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.
- 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 | ||||||||||||||
Find the area of the first rectangle.
$60$60 $7$7 Find the area of the second rectangle.
$5$5 $7$7 What is the total area of the two rectangles?
So what is $65\times7$65×7?
Question 2
Let's use the area model to find $67\times4$67×4.
Fill in the areas of each rectangle.
$67$67 $2$2 $\editable{}$ $2$2 $\editable{}$ What is the total area of both rectangles?
So what is $67\times4$67×4?
Question 3
Bianca, Derek and Sandy completed the following calculations using area models.
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
ASandy 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
BBianca 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
CWhere did Bianca make a mistake?
Calculating $3\times50$3×50 to be $180$180.
ACalculating $3\times8$3×8 to be $24$24.
B