Maths Words Children Mix Up: Difference, Share, More Than and Others

4 October 2026 · by Larry

A Primary 3 worksheet had this line on it: "Find the difference between 48 and 19." A neighbour's daughter wrote 67. When her mother asked why, the answer was perfectly sensible: "Difference means they are different, so you put them together."

Nothing was wrong with her arithmetic. She had added correctly. The word "difference" had simply never been explained as a maths word, and everyday English had filled the gap. A great many lost marks in primary maths look like this, and they are not fixed by more sums. They are fixed by a short list of words.

Why a few words cause so much trouble

Maths borrows ordinary words and gives each one an exact meaning. Difference, product, sum, share, left, each, more than. In daily life these are loose. In a question they are instructions, and the child has to know which instruction is hiding inside the word.

It can hit harder in Singapore because for many children English is not the main language at home, so the everyday meaning is the only one they have. A child who reads fluently can still miss the maths meaning of a word, which is why this often gets filed as "careless". If it keeps happening, it is worth sorting out whether it is a reading problem or a working-out problem. Careless mistakes in maths: what they usually are covers how to tell.

The words that catch children out

Difference. It means how far apart two numbers are, and you find it by taking the smaller from the larger. 48 and 19 have a difference of 29. A child who hears "difference" as "how are they different" tends to add, or to make something up.

Sum, product, quotient. The sum is the result of adding, the product the result of multiplying, the quotient the result of dividing. Parents rarely use these words at home, and "product" in particular sounds like something you buy. A question that says "find the product of 6 and 7" is just 6 × 7, and a child who has never met the word will stall on a sum they could do in their sleep.

More than, and less than. This pair is the most reliable trap in the syllabus, because it is used in two different ways.

• "Find a number that is 5 more than 12" is a small instruction: 12 + 5.
• "Tom has 5 more marbles than Ann" is a comparison between two people. If you are told Tom's number, Ann's is found by subtracting.

The words are identical and the working goes the opposite way. "Less than" has an extra twist: "3 less than 10" is 10 − 3, but a child who writes 3 − 10 because the 3 came first has read the sentence in the order it was printed. This is why the shortcut "more means add" breaks, which word problems where the sums are fine but the story is not explains at more length.

Each, per, every. These signal that one amount is being repeated: "4 packets, each with 6 sweets". They usually mean multiply or divide. A child who skips over "each" will add the 4 and the 6.

Share, share equally, share in the ratio. "Share 24 sweets equally among 4 children" is division. "Ann and Ben share their sweets in the ratio 2 : 3" is a different job. The word is the same; the rest of the sentence tells you which one it is. A child who sees "share" and divides every time will go wrong on the ratio question.

Left, remain, altogether, in all. "How many are left?" often means subtract, but not always. "She has 5 left after giving away 3. How many did she start with?" asks you to add. "Altogether" usually means a total, but a two-step problem can ask for an altogether that needs a subtraction first. These words point at a situation, and the situation decides the sum.

Twice as many, half as many, times as many. "Twice as many as" compares two amounts by multiplication. It is a different idea from "2 more than", and children mix the two up often. Getting it straight early helps a lot when ratio and fractions arrive in the upper years.

Round, estimate, nearest. "Round 4,576 to the nearest hundred" is a rule with a specific meaning. It does not mean "make it roughly right". There is more on that in rounding and estimation: where children lose marks.

Area, perimeter, volume, capacity. Four words, four different measurements, and each is used loosely at home. Area and perimeter: where children mix them up and volume and capacity: where children mix them up go through the pairs one at a time.

A five-minute check to do tonight

You do not need a worksheet. Write five short instructions on a scrap of paper, one for each of these words, with easy numbers:

• Find the difference between 30 and 12.
• Find the product of 4 and 5.
• What is 6 less than 20?
• Find the sum of 9 and 8.
• There are 3 bags, each with 4 apples. How many apples in all?

Ask your child to do them out loud, and listen to what they say before they write anything. If one of them stalls, you have found a gap, and it is a small and quick one to close. Do not explain it as a rule. Ask what they think the word means, then tell them what maths means by it, with one example they can picture.

What helps, and what does not

What helps:

• Keep a short list. A page of ten or twelve words, each with one example, kept in the maths folder. When a word catches your child out, it goes on the list.
• Let them say it in their own words. "Difference is how far apart they are" belongs to the child; "difference means subtract" is a rule they will apply to the wrong question.
• Act it out with coins or counters. "5 more than" and "Tom has 5 more than Ann" feel different once there are two real piles on the table.
• Draw the situation. A bar model makes a comparison visible, which is why the bar models guide is worth a look for upper primary.

What does not:

• Keyword tables. A chart saying "altogether = add, left = subtract" works until the first question where it does not, and then a child trusts the chart over the sentence.
• More of the same questions. If the child does not know what the word asks, a fifth identical question only rewards a guess.
• Timing. Reading a word properly takes a moment. A timer teaches a child to skip that moment.

When it is probably not about words

If your child can tell you what every word means when you ask aloud and still picks the wrong operation in a full question, the trouble is more likely holding the whole situation in their head than vocabulary. That needs a different kind of help, and reading fluently but comprehension marks are low is worth reading alongside this.

Frequently asked questions

What does "difference" mean in primary maths?
It is how far apart two numbers are, found by taking the smaller from the larger. The difference between 48 and 19 is 29.

Is "more than" always addition?
No. "5 more than 12" is 12 + 5. But in "Tom has 5 more than Ann", if you are given Tom's amount, you subtract to find Ann's. Read what is being compared before choosing.

What is the difference between sum and product?
The sum is the answer to an addition and the product is the answer to a multiplication. The sum of 3 and 4 is 7; the product of 3 and 4 is 12.

Why does my child get word problems wrong when they can do the sums?
Often a word is being read in its everyday meaning instead of its maths meaning, or the situation has not been pictured. Asking them to explain the word, or to retell the story without the numbers, usually shows which.

Should my child memorise keyword rules like "altogether means add"?
It is better not to. The rules fail on questions where the same word calls for the opposite working. Understanding what the situation is doing lasts longer.

Related: for how marks go even when the answer is right, the answer was right and the marks still went.