Equal groups become multiplication

What you will learn

• Recognise equal groups and describe them as groups of
• Write repeated addition as a multiplication
• Read an array as rows of equal groups
• Use turn-around facts to help recall

Models used: counters, equal groups, arrays, number lines, number sentences, stories.

Before you start

• Recognise equal groups and multiplication within 40
• Add and subtract numbers up to three digits

What × really means

Here is one plate with 4 biscuits.

1. There is 1 group, with 4 objects in each group. Count a group before counting them all.

   Here is one plate with 4 biscuits.

   4 = 1 × 4 = 4

2. There are 2 groups, with 4 objects in each group. Count a group before counting them all.

   A second plate has another 4. Both groups are the same size.

   4 + 4 = 2 × 4 = 8

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

   With three plates, we have three groups of four.

   4 + 4 + 4 = 12

   4 + 4 + 4 = 3 × 4 = 12

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

   We can turn the arrangement into rows. Every biscuit is still here.

   3 × 4 = 12

   3 rows of 4 = 3 × 4 = 12

Worked example

5 × 2 = ?

1. What does 5 × 2 mean?

   5 × 2 means…

   5 groups of 2

2. Build 5 groups with 2 in each.

   2 + 2 + 2 + 2 + 2 = 5 × 2 = 10

3. Add the groups.

   2 + 2 + 2 + 2 + 2

4. Count in 2s: 2, 4, 6, 8, 10.

   What is 5 × 2?

   10

5. So 5 × 2 = 10. The turn-around fact 2 × 5 = 10 gives the same answer.

   5 × 2 = 10 2 × 5 = 10

Common mistakes to discuss

• Adding the two numbers in a multiplication. 4 × 3 does not mean 4 + 3. It means 4 groups of 3, so we add 3 four times.
• Counting groups that are not equal. Multiplication only works when every group has the same amount. Check each group before multiplying.

Check your understanding

• make equal groups and say “4 groups of 3”
• change 3 + 3 + 3 + 3 into 4 × 3
• read an array as a multiplication
• use 4 × 3 = 3 × 4 to make facts easier

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.