NZ Level 3 Multiply a two digit number by a small single digit number using an area model
Lesson

## Multiplying a single digit number by a two digit number

When we solve a problem such as $4\times12$4×12, we can use some different methods to help us. Here, we look at how we can use the area of rectangles to solve these problems.

## The area of rectangles

When solving $4\times12$4×12,we can calculate the area of a rectangle that has sides that measure $4$4 and $12$12. To break this down into smaller problems, we can think of this as the area of two rectangles added together.

Let's take a look at how we do this in Video 1.

Sometimes, we are asked to calculate our answer, without drawing rectangles. When we do this, we can imagine the rectangles and calculate our separate answers, then add them together to get our total. For example, we could solve $5\times15$5×15 in a table like this:

x 5
10
5

Sometimes we can use information that we already know to help us break our multiplication into smaller problems. Using things such as multiplying by $10$10, times tables, or other multiplication facts we know, can help use solve multiplication questions. Let's have a look at some examples now.

Remember!

Calculating the area of a rectangle can help us solve our multiplication. We can also break our problem down into smaller chunks, by using smaller rectangles, to solve our problem.

#### Worked examples

##### Question 1

We want to find $76\times4$76×4 using the area model.

 $70$70 $6$6 $4$4
1. Find the area of the first rectangle.

 $70$70 $4$4
2. Find the area of the second rectangle.

 $6$6 $4$4
3. What is the total area of the two rectangles?

4. So what is $76\times4$76×4?

##### Question 2

Let's use the area model to find $77\times3$77×3.

1. Fill in the areas of each rectangle.

 $70$70 $7$7 $2$2 $\editable{}$ $\editable{}$ $1$1 $\editable{}$ $\editable{}$
2. What is the total area of all four rectangles?

3. So what is $77\times3$77×3?

##### Question 3

Kathleen, Uther and Ellie completed the following calculations using area models.

1. One of them did not get the right answer. Choose the person, and working, that is in error:

Ellie had to work out $86\times3$86×3 and split it up as follows:

 $80$80 $6$6 $3$3 $240$240 $18$18

She found the total area to be $A=258$A=258

A

Uther completed $68\times4$68×4 using:

 $60$60 $8$8 $2$2 $120$120 $16$16 $2$2 $120$120 $16$16 Total: $240$240 $32$32

He found the total area to be $A=272$A=272

B

Kathleen wanted to work out $67\times4$67×4 and had:

 $60$60 $7$7 $4$4 $280$280 $28$28

She found the total area to be $A=308$A=308

C

Ellie had to work out $86\times3$86×3 and split it up as follows:

 $80$80 $6$6 $3$3 $240$240 $18$18

She found the total area to be $A=258$A=258

A

Uther completed $68\times4$68×4 using:

 $60$60 $8$8 $2$2 $120$120 $16$16 $2$2 $120$120 $16$16 Total: $240$240 $32$32

He found the total area to be $A=272$A=272

B

Kathleen wanted to work out $67\times4$67×4 and had:

 $60$60 $7$7 $4$4 $280$280 $28$28

She found the total area to be $A=308$A=308

C
2. Where did Kathleen make a mistake?

Calculating $4\times60$4×60 to be $280$280.

A

Calculating $4\times7$4×7 to be $28$28.

B

Calculating $4\times60$4×60 to be $280$280.

A

Calculating $4\times7$4×7 to be $28$28.

B

### Outcomes

#### NA3-6

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