Mental Math: Techniques and Exercises for Kids

Mental math is the ability to solve addition, subtraction, multiplication and division without pencil, paper or a calculator, using strategies like rounding, decomposition and doubling. Kids start practicing it around age 6-7, and with regular practice it becomes faster and more automatic. This guide explains 4 concrete techniques, with step-by-step examples, for parents looking for practical exercises.

What is mental math?

Mental math means operating with numbers “in your head,” without relying on written algorithms or devices. It is not about guessing or memorizing random tables — it is a set of strategies that break a hard problem into simpler steps.

For example, adding 38 + 47 mentally does not mean lining up columns like on paper. It means seeing that 38 + 47 is the same as 40 + 45 (rounding and adjusting), which gives 85 in two steps instead of five.

These strategies rely on understanding place value (ones, tens, hundreds) and on already knowing the multiplication tables. The more automatic those basics are, the faster mental math becomes.

Decomposition technique: splitting into tens and units

Decomposition means splitting a number into parts that are easier to add or subtract, like tens and units, and working with each part separately. Split, then add.

Example: 47 + 26.

Step 1. Break down each number: 47 = 40 + 7, and 26 = 20 + 6.

Step 2. Add the tens: 40 + 20 = 60.

Step 3. Add the units: 7 + 6 = 13.

Step 4. Combine the results: 60 + 13 = 73.

Decomposition works the same way for subtraction: 84 − 29 is solved as 84 − 20 = 64, then 64 − 9 = 55. Breaking numbers into small parts keeps kids from losing track of the calculation, which tends to happen when they try to solve everything in a single mental leap.

Rounding and compensation technique

Rounding and compensation means bringing a number to a nearby ten to make the math easier, then adjusting the result by adding or subtracting the difference.

Example: 58 + 39.

Step 1. Round 39 up to 40 (you added 1 too many).

Step 2. Calculate 58 + 40 = 98.

Step 3. Subtract the extra 1: 98 − 1 = 97.

This is the technique adults use naturally when calculating change at a store: rounding to a comfortable number and adjusting at the end saves mental steps. It also works for subtraction, by rounding the number being subtracted and adding back the difference.

Doubles, halves and quick shortcuts

Doubles and halves are automatic shortcuts: knowing that double 8 is 16, or half of 30 is 15, lets kids solve multiplications and divisions without going through the full calculation.

Example: 16 × 5.

Step 1. Instead of multiplying directly, use the fact that 5 is half of 10.

Step 2. Multiply 16 × 10 = 160.

Step 3. Divide by 2: 160 ÷ 2 = 80.

This shortcut works because multiplying by 5 is always the same as multiplying by 10 and dividing by 2. Mastering doubles up to 20 and halves of even numbers is one of the most useful foundations of mental math — it shows up in dozens of different operations.

Which technique to use for which operation?

There is no single strategy for everything: each mental math technique works best depending on the type of operation and the numbers involved.

• If the numbers end in 8 or 9 → rounding and compensation.
• If the operation is by 5, 10 or a power of 2 → doubles and halves.
• If there is no obvious shortcut → decomposition into tens and units.

Practicing this question before calculating (“what shortcut applies here?”) is what separates a child who calculates fast from one who only adds slowly and correctly.

Common mistakes when calculating mentally

• Trying to do everything in a single step. Without decomposing, it is easy to lose a digit halfway through.
• Not checking whether the result makes sense. Rounding the original problem helps catch big errors.
• Relying only on memorized tables. Mental math combines tables with strategies, it does not replace them.
• Practicing only with worksheets. Without real context, the technique never becomes a habit.

How to practice mental math at home

You do not need a special notebook. Mental math shows up in everyday situations:

• At the store: calculating change before it is handed over.
• In the kitchen: doubling or halving a recipe.
• In the car: estimating how much longer a trip will take at a given speed.
• Playing cards or dice: adding up points quickly.

Turning these moments into short, pressure-free 30-second challenges is what helps most to automate the techniques.

Mental math exercises for kids

These exercises help practice the techniques above at home, with the solutions included. It helps to start with decomposition and move toward calculating by parts.

1. Decomposition: 36 + 28. (Solution: 30+20=50, 6+8=14, total 64.)
2. Rounding and compensation: 67 + 19. (Solution: 67+20=87, 87−1=86.)
3. Doubles and halves: 24 × 5. (Solution: 24×10=240, 240÷2=120.)

If your child solves these exercises without help, they already master the basics of mental math. To practice with a live teacher, try a free online math class, or check out how the rule of three works as the next step into proportions.

Summary

1. Mental math solves operations without pencil or calculator, using strategies, not pure memory.
2. Decomposition: split into tens and units and add by parts.
3. Rounding and compensation: bring a number to the nearest ten and adjust after.
4. Doubles and halves: shortcuts for multiplying and dividing by 2, 5 and 10.
5. The key question is always: which shortcut simplifies this operation the most?

Keep learning

• What are fractions? A simple explanation for kids
• What are decimal numbers?
• What are multiplication tables? An explanation for kids
• Rule of three: what it is and how to solve it
• Online math classes for kids: a parent's guide

Want your child to understand math instead of memorizing it? Book a free trial class at Algonova — 60 minutes, online and free.