Multiplication as repeated addition

Objective. Interpret a × b as a groups of b and as an array.

The key idea

4 × 3 is four groups of three. Drawn as an array of 4 rows and 3 columns, it is also clearly 3 groups of four — which is why multiplication is commutative.

Worked example

Show that 4 × 3 = 3 × 4.

1 $Draw an array with 4 rows of 3 dots: 12 dots.$
2 $Turn the array on its side: 3 rows of 4 dots.$
3 $The number of dots did not change.$

Answer: Both equal 12

Practice

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Multiplication as repeated addition

The key idea

Worked example

Practice

1. Write 6 + 6 + 6 + 6 + 6 as a multiplication.

2. 7 × 8

3. 9 × 6

Your progress