Pupils must learn to add and subtract using the formal written methods of columnar addition and columnar subtraction. Pupils should master columnar addition, including calculations involving regrouping (some columns sum to 10 or more), before learning columnar subtraction. However, guidance here is combined due to the similarities between the two algorithms.
Beginning with calculations that do not involve regrouping (no columns sum to 10 or more) or exchange (no columns have a minuend smaller than the subtrahend), pupils should:
- learn to lay out columnar calculations with like digits correctly aligned.
- learn to work from right to left, adding or subtracting the least significant digits first.
Teachers should initially use place-value equipment, such as Dienes, to model the algorithms and help pupils make connections to what they already know about addition and subtraction.
Pupils must also learn to carry out columnar addition calculations that involve regrouping, and columnar subtraction calculations that involve exchange. Regrouping and exchange build on pupils’ understanding that 10 ones is equivalent to 1 ten, and that 10 tens is equivalent to 1 hundred. Dienes can be used to model the calculations, and to draw attention to the regrouping/exchange. Dienes (or any other place-value apparatus) should be used, only initially, to support pupils understanding of the structure of the algorithms, and should not be used as a tool for finding the answer. Once pupils understand the algorithms, they should use known facts to perform the calculation in each column (3NF–1). For calculations with more than 2 addends, pupils should add the digits within a column in the most efficient order.
Pupils should use unitising language to describe within-column calculations.
“3 ones plus 5 ones is equal to 8 ones.”“4 tens plus 2 tens is equal to 6 tens.”
“5 ones minus 3 ones is equal to 2 ones.”“6 tens minus 2 tens is equal to 4 tens”
Pupils must learn that, although columnar methods can be used for any additive calculation, they are not always the most appropriate choice. For example, 164 + 36 can be calculated by recognising that 64 and 36 is a complement to 100, while 120 + 130 maybe be calculated by unitising in tens (12 tens + 13 tens = 25 tens) or by recognising that 20 + 30 = 50. Throughout, pupils should continue to recognise the inverse relationship between addition and subtraction. Pupils may represent calculations using partitioning diagrams or bar models, and should learn to check their answers using the inverse operation.