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

When we multiply a single-digit number by a two-digit number, there's a great way of using the area of rectangles to help us.

Remember, the area of a rectangle can be found using multiplication:

$\text{Area of a rectangle }=\text{length }\times\text{width }$Area of a rectangle =length ×width

Take a look at the video to see how you can break your multiplication problem up into smaller steps, using rectangles.

Remember!
• When multiplying a two digit number by a one digit number, we can use the area of a rectangle to help use find the answer.
• We can split up the length of a rectangle into smaller measurements so they are easier to multiply.
• Multiples of $10$10, or other multiplication facts that you know are a great way to split up a large rectangle in a smaller rectangle.

#### Worked examples

##### Question 1

Let's use the area model to find $65\times7$65×7.

 $60$60 $5$5 $7$7
1. Find the area of the first rectangle.

 $60$60 $7$7
2. Find the area of the second rectangle.

 $5$5 $7$7
3. What is the total area of the two rectangles?

4. So what is $65\times7$65×7?

##### Question 2

Let's use the area model to find $67\times4$67×4.

1. Fill in the areas of each rectangle.

 $67$67 $2$2 $\editable{}$ $2$2 $\editable{}$
2. What is the total area of both rectangles?

3. So what is $67\times4$67×4?

##### Question 3

Bianca, Derek and Sandy 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:

Derek completed $41\times7$41×7 using:

 $40$40 $1$1 $2$2 $80$80 $2$2 $5$5 $200$200 $5$5 Total: $280$280 $7$7

He found the total area to be $A=287$A=287

A

Sandy had to work out $54\times4$54×4 and split it up as follows:

 $50$50 $4$4 $4$4 $200$200 $16$16

She found the total area to be $A=216$A=216

B

Bianca wanted to work out $58\times3$58×3 and had:

 $50$50 $8$8 $3$3 $180$180 $24$24

She found the total area to be $A=204$A=204

C

Derek completed $41\times7$41×7 using:

 $40$40 $1$1 $2$2 $80$80 $2$2 $5$5 $200$200 $5$5 Total: $280$280 $7$7

He found the total area to be $A=287$A=287

A

Sandy had to work out $54\times4$54×4 and split it up as follows:

 $50$50 $4$4 $4$4 $200$200 $16$16

She found the total area to be $A=216$A=216

B

Bianca wanted to work out $58\times3$58×3 and had:

 $50$50 $8$8 $3$3 $180$180 $24$24

She found the total area to be $A=204$A=204

C
2. Where did Bianca make a mistake?

Calculating $3\times50$3×50 to be $180$180.

A

Calculating $3\times8$3×8 to be $24$24.

B

Calculating $3\times50$3×50 to be $180$180.

A

Calculating $3\times8$3×8 to be $24$24.

B

### Outcomes

#### NA3-6

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