1. Transforming lives through learning Scottish Survey of Literacy & Numeracy Support Material Produced by Education Scotland Transforming lives through learning

2. The move from answers such as 3 r 2 to 3.5 is a key milestone in progression. Changing the remainder to a fraction and finally a decimal fraction is a clear progression pathway. This process is challenging and different approaches should be investigated that promote pupil understanding. Multiplication / Division by 4 & 8 with decimal answers Second Level

3. Transforming lives through learning When number processes are carried out, checking the answer using reverse processes should be automatic. If 27 is divided by 4, giving an answer of 6 r 3 or a more sophisticated answer of 6.75, checking that (6 x 4) + 3 or (6.75 x 4) takes us back to 27, should become automatic classroom practice.

4. Transforming lives through learning The understanding that zeros can be added to a number such as 3 and the 3 is promoted up the powers of ten to give 30,300,3000,etc is developed in other sections of work, and should be re-visited. The progression milestone that when the zeros are added after the decimal point, the value of the number stays the same, is far more challenging. Using price tags, such as £3 and £3.00, introduces familiar contexts and aids understanding.

5. Transforming lives through learning As so many everyday contexts are based on the decimal system, practical approaches should always be encouraged. £3 shared equally among 4 would be ideal to investigate the answer of 0.75 This could be extended to 8 litres of water shared equally among 7 containers. Remember to tie in the practical with 8 divided by 7 on the calculator.

6. Transforming lives through learning Dividing by 2,4 and 8 through repeated halving is an excellent approach to arriving at answers with decimals. Dividing by 10 and then doubling the answer to divide by 5 is also a key step on the progression pathway. This may suggest that division by 3,6,7 and 9 could be investigated as a group, when division leads to a decimal answer.

7. Transforming lives through learning The most sophisticated step on the progression pathway is knowing how many zeros are needed to arrive at a suitable answer. If asked to divide 3 by 2 or 4 or 5 etc, should 3 become 3.0, 3.00, 3.000? Remember how effective a calculator could prove here.