Method. Put two quarters together and see what they make.
- Put the two quarters together. Each quarter is one of four equal parts.one quarter + one quarter
- Compare with a whole. Two of the four parts make only half of the whole.= one half
- Write the answer. No. Two quarters make one half.
Check. Four quarters make one whole, so two quarters are half of it. ✓
Watch out. Two quarters make one half. Four quarters make one whole.