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2. Partial Products Multiplication
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3. 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. 7 3

4. 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. 7 3

5. 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. 7 3
Blue × 5 = 15
Yellow × 2 = 6
Total = 21

6. This technique is useful for larger rectangles.

7. 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. 15

8. 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: × 6 = 60
Yellow: × 6 = 30
Total = 90 10 5

9. Now consider even larger rectangles

10. Here is a rectangle with sides 54 and 23.

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

12. 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

13. 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? 50 4 20 3

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

15. Here is a rectangle with sides 54 and 23
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)

16. Here is a rectangle with sides 54 and 23
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: x 20 = 1000 Yellow: x 20 = White: x 3 = Blue: x 3 =
Total:

17. Here is a rectangle with sides 54 and 23
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: x 20 = 1000 Yellow: x 20 = White: x 3 = Blue: x 3 =
Total:
These are sometimes
called
‘partial products’

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

19. 70 5 20
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)

20. 70 5 20
20 x 70 =1400
5 x 70 =350
20 x 5 =100
5 x 5 =25
Here are the 4 partial products for the 4 regions that were chosen.

21. 70 5 20
20 x 70 =1400
5 x 70 =350
20 x 5 =100
5 x 5 =25
So the result is found by adding the 4 partial products:
= 1875