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Multiply a single digit number by a two digit number using an area model


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    
  1. Find the area of the first rectangle.

  2. Find the area of the second rectangle.

  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.

    $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


    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

  2. Where did Bianca make a mistake?

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


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


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