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Step-by-step practice: Maths · Level 4Chapter 6 · Division as sharing and grouping
Level 4 · Chapter 6

Division as sharing and grouping

By the end of this chapter you will be able to

  • Share a set into equal groups
  • Find how many equal groups can be made
  • Write a division statement from a picture
  • Use multiplication to check a division
  • Solve sharing and grouping problems

You should already know

  • Times tables 3 and 4 (chapter 4)
  • Times tables 6, 8 and 9 (chapter 5)

Where this leads

  • Fractions of wholes and equivalent fractions (chapter 7)

Step-by-step practice: maths (Level 4). Small steps, repeated until fluent. Content: Share a set of objects into equal groups and say how many are in each group (Year 4 paraphrase), Find how many equal groups can be made from a set, by grouping (MD2, Year 4 paraphrase), Write a division statement with the division sign and = (MD2), Show that division is the inverse of multiplication (MD2), Solve sharing and grouping problems, including correspondence problems (MD3).

Exercise P  Do you remember?

Non-calculator
1
FWhat is 9 × 5?
2
FWhat is 6 × 6?
3
PSShare 14 counters equally between 2 children. How many does each child get?
4
FWhat is 5 × 4?
5
FWhat is 8 + 8 + 8?
6.1

Sharing into equal groups

Level 4
Share a set of objects into equal groups, and say how many are in each group
Video lesson: Sharing into equal groupsComing soon

Sharing means putting the same number into each group. Each friend, plate or box gets the same amount.

Share one at a time, or divide the total by the number of groups.

Key ideas

  • Sharing: the number of groups is known.
  • Share equally: each group has the same number.
  • Divide the total by the number of groups.
Worked example 6.1.1
Sam shares 24 sweets equally between 4 friends. How many sweets does each friend get?

Method. Sharing: put the same number into each group. Divide the total by the number of groups.

  1. Count the friends. Each friend gets the same number.
    4 friends
  2. Share the sweets one at a time. Put one in each group, then start again until none are left.
    24 shared into 4 groups
  3. Count the sweets in one group. Each group has the same number.
    24 ÷ 4 = 6
  4. Write the answer. This is how many each friend gets.
    6

Check. Check: 6 × 4 = 24.

Watch out. The number of friends is the number of groups.

Worked example 6.1.2
There are 20 buttons. How many bags of 4 can be made?

Method. Grouping: count how many groups of the size you are given can be made from the total.

  1. Count in fours until you reach 20. Each bag takes 4. Count one bag at a time.
    4, 8, 12, 16, 20
  2. Count the bags. Each count is one full bag of 4.
    5 bags
  3. Write the answer. This is the number of bags.
    5

Check. Check: 5 × 4 = 20.

Watch out. In grouping, you are given the size of each group.

Worked example 6.1.3
A class has 20 chairs for the children. Each table has 4 chairs. How many tables are needed?

Method. Each table connects to the same number of chairs. Find how many groups of the table size make the total.

  1. Work out what we need to find. We need the number of tables.
    20 chairs in all
  2. Count in fours until you reach 20. Each table takes 4 chairs.
    4, 8, 12, 16, 20
  3. Count the tables. Each count is one table.
    5 tables
  4. Write the answer. This is the number of tables.
    5

Check. Check: 5 tables × 4 chairs = 20.

Watch out. Each table is one group.

Watch out

Watch out. When you share 24 into 4 groups, each group gets 6. The number of groups is 4, not 6.

Exam tip

Grown-up tip. Use real objects. Ask the child to share 12 counters between 3 people, one at a time, then say how many each got.

Exercise 6A  Practice: sharing into equal groups

Non-calculator
1
PSRuby shares 12 buttons equally between 4 friends. How many buttons does each friend get?
2
PSAmira shares 24 sweets equally between 8 friends. How many sweets does each friend get?
3
PSNoah shares 16 sweets equally between 2 friends. How many sweets does each friend get?
4
PSMei shares 6 biscuits equally between 2 friends. How many biscuits does each friend get?
5
PSSam shares 12 buttons equally between 2 friends. How many buttons does each friend get?
6
PSNoah shares 24 sweets equally between 4 friends. How many sweets does each friend get?
7
PSKofi shares 45 pencils equally between 5 friends. How many pencils does each friend get?
8
PSSam shares 16 sweets equally between 4 friends. How many sweets does each friend get?
9
PSSam shares 12 buttons equally between 6 friends. How many buttons does each friend get?
10
PSKofi shares 48 sweets equally between 8 friends. How many sweets does each friend get?
11
PSAmira shares 30 biscuits equally between 5 friends. How many biscuits does each friend get?
12
PSMei shares 40 sweets equally between 5 friends. How many sweets does each friend get?
13
PSRuby shares 12 buttons equally between 3 friends. How many buttons does each friend get?
14
PSNoah shares 21 pencils equally between 3 friends. How many pencils does each friend get?
15
PSRuby shares 10 counters equally between 2 friends. How many counters does each friend get?
16
PSKofi shares 48 sweets equally between 6 friends. How many sweets does each friend get?
6.2

Grouping: how many groups can be made?

Level 4
Find how many equal groups of a given size can be made from a set
Video lesson: Grouping: how many groups can be made?Coming soon

In grouping, you know how big each group must be. You need to find how many groups you can make.

Count in steps of the group size until you reach the total. Count the steps.

Key ideas

  • Grouping: the size of each group is known.
  • Count in steps of the group size.
  • Count the groups you make.
Worked example 6.2.1
There are 20 buttons. How many bags of 4 can be made?

Method. Grouping: count how many groups of the size you are given can be made from the total.

  1. Count in fours until you reach 20. Each bag takes 4. Count one bag at a time.
    4, 8, 12, 16, 20
  2. Count the bags. Each count is one full bag of 4.
    5 bags
  3. Write the answer. This is the number of bags.
    5

Check. Check: 5 × 4 = 20.

Watch out. In grouping, you are given the size of each group.

Worked example 6.2.2
A class has 20 chairs for the children. Each table has 4 chairs. How many tables are needed?

Method. Each table connects to the same number of chairs. Find how many groups of the table size make the total.

  1. Work out what we need to find. We need the number of tables.
    20 chairs in all
  2. Count in fours until you reach 20. Each table takes 4 chairs.
    4, 8, 12, 16, 20
  3. Count the tables. Each count is one table.
    5 tables
  4. Write the answer. This is the number of tables.
    5

Check. Check: 5 tables × 4 chairs = 20.

Watch out. Each table is one group.

Worked example 6.2.3
Sam shares 24 sweets equally between 4 friends. How many sweets does each friend get?

Method. Sharing: put the same number into each group. Divide the total by the number of groups.

  1. Count the friends. Each friend gets the same number.
    4 friends
  2. Share the sweets one at a time. Put one in each group, then start again until none are left.
    24 shared into 4 groups
  3. Count the sweets in one group. Each group has the same number.
    24 ÷ 4 = 6
  4. Write the answer. This is how many each friend gets.
    6

Check. Check: 6 × 4 = 24.

Watch out. The number of friends is the number of groups.

Watch out

Watch out. In 20 buttons in bags of 4, there are 5 bags, not 4. Count the bags, not the buttons.

Exam tip

Grown-up tip. Ask: “How many in each bag? How many bags can you fill?”

Exercise 6B  Practice: grouping

Non-calculator
1
PSThere are 15 sweets. How many bags of 5 can be made?
2
PSThere are 12 marbles. How many bags of 4 can be made?
3
PSThere are 12 marbles. How many bags of 3 can be made?
4
PSThere are 30 cards. How many bags of 5 can be made?
5
PSThere are 28 cards. How many bags of 4 can be made?
6
PSThere are 8 biscuits. How many bags of 2 can be made?
7
PSThere are 36 buttons. How many bags of 6 can be made?
8
PSThere are 20 stickers. How many bags of 4 can be made?
9
PSThere are 10 marbles. How many bags of 5 can be made?
10
PSThere are 24 cards. How many bags of 3 can be made?
11
PSThere are 35 buttons. How many bags of 5 can be made?
12
PSThere are 18 cards. How many bags of 2 can be made?
13
PSThere are 12 sweets. How many bags of 6 can be made?
14
PSThere are 10 marbles. How many bags of 2 can be made?
15
PSThere are 16 sweets. How many bags of 4 can be made?
16
PSThere are 18 stickers. How many bags of 3 can be made?
6.3

Writing division statements

Level 4
Write a division statement with the division sign and =, Read a division from a picture of equal rows or groups
Video lesson: Writing division statementsComing soon

A division statement uses ÷ for division and = for the answer. For example, 24 ÷ 3 = 8.

An array of dots in equal rows can show a division. The total is the first number, the number of rows is the second.

Key ideas

  • ÷ means divide; = means the answer is.
  • The total is divided by the number of groups or rows.
  • Check the division with multiplication.
Worked example 6.3.1
The array shows 24 dots in 3 equal rows. How many dots are in each row? Write the division: 24 ÷ 3 = ___

Method. An array shows equal groups. Divide the total by the number of rows to find the number in each row.

  1. Read the array. The dots are in equal rows.
    3 rows, 24 dots
  2. Share the dots into the rows. Each row has the same number of dots.
    24 ÷ 3 = 8
  3. Check with multiplication. Rows × dots in each row gives the total.
    3 × 8 = 24
  4. Write the answer. This is the number in each row.
    8

Check. Check: 3 rows of 8 make 24.

Watch out. The number of rows is the divisor.

Worked example 6.3.2
The array shows 35 dots in 5 equal rows. How many dots are in each row? Write the division: 35 ÷ 5 = ___

Method. An array shows equal groups. Divide the total by the number of rows to find the number in each row.

  1. Read the array. The dots are in equal rows.
    5 rows, 35 dots
  2. Share the dots into the rows. Each row has the same number of dots.
    35 ÷ 5 = 7
  3. Check with multiplication. Rows × dots in each row gives the total.
    5 × 7 = 35
  4. Write the answer. This is the number in each row.
    7

Check. Check: 5 rows of 7 make 35.

Watch out. The number of rows is the divisor.

Worked example 6.3.3
Sam shares 24 sweets equally between 4 friends. How many sweets does each friend get?

Method. Sharing: put the same number into each group. Divide the total by the number of groups.

  1. Count the friends. Each friend gets the same number.
    4 friends
  2. Share the sweets one at a time. Put one in each group, then start again until none are left.
    24 shared into 4 groups
  3. Count the sweets in one group. Each group has the same number.
    24 ÷ 4 = 6
  4. Write the answer. This is how many each friend gets.
    6

Check. Check: 6 × 4 = 24.

Watch out. The number of friends is the number of groups.

Watch out

Watch out. 24 ÷ 3 is not 3 ÷ 24. The total goes first, then the number of groups.

Exam tip

Grown-up tip. Ask the child to read the division aloud: “Twenty-four shared into three groups is eight.”

Exercise 6C  Practice: division statements and arrays

Non-calculator
1
FThe array shows 9 dots in 3 equal rows. How many dots are in each row? Write the division: 9 ÷ 3 = ___
2
FThe array shows 14 dots in 2 equal rows. How many dots are in each row? Write the division: 14 ÷ 2 = ___
3
FThe array shows 4 dots in 2 equal rows. How many dots are in each row? Write the division: 4 ÷ 2 = ___
4
FThe array shows 24 dots in 3 equal rows. How many dots are in each row? Write the division: 24 ÷ 3 = ___
5
FThe array shows 12 dots in 4 equal rows. How many dots are in each row? Write the division: 12 ÷ 4 = ___
6
FThe array shows 18 dots in 2 equal rows. How many dots are in each row? Write the division: 18 ÷ 2 = ___
7
FThe array shows 30 dots in 6 equal rows. How many dots are in each row? Write the division: 30 ÷ 6 = ___
8
FThe array shows 40 dots in 5 equal rows. How many dots are in each row? Write the division: 40 ÷ 5 = ___
9
FThe array shows 27 dots in 3 equal rows. How many dots are in each row? Write the division: 27 ÷ 3 = ___
10
FThe array shows 48 dots in 6 equal rows. How many dots are in each row? Write the division: 48 ÷ 6 = ___
11
FThe array shows 15 dots in 5 equal rows. How many dots are in each row? Write the division: 15 ÷ 5 = ___
12
FThe array shows 6 dots in 3 equal rows. How many dots are in each row? Write the division: 6 ÷ 3 = ___
13
FThe array shows 16 dots in 4 equal rows. How many dots are in each row? Write the division: 16 ÷ 4 = ___
14
FThe array shows 12 dots in 6 equal rows. How many dots are in each row? Write the division: 12 ÷ 6 = ___
15
FThe array shows 20 dots in 4 equal rows. How many dots are in each row? Write the division: 20 ÷ 4 = ___
16
FThe array shows 42 dots in 6 equal rows. How many dots are in each row? Write the division: 42 ÷ 6 = ___
6.4

Division is the inverse of multiplication

Level 4
Show that division undoes multiplication, and use a times table fact to find a division
Video lesson: Division is the inverse of multiplicationComing soon

Multiplication and division are opposites. If 6 × 9 = 54, then 54 ÷ 6 = 9 and 54 ÷ 9 = 6.

Use the times table you know to find the division. Check by multiplying back.

Key ideas

  • A multiplication fact gives two divisions.
  • Division is the inverse of multiplication.
  • Check with multiplication: groups × size = total.
Worked example 6.4.1
We know that 6 × 9 = 54. Use this to find 54 ÷ 6. Write the answer.

Method. Division is the inverse of multiplication. Use the times table fact to find the division.

  1. Write the fact: 6 × 9 = 54. This is the multiplication we know.
    6 × 9 = 54
  2. Turn it round to division. Division undoes multiplication, so the total is shared into groups of 6.
    54 ÷ 6 = 9
  3. Write the answer. The number of groups is the answer.
    9

Check. Check: 9 × 6 = 54, so 54 ÷ 6 = 9.

Watch out. The same three numbers make the division.

Worked example 6.4.2
Sam shares 24 sweets equally between 4 friends. How many sweets does each friend get?

Method. Sharing: put the same number into each group. Divide the total by the number of groups.

  1. Count the friends. Each friend gets the same number.
    4 friends
  2. Share the sweets one at a time. Put one in each group, then start again until none are left.
    24 shared into 4 groups
  3. Count the sweets in one group. Each group has the same number.
    24 ÷ 4 = 6
  4. Write the answer. This is how many each friend gets.
    6

Check. Check: 6 × 4 = 24.

Watch out. The number of friends is the number of groups.

Worked example 6.4.3
There are 20 buttons. How many bags of 4 can be made?

Method. Grouping: count how many groups of the size you are given can be made from the total.

  1. Count in fours until you reach 20. Each bag takes 4. Count one bag at a time.
    4, 8, 12, 16, 20
  2. Count the bags. Each count is one full bag of 4.
    5 bags
  3. Write the answer. This is the number of bags.
    5

Check. Check: 5 × 4 = 20.

Watch out. In grouping, you are given the size of each group.

Watch out

Watch out. 54 ÷ 6 is 9, because 6 × 9 = 54. Do not divide 6 by 54.

Exam tip

Grown-up tip. Ask: “Which times table fact helps you here?” before the child works out the division.

Exercise 6D  Practice: division and multiplication together

Non-calculator
1
FWe know that 2 × 11 = 22. Use this to find 22 ÷ 2. Write the answer.
2
FWe know that 6 × 3 = 18. Use this to find 18 ÷ 6. Write the answer.
3
FWe know that 2 × 5 = 10. Use this to find 10 ÷ 2. Write the answer.
4
FWe know that 8 × 11 = 88. Use this to find 88 ÷ 8. Write the answer.
5
FWe know that 10 × 2 = 20. Use this to find 20 ÷ 10. Write the answer.
6
FWe know that 10 × 12 = 120. Use this to find 120 ÷ 10. Write the answer.
7
FWe know that 8 × 6 = 48. Use this to find 48 ÷ 8. Write the answer.
8
FWe know that 9 × 6 = 54. Use this to find 54 ÷ 9. Write the answer.
9
FWe know that 8 × 5 = 40. Use this to find 40 ÷ 8. Write the answer.
10
FWe know that 2 × 6 = 12. Use this to find 12 ÷ 2. Write the answer.
11
FWe know that 8 × 3 = 24. Use this to find 24 ÷ 8. Write the answer.
12
FWe know that 5 × 10 = 50. Use this to find 50 ÷ 5. Write the answer.
13
FWe know that 9 × 2 = 18. Use this to find 18 ÷ 9. Write the answer.
14
FWe know that 3 × 11 = 33. Use this to find 33 ÷ 3. Write the answer.
15
FWe know that 6 × 8 = 48. Use this to find 48 ÷ 6. Write the answer.
16
FWe know that 4 × 4 = 16. Use this to find 16 ÷ 4. Write the answer.
6.5

Sharing and grouping problems

Level 4
Solve sharing and grouping problems with the tables the child knows, Solve correspondence problems: each table takes the same number of places
Video lesson: Sharing and grouping problemsComing soon

Read the question carefully. Ask: am I sharing into a number of groups, or making groups of a set size?

A correspondence problem links two sets. Each table has the same number of chairs, so the number of chairs is shared out by the tables.

Key ideas

  • Sharing: the number of groups is known.
  • Grouping: the size of each group is known.
  • Correspondence: each group matches a fixed number.
Worked example 6.5.1
A class has 20 chairs for the children. Each table has 4 chairs. How many tables are needed?

Method. Each table connects to the same number of chairs. Find how many groups of the table size make the total.

  1. Work out what we need to find. We need the number of tables.
    20 chairs in all
  2. Count in fours until you reach 20. Each table takes 4 chairs.
    4, 8, 12, 16, 20
  3. Count the tables. Each count is one table.
    5 tables
  4. Write the answer. This is the number of tables.
    5

Check. Check: 5 tables × 4 chairs = 20.

Watch out. Each table is one group.

Worked example 6.5.2
Sam shares 24 sweets equally between 4 friends. How many sweets does each friend get?

Method. Sharing: put the same number into each group. Divide the total by the number of groups.

  1. Count the friends. Each friend gets the same number.
    4 friends
  2. Share the sweets one at a time. Put one in each group, then start again until none are left.
    24 shared into 4 groups
  3. Count the sweets in one group. Each group has the same number.
    24 ÷ 4 = 6
  4. Write the answer. This is how many each friend gets.
    6

Check. Check: 6 × 4 = 24.

Watch out. The number of friends is the number of groups.

Worked example 6.5.3
There are 20 buttons. How many bags of 4 can be made?

Method. Grouping: count how many groups of the size you are given can be made from the total.

  1. Count in fours until you reach 20. Each bag takes 4. Count one bag at a time.
    4, 8, 12, 16, 20
  2. Count the bags. Each count is one full bag of 4.
    5 bags
  3. Write the answer. This is the number of bags.
    5

Check. Check: 5 × 4 = 20.

Watch out. In grouping, you are given the size of each group.

Watch out

Watch out. Find the question word first: “how many each” means sharing, “how many groups” means grouping.

Exam tip

Grown-up tip. Ask the child to say: “Am I sharing or grouping?” before writing the division.

Exercise 6E  Practice: sharing and grouping problems

Non-calculator
1
PSA class has 42 seats for the children. Each table has 6 seats. How many tables are needed?
2
PSThere are 35 buttons. How many bags of 5 can be made?
3
PSPriya shares 72 sweets equally between 8 friends. How many sweets does each friend get?
4
PSNoah shares 25 stickers equally between 5 friends. How many stickers does each friend get?
5
PSLeo shares 32 sweets equally between 8 friends. How many sweets does each friend get?
6
PSA class has 8 seats for the children. Each table has 4 seats. How many tables are needed?
7
PSA class has 36 chairs for the children. Each table has 4 chairs. How many tables are needed?
8
PSPriya shares 18 counters equally between 3 friends. How many counters does each friend get?
9
PSRuby shares 54 biscuits equally between 6 friends. How many biscuits does each friend get?
10
PSSam shares 12 buttons equally between 6 friends. How many buttons does each friend get?
11
PSA class has 42 chairs for the children. Each table has 6 chairs. How many tables are needed?
12
PSA class has 25 seats for the children. Each table has 5 seats. How many tables are needed?
13
PSThere are 12 marbles. How many bags of 3 can be made?
14
PSA class has 12 places for the children. Each table has 4 places. How many tables are needed?
15
PSA class has 40 places for the children. Each table has 5 places. How many tables are needed?
16
PSThere are 4 buttons. How many bags of 2 can be made?

Chapter summary

SkillMethod
SharingPut the same number into each group; divide the total by the number of groups
GroupingCount in steps of the group size; count the groups
Division statementsTotal ÷ number of groups = number in each group
InverseUse a times table fact to find a division; check by multiplying back
ProblemsAsk: am I sharing into groups, or making groups of a set size?

Can you…?

  • I can share a set into equal groups and say how many are in each group
  • I can find how many equal groups can be made from a set
  • I can write a division statement with the division sign and =
  • I can use a multiplication fact to find a division
  • I can solve sharing, grouping and correspondence problems

Key terms

divide
share into equal groups or find how many groups; the sign is ÷
share
put the same number into each group
group
put together a set of items in equal sets of a given size
inverse
the operation that undoes another; division undoes multiplication

Exercise 6Z  Check-up

Non-calculator
1
We know that 8 × 4 = 32. Use this to find 32 ÷ 8. Write the answer.
2
The array shows 12 dots in 3 equal rows. How many dots are in each row? Write the division: 12 ÷ 3 = ___
3
There are 27 buttons. How many bags of 3 can be made?
4
The array shows 32 dots in 4 equal rows. How many dots are in each row? Write the division: 32 ÷ 4 = ___
5
There are 6 pencils. How many bags of 3 can be made?
6
We know that 9 × 11 = 99. Use this to find 99 ÷ 9. Write the answer.
7
There are 16 counters. How many bags of 2 can be made?
8
Leo shares 32 sweets equally between 8 friends. How many sweets does each friend get?
9
Leo shares 4 buttons equally between 2 friends. How many buttons does each friend get?
10
Ruby shares 54 biscuits equally between 6 friends. How many biscuits does each friend get?

Total 19 marks. Allow about 19 minutes.

Exercise 6X  Practice test questions

Non-calculator
1
PSA class has 32 places for the children. Each table has 4 places. How many tables are needed?[1 mark]
2
PSThere are 16 counters. How many bags of 2 can be made?[1 mark]
3
PSThere are 28 cards. How many bags of 4 can be made?[1 mark]
4
FThe array shows 4 dots in 2 equal rows. How many dots are in each row? Write the division: 4 ÷ 2 = ___[1 mark]
5
FWe know that 3 × 6 = 18. Use this to find 18 ÷ 3. Write the answer.[2 marks]
6
FWe know that 6 × 8 = 48. Use this to find 48 ÷ 6. Write the answer.[2 marks]
7
PSPriya shares 72 sweets equally between 8 friends. How many sweets does each friend get?[2 marks]
8
FThe array shows 25 dots in 5 equal rows. How many dots are in each row? Write the division: 25 ÷ 5 = ___[3 marks]
9
FThe array shows 6 dots in 2 equal rows. How many dots are in each row? Write the division: 6 ÷ 2 = ___[3 marks]
10
FThe array shows 36 dots in 6 equal rows. How many dots are in each row? Write the division: 36 ÷ 6 = ___[3 marks]
← Chapter 5: Times tables 6, 8 and 9Chapter 7: Fractions of wholes and equivalent fractions →

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