Rectangles and Multiplication Here is a rectangle with sides 3 and 7. The total number of squares can be found by multiplying 3 and

Here is a rectangle with sides 3 and 7. The total number of squares can be found by multiplying 3 and 7. Note that if we colour the squares we can work out the number of blue squares and the number of yellow squares separately and add. 3 7 Rectangles and Multiplication

Here is a rectangle with sides 3 and 7. The total number of squares can be found by multiplying 3 and 7. Note that if we colour the squares we can work out the number of blue squares and the number of yellow squares separately and add. 3 7 Blue 3 × 5 = 15 Yellow 3 × 2 = 6 Total = 21 Rectangles and Multiplication

This technique is useful for larger rectangles.

Here is a rectangle with sides 15 and 6, so the total number of squares can be found from: 15 × 6. Again, if we colour the squares we can work out the number of blue squares and the number of yellow squares separately and add. 15 6

Here is a rectangle with sides 15 and 6, so the total number of squares can be found from: 15 × 6. Again, if we colour the squares we can work out the number of blue squares and the number of yellow squares separately and add. Blue: 10 × 6 = 60 Yellow: 5 × 6 = 30 Total =

Now consider even larger rectangles

Here is a rectangle with sides 54 and

Here is a rectangle with sides 54 and 23. The total number of squares can be found from 54 ×

Here is a rectangle with sides 54 and 23. The total number of squares can be found from 54 × 23. Again, we can divide the rectangle into regions. What regions will you choose? 54 23

Here is a rectangle with sides 54 and 23. The total number of squares can be found from 54 × 23. Again, we can divide the rectangle into regions. What regions will you choose? Did you choose these 4 regions?

It would be easier if we drew the rectangle on grid paper.

Here is a rectangle with sides 54 and 23. The total number of squares can be found from 54 × 23. One of the ways to calculate 54 × 23 is to divide the rectangle into 4 regions (as shown)

Here is a rectangle with sides 54 and 23. The total number of squares can be found from 54 × 23. One of the ways to calculate 54 × 23 is to divide the rectangle into 4 regions (as shown) Orange: 50 x 20 = 1000 Yellow: 4 x 20 = 80 White: 50 x 3 = 150 Blue: 4 x 3 = 12 Total: 1242

Here is a rectangle with sides 54 and 23. The total number of squares can be found from 54 × 23. One of the ways to calculate 54 × 23 is to divide the rectangle into 4 regions (as shown) Orange: 50 x 20 = 1000 Yellow: 4 x 20 = 80 White: 50 x 3 = 150 Blue: 4 x 3 = 12 Total: 1242 These are sometimes called ‘partial products’

Now your turn: Sketch a rectangle and label the sides with 25 and 75. What regions will you choose to divide it into?

Did you choose these four regions? No matter what regions you choose, if you work out the partial products and then add, you will still get the same answer (25 ×75 = 1875)

x 70 = x 70 = x 5 =100 5 x 5 =25 Here are the 4 partial products for the 4 regions that were chosen.

x 70 = x 70 = x 5 =100 5 x 5 =25 So the result is found by adding the 4 partial products: = 1875