Transcript Rectangles and Multiplication

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
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
Rectangles and Multiplication
Here is a rectangle with
sides 3 and 7.
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
Blue
Yellow
Total
3 × 5 = 15
3×2=6
15 + 6 = 21
This technique is useful for larger
rectangles.
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
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
60 + 30 = 90
10
5
Now consider even larger rectangles
Here is a rectangle
with sides 54 and
23.
54
23
Here is a rectangle
with sides 54 and
23.
The total number of
squares can be
found from
54
54 × 23.
23
Here is a rectangle
with sides 54 and
23.
The total number of
squares can be
found from
54
54 × 23.
Again, we can
divide the rectangle
into regions. What
regions will you
choose?
23
Here is a rectangle
with sides 54 and
23.
The total number of
squares can be
found from
50
54 × 23.
Again, we can
divide the rectangle
into regions. What
regions will you
choose?
Did you choose
these 4 regions?
4
20
33
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:
Yellow:
White:
Blue:
Total:
50 x 20
4 x 20
50 x 3
4x3
= 1000
= 80
= 150
= 12
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:
Yellow:
White:
Blue:
Total:
50 x 20
4 x 20
50 x 3
4x3
= 1000
= 80
= 150
= 12
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?
70
5
20
5
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)
70
20
5
20 x 70 =1400
5 x 70 =350
5
20 x 5 =100
5 x 5 =25
Here are the 4 partial products for the 4 regions that were
chosen.
70
20
5
20 x 70 =1400
5 x 70 =350
5
20 x 5 =100
5 x 5 =25
So the result is found by adding the 4 partial products:
1400 + 100 + 250 + 25 = 1875