Pupils should recognise that a remainder arises when there is something ‘left over’ in a division calculation. Pupils should recognise and understand why remainders only occur when the dividend is not a multiple of the divisor. This can be achieved by discussing the patterns seen when the dividend is incrementally increased by 1 while the divisor is kept the same.
A common mistake made by pupils is not making the maximum number of groups possible, for example:
17 ÷ 4 = 3 r 5 (incorrect)
The table above can be used to help pupils recognise and understand that the remainder is always smaller than the divisor. Note that when pupils use the short division algorithm in year 5, if they ‘carry over’ remainders that are larger than the divisor, the algorithm will not work.
“If the dividend is a multiple of the divisor there is no remainder.”
“If the dividend is not a multiple of the divisor, there is a remainder.”
“The remainder is always less than the divisor.”
Once pupils can correctly perform division calculations that involve remainders, they need to recognise that, when solving contextual division problems, the answer to the division calculation must be interpreted carefully to determine how to make sense of the remainder. The answer to the calculation is not always the answer to the contextual problem. Consider the following context: Four scouts can fit in each tent. How many tents will be needed for thirty scouts?
Pupils may simply say that “7 remainder 2 tents are needed”, but this does not answer the question. Pupils should identify what each number in the equation represents to help them correctly interpret the result of the calculation in context.
“The 30 represents the total number of scouts.”
“The 4 represents the number of scouts in each tent.”
“The 7 represents the number of full tents.”
“The 2 represents the number of scouts left over.”
“We need another tent for the 2 left-over scouts. 8 tents are needed.”