## Calculating multiples

When dividing by single digits, pupils are used to using their knowledge of the times tables or counting up in the relevant increments when necessary. When dividing by a 2-digit number (e.g. 16), they may say, ‘I don’t know my 16 times table,’ or ‘I don’t know how to count in 16s’. It is then necessary to reinforce the fact that when we count up in 6s, we are repeatedly adding on 6. So if we want to count up in 16s, we just need to keep adding on 16. This process means that pupils need to be secure with adding 2 digit numbers mentally.

32

48

64

Multiples should be clearly recorded when they are calculated, as they will probably be needed several times during the long division. Recording them in a column makes it easier to correctly count the number of multiples and to calculate with them. Some pupils may look at the last multiple and mentally perform a column method addition. Other pupils will partition the tens and units to add separately.

32

64

Because the initial calculation here is 16 + 16 = 32, some pupils will see this as doubling and then go on to double 32. When looking at their answer of 64, they will see this as 3 x 16, because it is the 3rd multiple they’ve written. Doubling is a useful strategy, but pupils must understand that they are also doubling the number of multiples as well as the multiple itself.

This obviously leads to gaps in the sequence of multiples which may need filling in to enable the pupil to complete the long divison.

64

96

128

150

Looking at the pattern formed by the digits in the units and tens columns can sometimes be quite useful when calculating multiples. However, it can lead to errors when addition of the units crosses the tens. When calculating the multiples of 32, this pupil has seen that the units increase by 2 each time, and the tens increase by 3. In continuing this pattern, they have failed to see that when the units become zero, it is because an additional ten has been made, making a total of 1 6 0 rather than 1 5 0.