Transcript Cross Products - Teacher Tools

Cross Products
I am learning to multiply multi-digit whole numbers.
37 X 28 = ?
Before starting this lesson make sure you are confident with the
lesson Paper Power (for multiplication).
There are 17 rows with 32 counters in each row. How many
counters are there in total? 17 X 32= ?
Imagine this displayed as a rectangle.
Now split the 32 and 17 into a tidy number and an amount left over.
You can see there are 4 rectangles. By finding the area of each of these
we can work out the area of the whole rectangle and the answer to our
question.
30 X 10 = 300
2 X 10 = 20
2 X 7 = 14
32
30
30 X 7 = 210
Add all the areas together.
2
300 + 20 + 14 + 210 = 544
10
7
17
So 17 X 32 = 544
There are 27 rows with 47 counters in each row. How many
counters are there in total? 27 X 47= ?
Imagine this displayed as a rectangle.
Now split the 27 and 47 into a tidy number and an amount left over.
You can see there are 4 rectangles. By finding the area of each of these
we can work out the area of the whole rectangle and the answer to our
question.
40 X 20 = 800
7 X 20 = 140
7 X 7 = 49
47
40
40 X 7 = 280
Add all the areas together.
7
800 + 140 + 49 + 280 = 1,269
20
7
27
So 27 X 47 = 1,269
Now let’s try an example without the diagram.
Firstly split the numbers into a tidy number and an
amount left over.
18 X 43 = ?
(10 + 8) X (40 + 3) = ?
10 X 40 = 400
You saw from our earlier diagrams that every
number on the left hand side of the multiplication
sign must be multiplied by every number on the right
hand side of this sign.
10 X 3 = 30
Now add the amounts together.
8 X 40 = 320
8 X 3 = 24
400 + 30 + 320 + 24 = 774
18 X 43 = 774
Below is an example of how I like to set out my working for these
types of question.
32 X 52 = ?
(30 + 2) X (50 + 2) = ?
Step 1: I expand the number
Step 2: I draw in lines showing all the
numbers I must multiply together. I always do
2 above and 2 below so I don’t mix any of my
lines up.
As I draw in the lines I record each part of
the multiplication.
(30 X 50) + (30 X 2) + (2 X 50) + (2 X 2)
1500
+
60
+
100
+
4 = 1,664
So 32 X 52 = 1,664
Step 3: Below this I record
the answers.
Use this strategy (cross products) to work out answers to the
questions below.
1) 25 X 33 = ?
825
2) 17 X 42 = ?
714
3) 32 X 45 = ?
1,440
4) 18 X 23 = ?
414
Click again when you have worked out
all your answers.
5) 26 X 23 = ?
598
Need some more practise? Try Pg45 & 46 of Teacher Tools Multiplication
and Division Book Numeracy resources