Grouping and sharing
By the end of this chapter you will be able to
- Count in 2s, 5s and 10s
- Say whether groups are equal, and make equal groups
- Add equal groups to find the total
- Count the rows and columns of an array
- Find a double by adding a number to itself
- Share things equally, and put them into equal groups
You should already know
- Counting and the numbers to 20 (Chapters 1, 4 and 6)
- Adding within 20 (Chapters 2 and 5)
- Comparing groups (Chapter 1)
Where this leads
- Money (Year 1 Chapter 12)
- Multiplication and division (Year 2)
National Curriculum for England, Key Stage 1 mathematics, Year 1. Content: Count in multiples of 2, 5 and 10, Make equal groups and say how many are in each, Add equal groups to find the total, Make and count arrays of rows and columns, Find doubles as two equal groups, Share equally and group, using objects, pictures and arrays.
- 9.1 Counting in 2s, 5s and 10s: Worksheet (PDF) · Answers (PDF) · lesson page
- 9.2 Making equal groups: Worksheet (PDF) · Answers (PDF) · lesson page
- 9.3 Adding equal groups: Worksheet (PDF) · Answers (PDF) · lesson page
- 9.4 Arrays: rows and columns: Worksheet (PDF) · Answers (PDF) · lesson page
- 9.5 Doubles: two equal groups: Worksheet (PDF) · Answers (PDF) · lesson page
- 9.6 Sharing and grouping: 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-calculatorKey words. To count is to say one number for each thing, in order: 1, 2, 3, and so on.
Method. Say one number for each thing, and touch each one only once. The last number is how many there are.
- Count each thing and say its number. Each thing gets one number.1, 2, 3, 4, 5, 6
- Look at the last number you said. The last number tells us how many there are altogether.The last number is 6.
- Write the answer. There are 6 balls.
Check. Count again from the other side. You get 6 again. ✓
Watch out. Move each thing to one side as you count it, so you do not count it twice.
Method. Start at 5. Count on 2 more to add them.
- Start at 5. Put your finger on the first number.5
- Count on 2 more. Say each number as you touch the next one.6, 7
- Write the total. The last number you said is the total.5 + 2 = 7
Check. Start at 2 and count on 5 to check: you also get 7. ✓
Watch out. Start with the bigger number and count on the smaller one, if you like. The total is the same.
Method. Start at 7. Count on in 1s to find the next 3 numbers.
- Start at 7. Start with the number you are given.7
- Jump on by 1 each time. Each new number is the last one plus the jump.7 + 1 = 8
8 + 1 = 9
9 + 1 = 10 - Write the next numbers. Do not write the start number again.8, 9, 10
Check. Count back in 1s from 10 to 7 to check. ✓
Watch out. Do not write the number you start at. Start with the next one.
Key words. Double means two of the same, so double 4 is 4 + 4.
Method. A double is two equal groups. Double 4 is 4 + 4.
- Find the two equal groups. Both groups must be the same size.4 and 4
- Add the two groups together. Add 4 + 4.4 + 4 = 8
- Write the answer. 8
Check. Count in 4s: 4, 8. Two groups of 4 make 8. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Method. Compare the two numbers. The bigger number has more.
- Look at Sam’s number. Sam has 6 stickers.Sam: 6
- Look at Ali’s number. Ali has 9 stickers.Ali: 9
- Compare the two numbers. The bigger number has more.9 is bigger than 6
- Write the answer. Ali has more stickers.
Check. Count on from 6 to 9: 7, 8, 9. Ali has more. ✓
Watch out. Compare the numbers, not the names.
Counting in 2s, 5s and 10s
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
When we count in 2s, we jump on by 2 each time: 2, 4, 6, 8. When we count in 5s, we jump on by 5: 5, 10, 15, 20. When we count in 10s, we jump on by 10: 10, 20, 30, 40.
Look at the boxes. Each box has 2 biscuits. Counting in 2s is a quick way to count them.
Key ideas
- Counting in 2s means jumping on by 2 each time.
- Counting in 5s means jumping on by 5 each time.
- Counting in 10s means jumping on by 10 each time.
- Every jump is the same size.
Key words. Counting in 2s means jumping on by 2 each time.
Method. Count in 2s. Every jump is the same size: 2.
- Start at 2. Put your finger on the first number.2
- Jump on by 2 each time. Each number is 2 more than the one before.2 + 2 = 4
4 + 2 = 6
6 + 2 = 8
8 + 2 = 10
10 + 2 = 12 - Write the numbers. Say them in order, one jump at a time.2, 4, 6, 8, 10, 12
Check. Count back in 2s from 12 to check. ✓
Watch out. Keep the same jump all the way. Every number must be 2 more than the one before.
Key words. Counting in 2s means jumping on by 2 each time.
Method. Count in 2s. Every jump is the same size: 2.
- Start at 2. Put your finger on the first number.2
- Jump on by 2 each time. Each number is 2 more than the one before.2 + 2 = 4
4 + 2 = 6
6 + 2 = 8 - Write the numbers. Say them in order, one jump at a time.2, 4, 6, 8
Check. Count back in 2s from 8 to check. ✓
Watch out. Keep the same jump all the way. Every number must be 2 more than the one before.
Key words. Counting in 5s means jumping on by 5 each time.
Method. Count in 5s. Every jump is the same size: 5.
- Start at 5. Put your finger on the first number.5
- Jump on by 5 each time. Each number is 5 more than the one before.5 + 5 = 10
10 + 5 = 15
15 + 5 = 20
20 + 5 = 25
25 + 5 = 30 - Write the numbers. Say them in order, one jump at a time.5, 10, 15, 20, 25, 30
Check. Count back in 5s from 30 to check. ✓
Watch out. Keep the same jump all the way. Every number must be 5 more than the one before.
Watch out
Watch out: keep the same jump all the way. 2, 4, 6, 9 is wrong, because the last jump is not 2.
Exam tip
Grown-up tip. Count out loud together. Use pairs of socks for 2s, one hand for 5s and two hands for 10s. Ask: “What is the next number?” before your child says it.
Exercise 9A Counting in 2s, 5s and 10s
Non-calculatorMethod. Count in 2s. Each number is 2 more than the one before it.
- Look at the numbers before and after each gap. The jump is the same every time.2, 4, ?, 8, ?, 12
- Add 2 to the number before each gap. That gives the missing number.Gap 3: 4 + 2 = 6
Gap 5: 8 + 2 = 10 - Write the missing numbers. 6, 10
Check. Count in 2s all the way along the list. Every number fits. ✓
Watch out. Check the numbers after the gap too. They should still go up in the same jump.
Method. Count in 5s. Each number is 5 more than the one before it.
- Look at the numbers before and after each gap. The jump is the same every time.5, ?, 15, 20, ?, 30
- Add 5 to the number before each gap. That gives the missing number.Gap 2: 5 + 5 = 10
Gap 5: 20 + 5 = 25 - Write the missing numbers. 10, 25
Check. Count in 5s all the way along the list. Every number fits. ✓
Watch out. Check the numbers after the gap too. They should still go up in the same jump.
Method. Count in 10s. Each number is 10 more than the one before it.
- Look at the numbers before and after each gap. The jump is the same every time.10, 20, 30, ?, 50
- Add 10 to the number before each gap. That gives the missing number.Gap 4: 30 + 10 = 40
- Write the missing numbers. 40
Check. Count in 10s all the way along the list. Every number fits. ✓
Watch out. Check the numbers after the gap too. They should still go up in the same jump.
Method. Start at 30. Count on in 5s to find the next 3 numbers.
- Start at 30. Start with the number you are given.30
- Jump on by 5 each time. Each new number is the last one plus the jump.30 + 5 = 35
35 + 5 = 40
40 + 5 = 45 - Write the next numbers. Do not write the start number again.35, 40, 45
Check. Count back in 5s from 45 to 30 to check. ✓
Watch out. Do not write the number you start at. Start with the next one.
Key words. Counting in 2s means jumping on by 2 each time.
Method. Count in 2s. Every jump is the same size: 2.
- Start at 2. Put your finger on the first number.2
- Jump on by 2 each time. Each number is 2 more than the one before.2 + 2 = 4
4 + 2 = 6
6 + 2 = 8
8 + 2 = 10 - Write the numbers. Say them in order, one jump at a time.2, 4, 6, 8, 10
Check. Count back in 2s from 10 to check. ✓
Watch out. Keep the same jump all the way. Every number must be 2 more than the one before.
Key words. Counting in 5s means jumping on by 5 each time.
Method. Count in 5s. Every jump is the same size: 5.
- Start at 5. Put your finger on the first number.5
- Jump on by 5 each time. Each number is 5 more than the one before.5 + 5 = 10
10 + 5 = 15
15 + 5 = 20 - Write the numbers. Say them in order, one jump at a time.5, 10, 15, 20
Check. Count back in 5s from 20 to check. ✓
Watch out. Keep the same jump all the way. Every number must be 5 more than the one before.
Key words. Counting in 10s means jumping on by 10 each time.
Method. Count in 10s. Every jump is the same size: 10.
- Start at 10. Put your finger on the first number.10
- Jump on by 10 each time. Each number is 10 more than the one before.10 + 10 = 20
20 + 10 = 30
30 + 10 = 40
40 + 10 = 50
50 + 10 = 60 - Write the numbers. Say them in order, one jump at a time.10, 20, 30, 40, 50, 60
Check. Count back in 10s from 60 to check. ✓
Watch out. Keep the same jump all the way. Every number must be 10 more than the one before.
Key words. Counting in 5s means jumping on by 5 each time.
Method. Count in 5s. Every jump is the same size: 5.
- Start at 5. Put your finger on the first number.5
- Jump on by 5 each time. Each number is 5 more than the one before.5 + 5 = 10
10 + 5 = 15
15 + 5 = 20 - Write the numbers. Say them in order, one jump at a time.5, 10, 15, 20
Check. Count back in 5s from 20 to check. ✓
Watch out. Keep the same jump all the way. Every number must be 5 more than the one before.
Key words. Counting in 10s means jumping on by 10 each time.
Method. Count in 10s. Every jump is the same size: 10.
- Start at 10. Put your finger on the first number.10
- Jump on by 10 each time. Each number is 10 more than the one before.10 + 10 = 20
20 + 10 = 30 - Write the numbers. Say them in order, one jump at a time.10, 20, 30
Check. Count back in 10s from 30 to check. ✓
Watch out. Keep the same jump all the way. Every number must be 10 more than the one before.
Key words. Counting in 5s means jumping on by 5 each time.
Method. Count in 5s. Every jump is the same size: 5.
- Start at 5. Put your finger on the first number.5
- Jump on by 5 each time. Each number is 5 more than the one before.5 + 5 = 10
10 + 5 = 15
15 + 5 = 20 - Write the numbers. Say them in order, one jump at a time.5, 10, 15, 20
Check. Count back in 5s from 20 to check. ✓
Watch out. Keep the same jump all the way. Every number must be 5 more than the one before.
Key words. Counting in 2s means jumping on by 2 each time.
Method. Count in 2s. Every jump is the same size: 2.
- Start at 2. Put your finger on the first number.2
- Jump on by 2 each time. Each number is 2 more than the one before.2 + 2 = 4
4 + 2 = 6
6 + 2 = 8
8 + 2 = 10
10 + 2 = 12 - Write the numbers. Say them in order, one jump at a time.2, 4, 6, 8, 10, 12
Check. Count back in 2s from 12 to check. ✓
Watch out. Keep the same jump all the way. Every number must be 2 more than the one before.
Method. Write the numbers in the 5s and the 10s. Then check each 10 is in the 5s.
- Write the 5s. Count in 5s.5, 10, 15, 20, 25, 30
- Write the 10s. Count in 10s.10, 20, 30, 40
- Check each 10 is in the 5s. 10, 20 and 30 are all in the list of 5s.10 is in the 5s, 20 is in the 5s, 30 is in the 5s
- Write the answer. Yes. Every number in the 10s is in the 5s.
Check. Count in 5s to 40: 5, 10, 15, 20, 25, 30, 35, 40. 40 is in the list too. ✓
Watch out. Every jump of 10 is two jumps of 5, so the 10s always land on the 5s.
Method. Count in 2s and see if 7 comes up.
- Count in 2s. Start at 2 and jump on by 2.2, 4, 6, 8
- Look for 7. The numbers jump from 6 to 8. 7 is skipped.6, then 8. No 7.
- Write the answer. No. 7 is not in the 2s.
Check. Every number in the 2s is even. 7 is odd, so it is not there. ✓
Watch out. Do not guess. Count in 2s and see which numbers come up.
Making equal groups
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
Equal groups have the same number of things in each group. Here are three groups. Each group has 4 biscuits. The groups are equal.
When we make groups, we put things into groups with the same number in each. Then we count how many groups there are.
Key ideas
- Equal groups have the same number of things in each group.
- Count how many things are in one group.
- Count how many groups there are.
- Groups can look the same but have different numbers. Count each group.
Method. Equal groups have the same number of things in each group.
- Count the things in each group. Touch each thing once.group 1 has 3, group 2 has 3, group 3 has 3
- Compare the numbers. The groups are equal only if every number is the same.All the same
- Write the answer. Yes. The groups are equal.
Check. Count the things in each group again. ✓
Watch out. Groups can look the same size on the page. Always count each group.
Method. Equal groups have the same number of things in each group.
- Count the things in each group. Touch each thing once.group 1 has 2, group 2 has 4, group 3 has 2
- Compare the numbers. The groups are equal only if every number is the same.Not all the same
- Write the answer. No. The groups are not equal.
Check. Count the things in each group again. ✓
Watch out. Groups can look the same size on the page. Always count each group.
Key words. A group is a set of things that belong together.
Method. Put 2 in each group, and keep going until none are left. Then count the groups.
- Make a group with 2 apples. Each group must have the same number.1 group of 2
- Keep making groups until none are left. There are 6 in all, so count the groups as you make them.2 + 2 + 2 = 6
- Count the groups. Each group is one group.3 groups
Check. Each group has 2, and 3 groups make 6. ✓
Watch out. Count the groups, not the apples. There are 3 groups.
Watch out
Watch out: groups can look the same size but have a different number of things. Always count each group.
Exam tip
Grown-up tip. Lay out buttons or pasta shapes in egg boxes or cups. Ask: “Are all the cups the same? How many are in each cup?”
Exercise 9B Equal groups
Non-calculatorMethod. Equal groups have the same number of things in each group.
- Count the things in each group. Touch each thing once.group 1 has 2, group 2 has 2, group 3 has 2, group 4 has 2
- Compare the numbers. The groups are equal only if every number is the same.All the same
- Write the answer. Yes. The groups are equal.
Check. Count the things in each group again. ✓
Watch out. Groups can look the same size on the page. Always count each group.
Method. Equal groups have the same number of things in each group.
- Count the things in each group. Touch each thing once.group 1 has 3, group 2 has 4, group 3 has 3
- Compare the numbers. The groups are equal only if every number is the same.Not all the same
- Write the answer. No. The groups are not equal.
Check. Count the things in each group again. ✓
Watch out. Groups can look the same size on the page. Always count each group.
Method. Count the things in one group. Every group is the same, so one group tells us about all of them.
- Look at one group. Count the things in it.One group has 4
- Check the other groups. Each group has the same number.All 3 groups have 4
- Write the answer. 4
Check. Count one group again: 1, 2, 3, 4. ✓
Watch out. Check that every group is the same before you use one of them.
Method. Count the groups. Each one is counted once.
- Count the groups. Touch each one once.1, 2, 3, 4
- Look at the last number you said. That is how many groups there are.The last number is 4.
- Write the answer. 4 groups
Check. Count the groups from the other side. You get 4 again. ✓
Watch out. Count the groups, not the things inside them.
Key words. A group is a set of things that belong together.
Method. Put 2 in each group, and keep going until none are left. Then count the groups.
- Make a group with 2 cubes. Each group must have the same number.1 group of 2
- Keep making groups until none are left. There are 8 in all, so count the groups as you make them.2 + 2 + 2 + 2 = 8
- Count the groups. Each group is one group.4 groups
Check. Each group has 2, and 4 groups make 8. ✓
Watch out. Count the groups, not the cubes. There are 4 groups.
Key words. A group is a set of things that belong together.
Method. Put 3 in each group, and keep going until none are left. Then count the groups.
- Make a group with 3 balls. Each group must have the same number.1 group of 3
- Keep making groups until none are left. There are 9 in all, so count the groups as you make them.3 + 3 + 3 = 9
- Count the groups. Each group is one group.3 groups
Check. Each group has 3, and 3 groups make 9. ✓
Watch out. Count the groups, not the balls. There are 3 groups.
Key words. A group is a set of things that belong together.
Method. Put 5 in each group, and keep going until none are left. Then count the groups.
- Make a group with 5 stars. Each group must have the same number.1 group of 5
- Keep making groups until none are left. There are 10 in all, so count the groups as you make them.5 + 5 = 10
- Count the groups. Each group is one group.2 groups
Check. Each group has 5, and 2 groups make 10. ✓
Watch out. Count the groups, not the stars. There are 2 groups.
Key words. A group is a set of things that belong together.
Method. Put 4 in each group, and keep going until none are left. Then count the groups.
- Make a group with 4 biscuits. Each group must have the same number.1 group of 4
- Keep making groups until none are left. There are 12 in all, so count the groups as you make them.4 + 4 + 4 = 12
- Count the groups. Each group is one group.3 groups
Check. Each group has 4, and 3 groups make 12. ✓
Watch out. Count the groups, not the biscuits. There are 3 groups.
Key words. A group is a set of things that belong together.
Method. Put 2 in each group, and keep going until none are left. Then count the groups.
- Make a group with 2 apples. Each group must have the same number.1 group of 2
- Keep making groups until none are left. There are 10 in all, so count the groups as you make them.2 + 2 + 2 + 2 + 2 = 10
- Count the groups. Each group is one group.5 groups
Check. Each group has 2, and 5 groups make 10. ✓
Watch out. Count the groups, not the apples. There are 5 groups.
Method. Make as many groups of 2 as you can. Then check if any stars are left over.
- Make groups of 2. Put 2 stars in each group.4 groups of 2 use 8 stars
- Count the stars left over. Stars that are not in a group are left over.9 − 8 = 1
- Write the answer. A star left over means the groups are not equal.No. 1 star is left over.
Check. Count the groups: 4 groups with 2 in each, and 1 star on its own. ✓
Watch out. Count the things left over. If there are any, the groups cannot all be the same.
Adding equal groups
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
When there are equal groups, we can add them. Each group has the same number, so we add that number again and again.
Here are 3 groups with 4 biscuits in each. We add 4 + 4 + 4 to find the total. It makes 12. Count in 4s to check: 4, 8, 12.
Key ideas
- Write one number for each group.
- Add the same number again and again.
- Count in the same steps to check the total.
- The total is the answer.
Key words. Equal groups have the same number of biscuits in each group.
Method. Add the same number 2 times, once for each group. Each group has 5.
- Write one 5 for each group. There are 2 groups, so there are 2 numbers to add.5 + 5
- Add the numbers together. Count in 5s to add them up: 5, 10.5 + 5 = 10
- Write the answer. 10
Check. Count in 5s: 5, 10. The last number is 10. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. Equal groups have the same number of biscuits in each group.
Method. Add the same number 3 times, once for each group. Each group has 2.
- Write one 2 for each group. There are 3 groups, so there are 3 numbers to add.2 + 2 + 2
- Add the numbers together. Count in 2s to add them up: 2, 4, 6.2 + 2 + 2 = 6
- Write the answer. 6
Check. Count in 2s: 2, 4, 6. The last number is 6. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. Equal groups have the same number of flowers in each group.
Method. Add the same number 4 times, once for each group. Each group has 3.
- Write one 3 for each group. There are 4 groups, so there are 4 numbers to add.3 + 3 + 3 + 3
- Add the numbers together. Count in 3s to add them up: 3, 6, 9, 12.3 + 3 + 3 + 3 = 12
- Write the answer. 12
Check. Count in 3s: 3, 6, 9, 12. The last number is 12. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Watch out
Watch out: write one number for each group. Three groups of 4 is 4 + 4 + 4, not 3 + 3 + 3 + 3.
Exam tip
Grown-up tip. Put out equal plates or cups with the same number of pasta shapes in each. Ask your child to add one number for each plate, then count in that number to check.
Exercise 9C Adding equal groups
Non-calculatorKey words. Equal groups have the same number of things in each group.
Method. Add the same number 3 times, once for each group. Each group has 2.
- Write one 2 for each group. There are 3 groups, so there are 3 numbers to add.2 + 2 + 2
- Add the numbers together. Count in 2s to add them up: 2, 4, 6.2 + 2 + 2 = 6
- Write the answer. 6
Check. Count in 2s: 2, 4, 6. The last number is 6. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. Equal groups have the same number of things in each group.
Method. Add the same number 2 times, once for each group. Each group has 5.
- Write one 5 for each group. There are 2 groups, so there are 2 numbers to add.5 + 5
- Add the numbers together. Count in 5s to add them up: 5, 10.5 + 5 = 10
- Write the answer. 10
Check. Count in 5s: 5, 10. The last number is 10. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. Equal groups have the same number of things in each group.
Method. Add the same number 4 times, once for each group. Each group has 3.
- Write one 3 for each group. There are 4 groups, so there are 4 numbers to add.3 + 3 + 3 + 3
- Add the numbers together. Count in 3s to add them up: 3, 6, 9, 12.3 + 3 + 3 + 3 = 12
- Write the answer. 12
Check. Count in 3s: 3, 6, 9, 12. The last number is 12. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. Equal groups have the same number of stars in each group.
Method. Add the same number 2 times, once for each group. Each group has 4.
- Write one 4 for each group. There are 2 groups, so there are 2 numbers to add.4 + 4
- Add the numbers together. Count in 4s to add them up: 4, 8.4 + 4 = 8
- Write the answer. 8
Check. Count in 4s: 4, 8. The last number is 8. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. Equal groups have the same number of cubes in each group.
Method. Add the same number 3 times, once for each group. Each group has 2.
- Write one 2 for each group. There are 3 groups, so there are 3 numbers to add.2 + 2 + 2
- Add the numbers together. Count in 2s to add them up: 2, 4, 6.2 + 2 + 2 = 6
- Write the answer. 6
Check. Count in 2s: 2, 4, 6. The last number is 6. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. Equal groups have the same number of balls in each group.
Method. Add the same number 4 times, once for each group. Each group has 5.
- Write one 5 for each group. There are 4 groups, so there are 4 numbers to add.5 + 5 + 5 + 5
- Add the numbers together. Count in 5s to add them up: 5, 10, 15, 20.5 + 5 + 5 + 5 = 20
- Write the answer. 20
Check. Count in 5s: 5, 10, 15, 20. The last number is 20. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. Equal groups have the same number of marbles in each group.
Method. Add the same number 3 times, once for each group. Each group has 5.
- Write one 5 for each group. There are 3 groups, so there are 3 numbers to add.5 + 5 + 5
- Add the numbers together. Count in 5s to add them up: 5, 10, 15.5 + 5 + 5 = 15
- Write the answer. 15
Check. Count in 5s: 5, 10, 15. The last number is 15. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. Equal groups have the same number of pears in each group.
Method. Add the same number 4 times, once for each group. Each group has 2.
- Write one 2 for each group. There are 4 groups, so there are 4 numbers to add.2 + 2 + 2 + 2
- Add the numbers together. Count in 2s to add them up: 2, 4, 6, 8.2 + 2 + 2 + 2 = 8
- Write the answer. 8
Check. Count in 2s: 2, 4, 6, 8. The last number is 8. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Method. Find the number that fits in each box, so that three equal numbers make 9.
- Try 3 in each box. Three threes make 9, so each box has 3.3 + 3 + 3
- Add the three numbers. Count in 3s to check: 3, 6, 9.3 + 3 + 3 = 9
- Write the answer. 3 goes in each box.
Check. Each box has 3, and 3 + 3 + 3 = 9. ✓
Watch out. Count in the number you put in each box. You should land on 9.
Key words. Equal groups have the same number of sweets in each group.
Method. Add the same number 4 times, once for each group. Each group has 3.
- Write one 3 for each group. There are 4 groups, so there are 4 numbers to add.3 + 3 + 3 + 3
- Add the numbers together. Count in 3s to add them up: 3, 6, 9, 12.3 + 3 + 3 + 3 = 12
- Write the answer. 12
Check. Count in 3s: 3, 6, 9, 12. The last number is 12. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. Equal groups have the same number of flowers in each group.
Method. Add the same number 5 times, once for each group. Each group has 2.
- Write one 2 for each group. There are 5 groups, so there are 5 numbers to add.2 + 2 + 2 + 2 + 2
- Add the numbers together. Count in 2s to add them up: 2, 4, 6, 8, 10.2 + 2 + 2 + 2 + 2 = 10
- Write the answer. 10
Check. Count in 2s: 2, 4, 6, 8, 10. The last number is 10. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Method. Add up the numbers in each sum, then compare the totals.
- Add the first sum. Five plus five plus five.5 + 5 + 5 = 15
- Add the second sum. Three plus three plus three plus three plus three.3 + 3 + 3 + 3 + 3 = 15
- Compare the totals. If both totals are the same, Mia is right.15 = 15
- Write the answer. Yes. Both sums make 15.
Check. Count in 5s to 15: 5, 10, 15. Count in 3s to 15: 3, 6, 9, 12, 15. ✓
Watch out. Different sums can make the same total. Add each sum to check.
Method. Find the total for each person. Then compare.
- Add Ali’s sweets. Two bags with 3 in each bag.3 + 3 = 6
- Add Jo’s sweets. Three bags with 2 in each bag.2 + 2 + 2 = 6
- Compare the totals. Both totals are 6, so the numbers are the same.6 = 6
- Write the answer. Neither. They both have 6 sweets.
Check. Count in 3s to 6: 3, 6. Count in 2s to 6: 2, 4, 6. ✓
Watch out. Different groups can have the same total. Count the sweets, not the bags.
Arrays: rows and columns
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
An array is a neat set of things in rows and columns. A row goes across. A column goes down. Every row has the same number of things.
This tray has 3 rows with 4 biscuits in each row. Count the biscuits in each row and add them: 4 + 4 + 4 = 12.
Key ideas
- A row goes across.
- A column goes down.
- An array has the same number in each row.
- Turning an array round does not change how many things there are.
Key words. A row goes across. A column goes down. An array is things in rows and columns.
Method. Count the rows. Every row has the same number, so add that number once for each row.
- Count the rows. A row goes across.2 rows
- Count the things in one row. Every row has the same number.4 in each row
- Add one number for each row. Add the rows together.4 + 4 = 8
- Write the answer. 8
Check. Count down the columns too: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Count each row once. Do not count a thing twice.
Key words. A row goes across. A column goes down. An array is things in rows and columns.
Method. Count the rows. Every row has the same number, so add that number once for each row.
- Count the rows. A row goes across.3 rows
- Count the things in one row. Every row has the same number.5 in each row
- Add one number for each row. Add the rows together.5 + 5 + 5 = 15
- Write the answer. 15
Check. Count down the columns too: 3 + 3 + 3 + 3 + 3 = 15. ✓
Watch out. Count each row once. Do not count a thing twice.
Key words. A row goes across. A column goes down. An array is things in rows and columns.
Method. Count the rows. Every row has the same number, so add that number once for each row.
- Count the rows. A row goes across.4 rows
- Count the things in one row. Every row has the same number.2 in each row
- Add one number for each row. Add the rows together.2 + 2 + 2 + 2 = 8
- Write the answer. 8
Check. Count down the columns too: 4 + 4 = 8. ✓
Watch out. Count each row once. Do not count a thing twice.
Watch out
Watch out: count each thing once. Count one row at a time, then add the rows, so you do not miss any.
Exam tip
Grown-up tip. Use an egg box or an ice cube tray. Ask: “How many rows? How many in each row? How many altogether?” Then turn the box round and ask the same questions again.
Exercise 9D Arrays
Non-calculatorKey words. A row goes across. A column goes down. An array is things in rows and columns.
Method. Count the rows. Every row has the same number, so add that number once for each row.
- Count the rows. A row goes across.2 rows
- Count the things in one row. Every row has the same number.4 in each row
- Add one number for each row. Add the rows together.4 + 4 = 8
- Write the answer. 8
Check. Count down the columns too: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Count each row once. Do not count a thing twice.
Key words. A row goes across. A column goes down. An array is things in rows and columns.
Method. Count the rows. Every row has the same number, so add that number once for each row.
- Count the rows. A row goes across.3 rows
- Count the things in one row. Every row has the same number.3 in each row
- Add one number for each row. Add the rows together.3 + 3 + 3 = 9
- Write the answer. 9
Check. Count down the columns too: 3 + 3 + 3 = 9. ✓
Watch out. Count each row once. Do not count a thing twice.
Key words. A row goes across. A column goes down. An array is things in rows and columns.
Method. Count the rows. Every row has the same number, so add that number once for each row.
- Count the rows. A row goes across.5 rows
- Count the things in one row. Every row has the same number.2 in each row
- Add one number for each row. Add the rows together.2 + 2 + 2 + 2 + 2 = 10
- Write the answer. 10
Check. Count down the columns too: 5 + 5 = 10. ✓
Watch out. Count each row once. Do not count a thing twice.
Method. Count the rows. Each one is counted once.
- Count the rows. Touch each one once.1, 2, 3
- Look at the last number you said. That is how many rows there are.The last number is 3.
- Write the answer. 3 rows
Check. Count the rows from the other side. You get 3 again. ✓
Watch out. Count the rows, not the things inside them.
Method. Count the things in one row. Every row is the same, so one row tells us about all of them.
- Look at one row. Count the things in it.One row has 5
- Check the other rows. Each row has the same number.All 3 rows have 5
- Write the answer. 5
Check. Count one row again: 1, 2, 3, 4, 5. ✓
Watch out. Check that every row is the same before you use one of them.
Key words. A row goes across. A column goes down. An array is things in rows and columns.
Method. Count the rows. Every row has the same number, so add that number once for each row.
- Count the rows. A row goes across.3 rows
- Count the things in one row. Every row has the same number.5 in each row
- Add one number for each row. Add the rows together.5 + 5 + 5 = 15
- Write the answer. 15
Check. Count down the columns too: 3 + 3 + 3 + 3 + 3 = 15. ✓
Watch out. Count each row once. Do not count a thing twice.
Method. Count the biscuits in both trays. Turning a tray round does not change the total.
- Count the first tray. Two rows of 5.5 + 5 = 10
- Count the second tray. Five rows of 2. It is the first tray turned round.2 + 2 + 2 + 2 + 2 = 10
- Compare the totals. Both totals are the same.10 = 10
- Write the answer. Yes. Both trays have 10 biscuits.
Check. Count the biscuits in each row and each column. Both give 10. ✓
Watch out. Turning a tray round does not add or take away any biscuits.
Key words. A row goes across. A column goes down. An array is things in rows and columns.
Method. Count the rows. Every row has the same number, so add that number once for each row.
- Count the rows. A row goes across.2 rows
- Count the things in one row. Every row has the same number.3 in each row
- Add one number for each row. Add the rows together.3 + 3 = 6
- Write the answer. 6
Check. Count down the columns too: 2 + 2 + 2 = 6. ✓
Watch out. Count each row once. Do not count a thing twice.
Key words. Equal groups have the same number of eggs in each group.
Method. Add the same number 2 times, once for each group. Each group has 6.
- Write one 6 for each group. There are 2 groups, so there are 2 numbers to add.6 + 6
- Add the numbers together. Count in 6s to add them up: 6, 12.6 + 6 = 12
- Write the answer. 12
Check. Count in 6s: 6, 12. The last number is 12. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. A group is a set of things that belong together.
Method. Put 5 in each group, and keep going until none are left. Then count the groups.
- Make a group with 5 chairs. Each group must have the same number.1 group of 5
- Keep making groups until none are left. There are 10 in all, so count the groups as you make them.5 + 5 = 10
- Count the groups. Each group is one group.2 groups
Check. Each group has 5, and 2 groups make 10. ✓
Watch out. Count the groups, not the chairs. There are 2 groups.
Method. Write one number for each row, then add them.
- Count the rows. There are 4 rows.4 rows
- Count the biscuits in each row. Each row has 2 biscuits.2 in each row
- Write the addition. Add one 2 for each row.2 + 2 + 2 + 2 = 8
- Write the answer. 2 + 2 + 2 + 2 = 8
Check. Count in 2s: 2, 4, 6, 8. The last number is 8. ✓
Watch out. Write one number for each row, not for each biscuit.
Method. Count the biscuits on the tray. Then check Ali and Jo.
- Count the rows. There are 2 rows.2 rows
- Count the biscuits in each row. Each row has 6 biscuits.6 in each row
- Add the rows. Add the two rows together.6 + 6 = 12
- Write the answer. Ali is right. Jo counted only one row.Ali is right. There are 12 biscuits.
Check. Count every row, and the total is 12. ✓
Watch out. Count every row. Jo counted only one row.
Method. Count the things in both arrays. Then explain why they match.
- Count the first array. 3 rows of 4 make 12.4 + 4 + 4 = 12
- Count the second array. 4 rows of 3 make 12.3 + 3 + 3 + 3 = 12
- Compare them. It is the same things, turned round.12 = 12
- Write the answer. Both have 12 things. Turning the array round does not change the total.
Check. Count the things in both arrays. Both give 12. ✓
Watch out. The rows and columns swap over, but the number of things stays the same.
Doubles: two equal groups
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
A double is two equal groups added together. Double 3 means two groups of 3: 3 + 3 = 6.
Look at the two groups. They are the same. Double 4 is 4 + 4 = 8.
Key ideas
- A double is two equal groups.
- To double a number, add it to itself.
- Double 5 is 5 + 5 = 10.
- Doubles can help you add quickly.
Key words. Double means two of the same, so double 2 is 2 + 2.
Method. A double is two equal groups. Double 2 is 2 + 2.
- Find the two equal groups. Both groups must be the same size.2 and 2
- Add the two groups together. Add 2 + 2.2 + 2 = 4
- Write the answer. 4
Check. Count in 2s: 2, 4. Two groups of 2 make 4. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. Double means two of the same, so double 4 is 4 + 4.
Method. A double is two equal groups. Double 4 is 4 + 4.
- Find the two equal groups. Both groups must be the same size.4 and 4
- Add the two groups together. Add 4 + 4.4 + 4 = 8
- Write the answer. 8
Check. Count in 4s: 4, 8. Two groups of 4 make 8. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. Double means two of the same, so double 6 is 6 + 6.
Method. A double is two equal groups. Double 6 is 6 + 6.
- Find the two equal groups. Both groups must be the same size.6 and 6
- Add the two groups together. Add 6 + 6.6 + 6 = 12
- Write the answer. 12
Check. Count in 6s: 6, 12. Two groups of 6 make 12. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Watch out
Watch out: a double is two of the same number. Double 4 is 4 + 4, not 4 + 5.
Exam tip
Grown-up tip. Lay out two identical rows of buttons. Ask: “Are the rows the same? How many altogether?” Then ask your child to say the double sum out loud.
Exercise 9E Doubles
Non-calculatorKey words. Double means two of the same, so double 2 is 2 + 2.
Method. A double is two equal groups. Double 2 is 2 + 2.
- Find the two equal groups. Both groups must be the same size.2 and 2
- Add the two groups together. Add 2 + 2.2 + 2 = 4
- Write the answer. 4
Check. Count in 2s: 2, 4. Two groups of 2 make 4. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. Double means two of the same, so double 3 is 3 + 3.
Method. A double is two equal groups. Double 3 is 3 + 3.
- Find the two equal groups. Both groups must be the same size.3 and 3
- Add the two groups together. Add 3 + 3.3 + 3 = 6
- Write the answer. 6
Check. Count in 3s: 3, 6. Two groups of 3 make 6. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. Double means two of the same, so double 4 is 4 + 4.
Method. A double is two equal groups. Double 4 is 4 + 4.
- Find the two equal groups. Both groups must be the same size.4 and 4
- Add the two groups together. Add 4 + 4.4 + 4 = 8
- Write the answer. 8
Check. Count in 4s: 4, 8. Two groups of 4 make 8. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. Double means two of the same, so double 1 is 1 + 1.
Method. A double is two equal groups. Double 1 is 1 + 1.
- Find the two equal groups. Both groups must be the same size.1 and 1
- Add the two groups together. Add 1 + 1.1 + 1 = 2
- Write the answer. 2
Check. Count in 1s: 1, 2. Two groups of 1 make 2. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. Double means two of the same, so double 5 is 5 + 5.
Method. A double is two equal groups. Double 5 is 5 + 5.
- Find the two equal groups. Both groups must be the same size.5 and 5
- Add the two groups together. Add 5 + 5.5 + 5 = 10
- Write the answer. 10
Check. Count in 5s: 5, 10. Two groups of 5 make 10. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. Double means two of the same, so double 9 is 9 + 9.
Method. A double is two equal groups. Double 9 is 9 + 9.
- Find the two equal groups. Both groups must be the same size.9 and 9
- Add the two groups together. Add 9 + 9.9 + 9 = 18
- Write the answer. 18
Check. Count in 9s: 9, 18. Two groups of 9 make 18. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. Double means two of the same, so double 3 is 3 + 3.
Method. A double is two equal groups. Double 3 is 3 + 3.
- Find the two equal groups. Both groups must be the same size.3 and 3
- Add the two groups together. Add 3 + 3.3 + 3 = 6
- Write the answer. 6
Check. Count in 3s: 3, 6. Two groups of 3 make 6. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. Double means two of the same, so double 7 is 7 + 7.
Method. A double is two equal groups. Double 7 is 7 + 7.
- Find the two equal groups. Both groups must be the same size.7 and 7
- Add the two groups together. Add 7 + 7.7 + 7 = 14
- Write the answer. 14
Check. Count in 7s: 7, 14. Two groups of 7 make 14. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. Double means two of the same, so double 6 is 6 + 6.
Method. A double is two equal groups. Double 6 is 6 + 6.
- Find the two equal groups. Both groups must be the same size.6 and 6
- Add the two groups together. Add 6 + 6.6 + 6 = 12
- Write the answer. 12
Check. Count in 6s: 6, 12. Two groups of 6 make 12. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. Double means two of the same, so double 5 is 5 + 5.
Method. A double is two equal groups. Double 5 is 5 + 5.
- Find the two equal groups. Both groups must be the same size.5 and 5
- Add the two groups together. Add 5 + 5.5 + 5 = 10
- Write the answer. 10
Check. Count in 5s: 5, 10. Two groups of 5 make 10. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Method. Use the double you know to help with the sum.
- Start with the double. Double 4 is 4 + 4.4 + 4 = 8
- Add one more. Four plus five is one more than four plus four.8 + 1 = 9
- Write the answer. 9
Check. Count on from 8 by one: 9. So 4 + 5 = 9. ✓
Watch out. The sum 4 + 5 is one more than 4 + 4, so the answer is one more than 8.
Method. Check the doubles of 4 and 5. Is 9 one of the answers?
- Find double 4. Four and four.4 + 4 = 8
- Find double 5. Five and five.5 + 5 = 10
- Look for 9. The answers are 8 and 10. There is no double that makes 9.8, then 10. Not 9.
- Write the answer. No. 9 cannot be made by doubling a number.
Check. Try the doubles of 1 to 5: 2, 4, 6, 8, 10. None of them is 9. ✓
Watch out. A double is always two equal groups. Check each double before you decide.
Sharing and grouping
Printable: Worksheet (PDF) · Answers (PDF) · Open this lesson on its own page
Sharing means dealing things out so everyone gets the same number. We know how many people there are, and we find how many each person gets.
Grouping means making groups of the same size. We know how many are in each group, and we find how many groups there are.
Key ideas
- Sharing: we know how many groups, and find how many in each.
- Grouping: we know how many in each group, and find how many groups.
- Deal one at a time to share fairly.
- Check that the shares add up to the total.
Key words. To share is to deal things out so everyone has the same number.
Method. Deal the things out one at a time, so that every person gets the same number.
- Count the cubes in the pile. Start with the whole pile.8
- Deal them out to 4 people, one at a time. Each person gets one, then the next one, until all are shared.Each person gets 2
- Check the shares. Every share is the same. Add them to check.2 + 2 + 2 + 2 = 8
- Write the answer. Each person gets 2.2
Check. Add the shares: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Give everyone one each, then go round again. Do not give one person all of the extra things.
Key words. To share is to deal things out so everyone has the same number.
Method. Deal the things out one at a time, so that every person gets the same number.
- Count the stars in the pile. Start with the whole pile.10
- Deal them out to 2 people, one at a time. Each person gets one, then the next one, until all are shared.Each person gets 5
- Check the shares. Every share is the same. Add them to check.5 + 5 = 10
- Write the answer. Each person gets 5.5
Check. Add the shares: 5 + 5 = 10. ✓
Watch out. Give everyone one each, then go round again. Do not give one person all of the extra things.
Key words. A group is a set of things that belong together.
Method. Put 3 in each group, and keep going until none are left. Then count the groups.
- Make a group with 3 cubes. Each group must have the same number.1 group of 3
- Keep making groups until none are left. There are 12 in all, so count the groups as you make them.3 + 3 + 3 + 3 = 12
- Count the groups. Each group is one group.4 groups
Check. Each group has 3, and 4 groups make 12. ✓
Watch out. Count the groups, not the cubes. There are 4 groups.
Watch out
Watch out: sharing asks how many in each group. Grouping asks how many groups. Read the question carefully to see which one it is.
Exam tip
Grown-up tip. Use a plate or cup for each person. Ask your child to deal one thing at a time to each plate, then ask: “Is it fair? How many are on each plate?”
Exercise 9F Sharing and grouping
Non-calculatorKey words. To share is to deal things out so everyone has the same number.
Method. Deal the things out one at a time, so that every person gets the same number.
- Count the biscuits in the pile. Start with the whole pile.4
- Deal them out to 2 people, one at a time. Each person gets one, then the next one, until all are shared.Each person gets 2
- Check the shares. Every share is the same. Add them to check.2 + 2 = 4
- Write the answer. Each person gets 2.2
Check. Add the shares: 2 + 2 = 4. ✓
Watch out. Give everyone one each, then go round again. Do not give one person all of the extra things.
Key words. To share is to deal things out so everyone has the same number.
Method. Deal the things out one at a time, so that every person gets the same number.
- Count the biscuits in the pile. Start with the whole pile.6
- Deal them out to 2 people, one at a time. Each person gets one, then the next one, until all are shared.Each person gets 3
- Check the shares. Every share is the same. Add them to check.3 + 3 = 6
- Write the answer. Each person gets 3.3
Check. Add the shares: 3 + 3 = 6. ✓
Watch out. Give everyone one each, then go round again. Do not give one person all of the extra things.
Key words. To share is to deal things out so everyone has the same number.
Method. Deal the things out one at a time, so that every person gets the same number.
- Count the stars in the pile. Start with the whole pile.9
- Deal them out to 3 people, one at a time. Each person gets one, then the next one, until all are shared.Each person gets 3
- Check the shares. Every share is the same. Add them to check.3 + 3 + 3 = 9
- Write the answer. Each person gets 3.3
Check. Add the shares: 3 + 3 + 3 = 9. ✓
Watch out. Give everyone one each, then go round again. Do not give one person all of the extra things.
Key words. To share is to deal things out so everyone has the same number.
Method. Deal the things out one at a time, so that every person gets the same number.
- Count the pencils in the pile. Start with the whole pile.10
- Deal them out to 5 people, one at a time. Each person gets one, then the next one, until all are shared.Each person gets 2
- Check the shares. Every share is the same. Add them to check.2 + 2 + 2 + 2 + 2 = 10
- Write the answer. Each person gets 2.2
Check. Add the shares: 2 + 2 + 2 + 2 + 2 = 10. ✓
Watch out. Give everyone one each, then go round again. Do not give one person all of the extra things.
Key words. A group is a set of things that belong together.
Method. Put 3 in each group, and keep going until none are left. Then count the groups.
- Make a group with 3 cubes. Each group must have the same number.1 group of 3
- Keep making groups until none are left. There are 6 in all, so count the groups as you make them.3 + 3 = 6
- Count the groups. Each group is one group.2 groups
Check. Each group has 3, and 2 groups make 6. ✓
Watch out. Count the groups, not the cubes. There are 2 groups.
Key words. A group is a set of things that belong together.
Method. Put 4 in each group, and keep going until none are left. Then count the groups.
- Make a group with 4 balls. Each group must have the same number.1 group of 4
- Keep making groups until none are left. There are 8 in all, so count the groups as you make them.4 + 4 = 8
- Count the groups. Each group is one group.2 groups
Check. Each group has 4, and 2 groups make 8. ✓
Watch out. Count the groups, not the balls. There are 2 groups.
Key words. A group is a set of things that belong together.
Method. Put 2 in each group, and keep going until none are left. Then count the groups.
- Make a group with 2 socks. Each group must have the same number.1 group of 2
- Keep making groups until none are left. There are 10 in all, so count the groups as you make them.2 + 2 + 2 + 2 + 2 = 10
- Count the groups. Each group is one group.5 groups
Check. Each group has 2, and 5 groups make 10. ✓
Watch out. Count the groups, not the socks. There are 5 groups.
Key words. To share is to deal things out so everyone has the same number.
Method. Deal the things out one at a time, so that every person gets the same number.
- Count the apples in the pile. Start with the whole pile.10
- Deal them out to 2 people, one at a time. Each person gets one, then the next one, until all are shared.Each person gets 5
- Check the shares. Every share is the same. Add them to check.5 + 5 = 10
- Write the answer. Each person gets 5.5
Check. Add the shares: 5 + 5 = 10. ✓
Watch out. Give everyone one each, then go round again. Do not give one person all of the extra things.
Key words. To share is to deal things out so everyone has the same number.
Method. Deal the things out one at a time, so that every person gets the same number.
- Count the apples in the pile. Start with the whole pile.10
- Deal them out to 5 people, one at a time. Each person gets one, then the next one, until all are shared.Each person gets 2
- Check the shares. Every share is the same. Add them to check.2 + 2 + 2 + 2 + 2 = 10
- Write the answer. Each person gets 2.2
Check. Add the shares: 2 + 2 + 2 + 2 + 2 = 10. ✓
Watch out. Give everyone one each, then go round again. Do not give one person all of the extra things.
Key words. To share is to deal things out so everyone has the same number.
Method. Deal the things out one at a time, so that every person gets the same number.
- Count the apples in the pile. Start with the whole pile.10
- Deal them out to 10 people, one at a time. Each person gets one, then the next one, until all are shared.Each person gets 1
- Check the shares. Every share is the same. Add them to check.1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10
- Write the answer. Each person gets 1.1
Check. Add the shares: 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10. ✓
Watch out. Give everyone one each, then go round again. Do not give one person all of the extra things.
Key words. To share is to deal things out so everyone has the same number.
Method. Deal the things out one at a time, so that every person gets the same number.
- Count the stickers in the pile. Start with the whole pile.15
- Deal them out to 3 people, one at a time. Each person gets one, then the next one, until all are shared.Each person gets 5
- Check the shares. Every share is the same. Add them to check.5 + 5 + 5 = 15
- Write the answer. Each person gets 5.5
Check. Add the shares: 5 + 5 + 5 = 15. ✓
Watch out. Give everyone one each, then go round again. Do not give one person all of the extra things.
Key words. A group is a set of things that belong together.
Method. Put 4 in each group, and keep going until none are left. Then count the groups.
- Make a group with 4 biscuits. Each group must have the same number.1 group of 4
- Keep making groups until none are left. There are 12 in all, so count the groups as you make them.4 + 4 + 4 = 12
- Count the groups. Each group is one group.3 groups
Check. Each group has 4, and 3 groups make 12. ✓
Watch out. Count the groups, not the biscuits. There are 3 groups.
Method. Count how many sweets each child has. Is the sharing equal?
- Count Ruby’s sweets. Ruby keeps 3 sweets.Ruby: 3
- Count her friend’s sweets. Her friend gets 5 sweets.Friend: 5
- Compare the numbers. Equal sharing means both get the same number.5 is not 3
- Write the answer. No. Ruby does not share equally, so it is not fair.
Check. Equal sharing of 8 between 2 people would give 4 each. 3 and 5 are not the same. ✓
Watch out. Fair sharing means the same number for each person.
Chapter summary
| Skill | Method |
|---|---|
| Count in 2s, 5s and 10s | Jump on by the same number each time, and say each number. |
| Equal groups | The same number in each group. Count one group to find how many are in each. |
| Adding equal groups | Write one number for each group and add them. For example 4 + 4 + 4 = 12. |
| Arrays | Count the rows, count the things in one row, then add the rows together. |
| Doubles | Two equal groups. Double 4 is 4 + 4 = 8. |
| Sharing and grouping | Sharing: deal the things out equally. Grouping: count how many groups of the same size. |
Can you…?
- I can count in 2s, 5s and 10s
- I can say whether groups are equal, and make equal groups
- I can add equal groups to find the total
- I can count the rows and columns of an array
- I can find a double as two equal groups
- I can share things equally and put them into equal groups
Key terms
- equal groups
- groups that have the same number of things in each group
- group
- a set of things that belong together
- array
- things arranged in neat rows and columns
- row
- things lined up across
- column
- things lined up down
- double
- two equal groups, or a number added to itself
- share
- to deal things out so everyone has the same number
- count in steps
- count on by the same number each time, such as 2s, 5s or 10s
Exercise 9Z Check-up
Non-calculatorMethod. Start at 6. Count on in 2s to find the next 3 numbers.
- Start at 6. Start with the number you are given.6
- Jump on by 2 each time. Each new number is the last one plus the jump.6 + 2 = 8
8 + 2 = 10
10 + 2 = 12 - Write the next numbers. Do not write the start number again.8, 10, 12
Check. Count back in 2s from 12 to 6 to check. ✓
Watch out. Do not write the number you start at. Start with the next one.
Key words. Counting in 5s means jumping on by 5 each time.
Method. Count in 5s. Every jump is the same size: 5.
- Start at 5. Put your finger on the first number.5
- Jump on by 5 each time. Each number is 5 more than the one before.5 + 5 = 10
10 + 5 = 15
15 + 5 = 20
20 + 5 = 25 - Write the numbers. Say them in order, one jump at a time.5, 10, 15, 20, 25
Check. Count back in 5s from 25 to check. ✓
Watch out. Keep the same jump all the way. Every number must be 5 more than the one before.
Method. Equal groups have the same number of things in each group.
- Count the things in each group. Touch each thing once.group 1 has 2, group 2 has 3
- Compare the numbers. The groups are equal only if every number is the same.Not all the same
- Write the answer. No. The groups are not equal.
Check. Count the things in each group again. ✓
Watch out. Groups can look the same size on the page. Always count each group.
Key words. A group is a set of things that belong together.
Method. Put 2 in each group, and keep going until none are left. Then count the groups.
- Make a group with 2 cubes. Each group must have the same number.1 group of 2
- Keep making groups until none are left. There are 8 in all, so count the groups as you make them.2 + 2 + 2 + 2 = 8
- Count the groups. Each group is one group.4 groups
Check. Each group has 2, and 4 groups make 8. ✓
Watch out. Count the groups, not the cubes. There are 4 groups.
Key words. Equal groups have the same number of things in each group.
Method. Add the same number 3 times, once for each group. Each group has 4.
- Write one 4 for each group. There are 3 groups, so there are 3 numbers to add.4 + 4 + 4
- Add the numbers together. Count in 4s to add them up: 4, 8, 12.4 + 4 + 4 = 12
- Write the answer. 12
Check. Count in 4s: 4, 8, 12. The last number is 12. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. A row goes across. A column goes down. An array is things in rows and columns.
Method. Count the rows. Every row has the same number, so add that number once for each row.
- Count the rows. A row goes across.2 rows
- Count the things in one row. Every row has the same number.5 in each row
- Add one number for each row. Add the rows together.5 + 5 = 10
- Write the answer. 10
Check. Count down the columns too: 2 + 2 + 2 + 2 + 2 = 10. ✓
Watch out. Count each row once. Do not count a thing twice.
Key words. Double means two of the same, so double 4 is 4 + 4.
Method. A double is two equal groups. Double 4 is 4 + 4.
- Find the two equal groups. Both groups must be the same size.4 and 4
- Add the two groups together. Add 4 + 4.4 + 4 = 8
- Write the answer. 8
Check. Count in 4s: 4, 8. Two groups of 4 make 8. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. To share is to deal things out so everyone has the same number.
Method. Deal the things out one at a time, so that every person gets the same number.
- Count the stars in the pile. Start with the whole pile.10
- Deal them out to 2 people, one at a time. Each person gets one, then the next one, until all are shared.Each person gets 5
- Check the shares. Every share is the same. Add them to check.5 + 5 = 10
- Write the answer. Each person gets 5.5
Check. Add the shares: 5 + 5 = 10. ✓
Watch out. Give everyone one each, then go round again. Do not give one person all of the extra things.
Key words. Counting in 2s means jumping on by 2 each time.
Method. Count in 2s. Every jump is the same size: 2.
- Start at 2. Put your finger on the first number.2
- Jump on by 2 each time. Each number is 2 more than the one before.2 + 2 = 4
4 + 2 = 6
6 + 2 = 8
8 + 2 = 10 - Write the numbers. Say them in order, one jump at a time.2, 4, 6, 8, 10
Check. Count back in 2s from 10 to check. ✓
Watch out. Keep the same jump all the way. Every number must be 2 more than the one before.
Key words. Equal groups have the same number of biscuits in each group.
Method. Add the same number 3 times, once for each group. Each group has 5.
- Write one 5 for each group. There are 3 groups, so there are 3 numbers to add.5 + 5 + 5
- Add the numbers together. Count in 5s to add them up: 5, 10, 15.5 + 5 + 5 = 15
- Write the answer. 15
Check. Count in 5s: 5, 10, 15. The last number is 15. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Total 14 marks. Allow about 14 minutes.
Exercise 9X End-of-chapter quiz
Non-calculatorMethod. Count in 2s. Each number is 2 more than the one before it.
- Look at the numbers before and after each gap. The jump is the same every time.2, 4, ?, 8
- Add 2 to the number before each gap. That gives the missing number.Gap 3: 4 + 2 = 6
- Write the missing numbers. 6
Check. Count in 2s all the way along the list. Every number fits. ✓
Watch out. Check the numbers after the gap too. They should still go up in the same jump.
Method. Count in 10s. Each number is 10 more than the one before it.
- Look at the numbers before and after each gap. The jump is the same every time.10, 20, ?, 40
- Add 10 to the number before each gap. That gives the missing number.Gap 3: 20 + 10 = 30
- Write the missing numbers. 30
Check. Count in 10s all the way along the list. Every number fits. ✓
Watch out. Check the numbers after the gap too. They should still go up in the same jump.
Key words. Equal groups have the same number of stars in each group.
Method. Add the same number 2 times, once for each group. Each group has 4.
- Write one 4 for each group. There are 2 groups, so there are 2 numbers to add.4 + 4
- Add the numbers together. Count in 4s to add them up: 4, 8.4 + 4 = 8
- Write the answer. 8
Check. Count in 4s: 4, 8. The last number is 8. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Key words. A row goes across. A column goes down. An array is things in rows and columns.
Method. Count the rows. Every row has the same number, so add that number once for each row.
- Count the rows. A row goes across.3 rows
- Count the things in one row. Every row has the same number.3 in each row
- Add one number for each row. Add the rows together.3 + 3 + 3 = 9
- Write the answer. 9
Check. Count down the columns too: 3 + 3 + 3 = 9. ✓
Watch out. Count each row once. Do not count a thing twice.
Key words. Double means two of the same, so double 5 is 5 + 5.
Method. A double is two equal groups. Double 5 is 5 + 5.
- Find the two equal groups. Both groups must be the same size.5 and 5
- Add the two groups together. Add 5 + 5.5 + 5 = 10
- Write the answer. 10
Check. Count in 5s: 5, 10. Two groups of 5 make 10. ✓
Watch out. A double is two groups of the same size. Do not add a different number.
Key words. A group is a set of things that belong together.
Method. Put 2 in each group, and keep going until none are left. Then count the groups.
- Make a group with 2 biscuits. Each group must have the same number.1 group of 2
- Keep making groups until none are left. There are 8 in all, so count the groups as you make them.2 + 2 + 2 + 2 = 8
- Count the groups. Each group is one group.4 groups
Check. Each group has 2, and 4 groups make 8. ✓
Watch out. Count the groups, not the biscuits. There are 4 groups.
Key words. To share is to deal things out so everyone has the same number.
Method. Deal the things out one at a time, so that every person gets the same number.
- Count the stickers in the pile. Start with the whole pile.12
- Deal them out to 4 people, one at a time. Each person gets one, then the next one, until all are shared.Each person gets 3
- Check the shares. Every share is the same. Add them to check.3 + 3 + 3 + 3 = 12
- Write the answer. Each person gets 3.3
Check. Add the shares: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Give everyone one each, then go round again. Do not give one person all of the extra things.
Key words. Equal groups have the same number of apples in each group.
Method. Add the same number 4 times, once for each group. Each group has 5.
- Write one 5 for each group. There are 4 groups, so there are 4 numbers to add.5 + 5 + 5 + 5
- Add the numbers together. Count in 5s to add them up: 5, 10, 15, 20.5 + 5 + 5 + 5 = 20
- Write the answer. 20
Check. Count in 5s: 5, 10, 15, 20. The last number is 20. ✓
Watch out. Write one number for every group. Do not write the number of groups instead.
Method. Add up each sum, then compare the totals.
- Add the first sum. Three plus three plus three plus three.3 + 3 + 3 + 3 = 12
- Add the second sum. Four plus four plus four.4 + 4 + 4 = 12
- Compare the totals. Both sums make the same total.12 = 12
- Write the answer. Yes. Both sums make 12.
Check. Count in 3s to 12: 3, 6, 9, 12. Count in 4s to 12: 4, 8, 12. ✓
Watch out. Count in the same jump to check each sum.
Method. Double 6 means two equal groups of 6. Add them to check Ruby.
- Find the two equal groups. Both groups must be the same size.6 and 6
- Add the two groups together. Add 6 + 6.6 + 6 = 12
- Compare with what Ruby said. Ruby said 12, which matches.12 = 12
- Write the answer. Yes. 6 + 6 = 12.
Check. Count in 6s: 6, 12. Two groups of 6 make 12. ✓
Watch out. Check the answer by adding the two groups, not by guessing.