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 let’s halve the number of groups there are.
Then double the amount you put in each group.
4 X 3 = 12
Do this by dividing by 2
Do this by multiplying by 2
2 X …. = 12 6
So…
4 X 3 = 12
and
2 X 6 = 12 ÷2 x2

3. Now let’s try a thirding and trebling example.
Below are 3 groups of 27 or 3 X 27 = ?
Now let’s 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
9 X …. = …. 9 81
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 didn’t 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.
1) 18 X 5 = ?
2) 21 X 3 = ?
3) 6 X 25 = ?
4) 33 x 3 = ?
5) 4 X 50 = ?
9 X 10 = 90
7 X 9 = 63
3 X 50 = 150
11 X 9 = 99
2 X 100 = 200
Need some more practise? Try Pg31 & 32 of Teacher Tools Multiplication and Division Book Numeracy resources