Mental Sums: Why a Child Who Can Do Column Sums Stalls With No Pencil

6 October 2026 · by Larry

You are in the car, or queuing for dinner, and you ask something easy. "What is 49 plus 26?" Your child, who got full marks on the column-sums page last week, goes quiet. Then comes a guess, or "I need paper", or the fingers come out under the table.

It is easy to read that as a gap in maths. Usually it is not. Adding on paper and adding in your head are two different jobs, and a child can be good at the first long before the second starts to work.

Why the pencil makes such a difference

A column sum does a lot of the remembering for the child. The numbers sit on the page, the tens and ones are lined up, and the carried digit has a small place to live. At any moment the child only has to deal with one small step, such as 9 + 6, and then write the result down.

A mental sum takes all of that away. The child has to hold both numbers, decide how to break them up, do a step, keep the partial answer, and then do the next step, all in their head at once. It is the same arithmetic, but a much heavier load. That is why a child can look completely fluent on paper and lost without it.

There is a second difference. On paper there is one method, and the school has taught it. In your head there are many methods, and nobody has said which to use. A child who has only ever met the column method has nothing to reach for when there are no columns.

Six sums to try at the table

Before changing anything, find out what your child actually does. Ask these aloud, one at a time, with no pencil, and after each answer ask: "How did you work that out?"

• 8 + 7
• 49 + 26
• 83 − 47
• 100 − 37
• 6 × 14
• 304 − 298

Do not mark them as right or wrong. Listen to the method. You will usually hear one of these:

• Counting. On fingers, or silently in steps of one. It works for 8 + 7 and falls apart at 83 − 47.
• The column method, pictured. The child is drawing the page in their head, ones first, with a carry. It is accurate but slow, and it uses up a lot of memory.
• A real mental strategy. "I did 50 plus 26 and took away 1." That child needs encouragement, not instruction.
• A guess. No method at all. This is the one to take seriously, because there is nothing to correct, only something to teach.

Five small strategies, with the sums above

None of these is a trick. Each is a way of turning a hard sum into an easy one that the child already knows. Teach one at a time, and let the child say it in their own words.

1. Make 10. For 8 + 7, take 2 from the 7. Now it is 8 + 2 = 10, and 5 left over, so 15. This leans on the pairs that make 10, which is the same idea as number bonds; the guide to what number bonds are goes through it for younger children.

2. Split by place value. For 49 + 26, add the tens (40 + 20 = 60) and the ones (9 + 6 = 15), then put them together: 75. For a child who is steady with tens and ones this is often the first strategy that sticks.

3. Go to a friendly number, then fix it. 49 is one less than 50, so do 50 + 26 = 76 and take away the 1: 75. The same move works for 198 + 67: do 200 + 67 = 267 and take away 2, giving 265. The new idea here is the fix at the end, and children often forget it, so ask for it out loud.

4. Subtract by counting up. Many children find taking away hard and adding easy. For 83 − 47, start at 47 and go up to 50 (that is 3), then up to 80 (30 more), then up to 83 (3 more). 3 + 30 + 3 = 36. For 100 − 37, go from 37 to 40 (3), then 40 to 100 (60): 63. For 304 − 298, the gap is only 2 to reach 300 and 4 more to reach 304, so 6. A child who subtracts it the long way, borrowing across the zero, gets there much more slowly and with more chances to slip. If borrowing is where the marks go on paper too, carrying and borrowing: why column sums go wrong looks at that side.

5. Split the multiplication. For 6 × 14, split the 14 into 10 and 4: 6 × 10 = 60 and 6 × 4 = 24, so 84. Two related shortcuts are worth a mention once the child is comfortable: 9 × 7 is one 7 fewer than 10 × 7 (70 − 7 = 63), and 5 × 18 is half of 10 × 18 (half of 180 is 90). Both depend on knowing the tables, so if those are still shaky, times tables: memorising, understanding, and the order that works comes first.

Why a timer makes it worse

It is tempting to turn mental sums into a speed game. For most children at the start this backfires. Under a clock the child grabs the quickest method they own, which is usually counting, and the thing you most wanted to see, a better method, never appears. Timing your child on maths: when it helps and when it backfires covers when a timer is worth using.

The same applies to correcting. If the answer is wrong, do not give the right one. Ask: "What did you do first?" Nine times out of ten the child hears the slip as they say it.

What does not help

• Banning the pencil for homework. Written working is still how school marks the paper. Mental sums are a separate skill to build alongside it, not a replacement.
• More of the same sums. A child with no strategy will count faster, not think differently.
• Calling it laziness or carelessness. A child who goes quiet is usually doing a lot of hard work with no method to help.
• Teaching all five strategies in one evening. They blur together. One strategy for a week is plenty.

A short routine for the week

• Day 1: the six-sum check above. Just listen.
• Day 2: pick the strategy that matches what you heard. Do three sums with it, out loud, in the car.
• Day 3: three more, but let the child be the teacher: "Tell me how you would show your little cousin."
• Day 4: mix in one sum where the strategy does not help, and ask your child to decide. Choosing is the real skill.
• Day 5: two sums, no discussion. Leave it there.

Three or four sums at a time, a few times a week, is plenty. The aim is a child who has two or three ways to start, not a child who answers faster.

If easy facts such as 8 + 7 stay slow for a long time, or counting is still the only method well past the early years, mention it to the class teacher. They see the whole class and can say what is typical for your child's school. What MOE expects at each level is in the primary mathematics syllabus on moe.gov.sg.

For some low-pressure practice alongside this, the free maths practice has a drill builder where you choose the operations and the number range, and it works on a phone.

Frequently asked questions

Why can my child do column sums but not mental sums?
A column sum keeps the numbers on the page, so the child only holds one small step at a time. A mental sum asks the child to hold the numbers, the step they are on and the partial answer all in their head. It is a different skill, not a weaker version of the same one.

Is it a problem if my child still uses fingers or a pencil for small sums?
Not by itself. Many children need a few weeks or months between understanding a sum and answering it quickly in their head. It is worth looking at once the same easy facts, such as 8 + 7, stay slow for a long time.

What is the make-10 strategy?
To add 8 + 7, take 2 from the 7 to make 8 + 2 = 10, then add the 5 that is left to get 15. It turns an awkward sum into one that passes through a friendly number.

Should I time my child on mental sums?
Not at first. A timer makes a child grab the nearest method, usually counting, and hides which strategy is actually missing. Get the method right and spoken aloud first, and add speed later if at all.

How often should we practise mental sums at home?
Three or four sums, a few times a week, spoken aloud in the car or while waiting. Short and frequent works better than one long session, and the child should say how they did it each time.

Related: if counting on fingers is still the only method, counting on fingers: when it matters and when it does not is the place to start. For answers that should be roughly right rather than exact, see rounding and estimation.