Recall related multiplication and division facts

What you will learn

• Recall related multiplication and division facts

Models used: number sentences, stories, diagrams.

Before you start

• Two kinds of division

Give everyone an equal share

Share 12 counters between 4 children. Nobody has any yet.

1. Each plate is one share. Counters outside the plates have not been shared yet.

   Share 12 counters between 4 children. Nobody has any yet.

   An array of 6 rows of 7 shows 6 × 7 = 42 and 7 × 6 = 42, and also 42 ÷ 6 = 7 and 42 ÷ 7 = 6.

   Friend 1: 0

   Friend 2: 0

   Friend 3: 0

   Friend 4: 0

2. Each plate is one share. Counters outside the plates have not been shared yet.

   Give each child one counter. Everyone must receive the same amount.

   Equal sharing means every share has the same amount. Check both conditions: the shares match, and all the starting objects are accounted for.

   Friend 1: 1

   Friend 2: 1

   Friend 3: 1

   Friend 4: 1

3. Each plate is one share. Counters outside the plates have not been shared yet.

   Keep going around. After three rounds, the counters are all shared.

   Equal sharing means every share has the same amount. Check both conditions: the shares match, and all the starting objects are accounted for.

   None left

   Friend 1: 3

   Friend 2: 3

   Friend 3: 3

   Friend 4: 3

4. There are 4 groups, with 3 objects in each group. Count a group before counting them all.

   Each child receives 3. Four equal shares of 3 make our original 12.

   12 ÷ 4 = 3

   3 + 3 + 3 + 3 = 4 × 3 = 12

Worked example: A new example, together

What is 9 × 3?

1. 9 rows run across the picture; each row contains 3 objects.

   Build the array, then read it along each side and back again.

   Multiplying each part of a amount and joining the products preserves the total.

2. 9 rows run across the picture; each row contains 3 objects.

   9 × 3 means 9 groups of 3.

   What is 9 × 3?

   27

3. 9 rows run across the picture; each row contains 3 objects.

   9 × 3 means 9 groups of 3.

   9 rows of 3 = 9 × 3 = 27

4. 9 rows run across the picture; each row contains 3 objects.

   Count in 3s, 9 times.

   9 rows of 3 = 9 × 3 = 27

5. 9 rows run across the picture; each row contains 3 objects.

   9 × 3 = 27.

   9 rows of 3 = 9 × 3 = 27

6. 9 rows run across the picture; each row contains 3 objects.

   Check the result against the question we started with.

   27 ÷ 3 = 9.

   We found 27. Multiplying each part of a amount and joining the products preserves the total.

   9 rows of 3 = 9 × 3 = 27

Common mistakes to discuss

• Learning each fact separately. One array gives four facts. 6 × 7 = 42 also tells us 7 × 6 = 42, 42 ÷ 6 = 7 and 42 ÷ 7 = 6.

Check your understanding

• Recall related multiplication and division facts
• recall a table fact together with the division facts that come with it
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.