Words First, Numbers Second: The KS2 Vocabulary That Changes What a Question Asks

A child who can add 47 and 38 without hesitation may still be floored by a question asking for the sum of 47 and 38. Nothing in the arithmetic has changed; only the wrapper has. At Key Stage 2, a striking proportion of errors in reasoning papers are not calculation errors at all. They are vocabulary errors, and they are frequently invisible to the adult marking the work, who reads the question fluently and assumes the child has done the same.

Why the words matter more than they appear to

Mathematics has a technical language, and SATs papers use it precisely. Words such as sum, difference and product carry everyday meanings close enough to the mathematical ones to cause interference. A child who hears 'difference' at home as a synonym for disagreement may reasonably conclude that the difference between 12 and 5 is not a number at all.

The encouraging news is that this kind of difficulty responds quickly to deliberate attention. Five minutes of precise talk, repeated over a few weeks, often resolves confusion that has persisted for months.

1. Sum

The sum is the result of an addition. It is not the calculation itself, and it is never the answer to a subtraction. A question such as 'What is the sum of 24 and 17?' can be rephrased as 'What do you get when you add 24 and 17?' If a child can move between the two versions, the word is secure.

Confusion also arises with 'a sum of money', where the everyday phrase simply means an amount. Parents can help by using the word deliberately in its mathematical sense while shopping or cooking, and by naming it: 'The sum of these two prices is...'

2. Difference

The difference is the result of a subtraction: the larger number minus the smaller. It is also a distance between two numbers on a number line, which is why the difference between 3 and 10 is 7 whichever way the subtraction is written.

Many children can compute the answer but cannot choose the operation when the word appears in prose. 'The difference between the number of boys and the number of girls' is a subtraction, however much it may sound like a comparison of two lists.

3. Product

Two meanings collide here. In everyday English, a product is a thing for sale; in mathematics, it is the result of a multiplication. Children who have only met the word on a supermarket shelf may not connect it to multiplying at all.

The word also appears in work on factors, where 'express 60 as the product of its prime factors' carries real weight. A useful routine is to have children write the multiplication alongside the answer, so that the word and the operation are paired in memory.

4. Fewer than, more than, and the traps in between

'Fewer than' means a smaller number; 'more than' means a larger one. The difficulty is rarely the words themselves but the direction of the required calculation. Asked how many more apples one child has than another, some pupils add when they should subtract.

A reliable scaffold is to turn the sentence into a bar model or a pair of lengths before choosing an operation. 'How many more' and 'what is the difference' ask the same question in different clothing. 'Five fewer than 20' is 15, not 25.

5. Array

An array is a set of objects arranged in rows and columns, and it is one of the most powerful images in primary mathematics. It links multiplication, division and factors in a single picture: a 3 by 4 array holds 12 counters, can be read as 3 × 4 or 4 × 3, and can be shared into three groups of four or four groups of three.

Children who can sketch an array for a word problem are rarely unsure whether to multiply or divide. The image does the reasoning for them.

6. Commutative

Commutative is a word many adults would struggle to define, but the idea is simple: addition and multiplication can be done in either order. 3 + 8 = 8 + 3, and 4 × 6 = 6 × 4. Subtraction and division cannot.

The term appears in reasoning papers and in teachers' explanations, and children are often expected to use it. Teaching it alongside examples is far more effective than teaching the definition alone. Ask a child to say the word, give an example and give a counter-example.

7. Share, divide and remainder

'Share' is friendly and familiar; 'divide' sounds formal. Both can mean partition, but 'share 12 sweets between 3 children' and 'divide 12 by 3' lead to the same answer only when the sharing is equal.

Remainder complicates matters further. A question asking 'how many are left over' wants a remainder; a question asking whether the answer should be rounded up or down requires the child to think about the context, not just the numbers.

Four routines that take five minutes

Small habits make a disproportionate difference.

First, ask the child to say the question in their own words before calculating. If they cannot, the barrier is language rather than mathematics, and more sums will not remove it.

Second, keep a working vocabulary list on the wall or the fridge, with an example beside each term. Words without examples fade quickly.

Third, use the words in ordinary conversation, deliberately. 'What is the difference between those two packets?' is a mathematics question in disguise.

Fourth, when a question is answered incorrectly, check whether the error lay in the reading or in the calculation. The two need different remedies, and treating a vocabulary problem with extra arithmetic is a common and frustrating mistake.

Teachers and parents, working from the same list

Children are quick to sense when a word is being taught rather than used. The most effective reinforcement happens when the vocabulary runs through everyday talk: at the table, in the car, over a recipe. A short conversation between parent and teacher about which six words the class is currently working on will achieve more than a printed glossary sent home unread.

The arithmetic, in most cases, is already there. It is the language around it that needs the practice.