Mental arithmetic — calculating in your head without paper, calculator or finger counting — is one of the most useful skills a child can build in primary school. It makes everyday maths faster, supports written methods and estimation, and gives children confidence with numbers.
But strong mental maths is not about memorising more facts. It comes from number sense: understanding how numbers can be split, combined and compared. This complete guide explains the main strategies with worked examples, shows how the soroban supports visual mental calculation and gives you a practical plan for home or class.
What mental arithmetic really is
Mental arithmetic has two parts. The first is quick recall of basic facts, such as 7 + 3 = 10 or 6 × 5 = 30. The second, more important part is strategies: ways of transforming a hard problem into easier steps. A child who knows that 8 + 5 can become 8 + 2 + 3 does not need to have memorised 8 + 5.
Good mental calculators choose flexibly between strategies and can explain their choice. That is why practice should always include the question “How did you do it?”.
Six mental math strategies for kids
These strategies cover most calculations up to 100. Introduce them one at a time, with objects, drawings or a soroban, before asking for purely mental answers.
| Strategy | Example | How it works |
|---|---|---|
| Make 10 | 8 + 5 = 13 | 8 + 2 = 10, then + 3 |
| Split tens and ones | 23 + 14 = 37 | 20 + 10 = 30, 3 + 4 = 7, then 30 + 7 |
| Compensate | 19 + 6 = 25 | 20 + 6 = 26, then − 1 |
| Doubles and near doubles | 6 + 7 = 13 | 6 + 6 = 12, then + 1 |
| Subtract through 10 | 14 − 6 = 8 | 14 − 4 = 10, then − 2 |
| Count up (difference) | 52 − 47 = 5 | 47 → 50 is 3, 50 → 52 is 2, total 5 |
All of these rely on the same foundations: knowing pairs that make 10, understanding tens and ones, and seeing numbers as made of parts. Those foundations are exactly what the soroban makes visible.
How the soroban supports mental arithmetic
On a soroban, 7 is not seven separate beads: it is one 5-bead and two 1-beads. Children stop counting one by one and start seeing numbers as structures. The rules they use — the friends of 5 and friends of 10 — are the same number pairs used in the “make 10” strategy.
After regular practice, many children picture the abacus in their heads and move imaginary beads. This visual method, called anzan, lets them handle multi-digit sums by updating a mental image. Studies of trained users show that they really do represent numbers visually (Frank & Barner, 2012), and a randomised trial found improved arithmetic for children who learned it (Barner et al., 2016).
The soroban is not the only path to mental maths, but it is a particularly concrete one — useful for children who find numbers abstract.
Why some children struggle with mental maths
Difficulties usually have identifiable causes rather than a lack of “maths talent”:
- Counting one by one: the child still counts on fingers for 8 + 5 because pairs that make 10 are not secure.
- Weak place value: tens and ones are mixed up in problems like 23 + 14.
- Overloaded memory: the child loses track of intermediate results in longer calculations.
- Anxiety: timed tests and comparison make the child freeze, even on known facts.
Each cause has a clear response: practise number pairs, make place value concrete, shorten the steps, and remove time pressure until accuracy is solid.
Worked examples to try together
Ask your child to solve each problem and explain the method. Accept any correct strategy, then show another one.
- 9 + 4: “What does 9 need to make 10?” (1). So 9 + 1 + 3 = 13.
- 35 + 21: 30 + 20 = 50, 5 + 1 = 6, so 56.
- 29 + 15: 30 + 15 = 45, then − 1 = 44.
- 8 + 7: 7 + 7 = 14, + 1 = 15 (or 8 + 8 = 16, − 1).
- 13 − 5: 13 − 3 = 10, − 2 = 8.
- 61 − 58: count up: 58 → 60 is 2, 60 → 61 is 1, so 3.
A four-week practice plan
Ten minutes a day is enough. Keep the structure fixed and change only the focus.
| Week | Focus | Daily activity |
|---|---|---|
| 1 | Pairs that make 10 | Call a number, the child says its partner (7 → 3) |
| 2 | Make 10 in addition | Five problems like 8 + 5, 9 + 6, 7 + 4 |
| 3 | Tens and ones | Problems like 23 + 14, 45 + 32 without carrying |
| 4 | Mixed strategies | Six problems, the child names the strategy |
If your child uses the soroban, combine this plan with the soroban learning path and short training sessions. Printable worksheets are useful for screen-free practice.
Tips for parents and teachers
How you practise matters as much as what you practise:
- Ask for explanations: “How did you get it?” builds flexible strategies.
- Accuracy before speed: introduce timing only when answers are reliably correct.
- Use everyday maths: prices, scores, recipes and travel times.
- Stay calm about mistakes: ask the child to check, then discuss which step went wrong.
Conclusion
Mental arithmetic for kids is built on number sense, a few powerful strategies and regular, calm practice. Teach pairs that make 10, place value and the six strategies above; ask children to explain their thinking; and add the soroban if your child benefits from a visual, hands-on method. Over time, calculations that once needed fingers become quick and confident.
To go further with the visual method, read when and how to introduce anzan.
Frequently asked questions
What is mental arithmetic for kids?
It is the ability to calculate in your head using number sense and strategies, such as making 10 or splitting tens and ones, rather than counting or writing.
How can I improve my child’s mental maths?
Practise pairs that make 10, teach one strategy at a time, ask for explanations and keep sessions short and regular. Visual tools such as the soroban help many children.
At what age should children start mental arithmetic?
Simple mental calculation with small numbers can start around 5 to 7 years old, once children count reliably and recognise numbers.
Is soroban necessary for mental maths?
No, but it is a very effective visual method. It makes number structure visible and leads naturally to calculating with mental images.
Should mental maths practice be timed?
Only once answers are reliably correct. Early timing increases anxiety and guessing.