# Extend multiplicative strategies to larger numbers

Lesson

## A toolkit

When we work out multiplication problems, there are many tips and tricks we can use to solve problems that might seem beyond us. Some of the things we can use include:

• turnarounds (or, the commutative law of multiplication)
• factor pairs, and
• the splitting strategy

This applet reminds you about the commutative law of multiplication and how when you turn around the multiplication the answer (size of the array) is the same.

How do we know which method to use ? In Video 1, we'll work through some problems, and look at which strategies might help us, and why. We might also think of other things to help us along the way.

### Larger numbers

Other methods that are really useful, particularly when multiplying by larger numbers, include doubling, and doubling again, and splitting and using the area model of multiplication.

Let's see how we use these methods to solve some problems where we multiply by larger numbers, in Video 2.

#### Worked Examples

##### Question 1

Consider the multiplication $20\times25$20×25

1. Fill in the blanks by breaking up $20$20 into factors.

$20\times25=\editable{}\times4\times25$20×25=×4×25

2. Solve $20\times25$20×25 by using the factor strategy from part (a).

 $20\times25$20×25 $=$= $5\times4\times25$5×4×25 $=$= $5\times\editable{}$5× $=$= $\editable{}$

##### Question 2

Use the double-double strategy to solve $4\times21$4×21.

1. First, evaluate $2\times21$2×21

2. Now, evaluate $2\times42$2×42

3. Hence, $4\times21$4×21

##### Question 3

Find $2\times69$2×69.

### Outcomes

#### NA3-6

Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality