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

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

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

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.

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

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