Associative law of addition: the principle that if there are three numbers to be added it makes no difference whether you start by adding the first and second, or by adding the second and third. In symbols, this law states that, for any three numbers a, b and c, (a + b) + c = a + (b + c)

Multiple of 10: a number that can be divided exactly by 10. So the multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, and so on. Similarly, multiples of 100 are 100, 200, 300 and so on.

Stepping stone: usually a multiple of 10 or 100 used to break down an addition or subtraction into easier steps. For example, to find what has to be added to 37 to get 75, the numbers 40 and 70 might be used as stepping stones.

Empty number line: a number line without a scale, used to support mental and informal additions and subtractions; numbers involved in the calculation can be placed anywhere on the line provided they are in the right order relative to each other.

Front-end approach: a method for doing a calculation that focuses on the digits at the front of the number. For example, to add 543 and 476, a front-end approach would start by adding the 500 and 400.

Partitioning (into hundreds, tens and ones): breaking a number up into hundreds, tens and ones as an aid to using it in a calculation. For example, 476 when partitioned is 400 + 70 + 6.

Compensation: a strategy that involves replacing a number in a calculation with an easier number close to it and then compensating for this later. For example, to subtract 38 you could subtract 49 instead and compensate by adding on the additional 2 at the end.

Sum: the result of doing an addition; for example, 25 is the sum of 27 and 8. The word ‘sum’ should not be used as a synonym for ‘calculation’.

Near-doubles: when two numbers involved in an addition are nearly the same, such as 46 + 48; or when one number involved in a subtraction is nearly double or half of the other, such as 87 – 43. Such calculations can be done by treating them as exact doubles and then compensating.

Friendly numbers: two numbers that are related to each other in a way that makes a calculation particularly easy; for example, 457 – 257. Often a calculation can be made easier by replacing one of the numbers with a more friendly number close to it and then compensating later.