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.
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?
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?
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
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
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
Where did Bianca make a mistake?
Calculating $3\times50$3×50 to be $180$180.
Calculating $3\times8$3×8 to be $24$24.