Finding a remainder requires the ability to calculate a difference mentally, and the process of switching from division to subtraction can lead pupils to make errors in both calculating and recording their answers. Two common errors are shown below.

Here the pupil has correctly worked out that 19 divided by 5 is 3, but in using 5 x 3 = 15 to enable calculation of the remainder, they have incorrectly recorded 15 instead of 3. They need to be encouraged to record the whole number part of the answer before calculating the remainder.

When calculating the remainder here, the pupil has used the multiple of 5 which is closest to 19 (so 4 x 5 = 20 is closer than 3 x 5 = 15) and then counted back to 19 to get the remainder of 1. Using objects to physically reinforce the concept of division will remind pupils why they can’t use a multiple greater than the number they begin with.