Recognise equal groups and multiplication within 40

What you will learn

• Recognise equal groups and multiplication within 40

Models used: number sentences, stories, diagrams.

Before you start

• Add or subtract ones and tens mentally without regrouping

Count equal groups

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: A new example, together

What is 11 × 3?

1. 11 rows run across the picture; each row contains 3 objects.

   Count one group. Check the other groups match.

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

2. 11 rows run across the picture; each row contains 3 objects.

   Split 11 by place value: 10 + 1.

   What is 11 × 3?

   33

3. 11 rows run across the picture; each row contains 3 objects.

   10 × 3 = 30; 1 × 3 = 3.

   11 rows of 3 = 11 × 3 = 33

4. 11 rows run across the picture; each row contains 3 objects.

   Join the products: 30 + 3 = 33.

   11 rows of 3 = 11 × 3 = 33

5. 11 rows run across the picture; each row contains 3 objects.

   Check the result against the question we started with.

   33 ÷ 3 = 11.

   We found 33. Multiplying each part of a amount and joining the products preserves the total.

   11 rows of 3 = 11 × 3 = 33

Common mistakes to discuss

• Groups that are not equal. Multiplication counts equal groups only. Four plates holding 3, 3, 2 and 3 cannot be read as 4 × 3.

Check your understanding

• Recognise equal groups and multiplication within 40
• recognise equal groups
• 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.