Cut and Paste

1
Cut and Paste
I am learning to solve multiplication problems
using doubling and halving, thirding and
trebling, and other proportional adjustments.
2
X 2
3
X 3
2
To start with lets use doubling and halving to
help us change a question and make it easier to
answer.
Below are 4 groups of 3 or 4 X 3 12
Now lets halve the number of groups there are.
Then double the amount you put in each group.
4 X 3 12
Do this by multiplying by 2
Do this by dividing by 2
2 X . 12
6
So 4 X 3 12 and 2 X 6 12
2
x2
3
Now lets try a thirding and trebling example.
Below are 3 groups of 27 or 3 X 27 ?
Now lets triple the number of groups there are.
Then third the amount you put in each group.
3 X 27 .
Do this by multiplying by 3
Do this by dividing by 3
81
9
9 X . .
9 X 9 81 so 3 X 27 81
4
We can also adjust our problems more than once if
it helps.
2 X 36 ?
2
X2
Doubling and halving once didnt help so we can
do it again.
4 X 18 ?
4
X4
X2
2
8 X 9 72
We could also have divided by 4 and multiplied by
4. This would have saved us the middle step and
we would still have got the same answer.
5
The questions on the left have a buddy question
to the right where, doubling and halving or
trebling and thirding has been used. Which
questions do you think go together?

• 5 X 14 ?
• 14 X 50 ?
• 3) 6 X 18 ?
• 4) 3 X 24 ?

9 X 8 72
Click again when you have worked out which
questions go together.
12 X 9 108
10 X 7 70
7 X 100 700
6
Use doubling and halving to help you work out the
answers to these questions.
Click again when you have worked out all your
answers.
9 X 10 90 7 X 9 63 3 X 50 150 11 X 9
99 2 X 100 200
1) 18 X 5 ? 2) 21 X 3 ? 3) 6 X 25 ?
4) 33 x 3 ? 5) 4 X 50 ?
Need some more practise? Try Pg31 32 of Teacher
Tools Multiplication and Division Book Numeracy
resources