Problem Solving for Kids: Mathematics can feel like a mountain, but the right mental maths strategies turn that mountain into a series of manageable steps. For children working through the UK National Curriculum from KS1 to KS2, the ability to solve maths problems confidently, without always reaching for a pencil, is one of the most transferable skills they will ever develop. LearningMole has supported thousands of parents and primary teachers across the UK in making this happen, and this guide brings together the most effective strategies in one place.
What separates children who struggle with maths from those who thrive is rarely raw intelligence — it is number sense. Number sense is the intuitive understanding of how numbers relate to one another, and it is the foundation on which every mental maths strategy is built. When children can partition 47 into 40 and 7 without thinking, they free up mental space to focus on the problem’s logic rather than the mechanics of the calculation. That shift — from slow arithmetic to fluent mental maths — is what this article is designed to help you achieve.
Whether you are a parent looking for practical activities to try at home or a teacher planning lessons aligned to the National Curriculum, this guide covers everything from the seven core mental maths strategies to how those strategies connect to Year 6 SATs success. You will also find a curriculum milestone tracker, classroom activities, and links to LearningMole resources and videos that bring every concept to life.
Mental maths is not simply the ability to answer questions quickly. Speed is a by-product; the real goal is efficiency — choosing the most sensible method to reach a correct answer without pen and paper.
There is an important distinction between arithmetic and mental maths. Arithmetic is the calculation itself (adding, subtracting, multiplying, dividing). Mental maths is the strategy used to carry out that calculation in your head. A child who adds 39 + 45 by counting up in ones is doing arithmetic. A child who thinks “40 + 45 = 85, minus 1 = 84” is doing mental maths.
This matters because the UK National Curriculum explicitly expects children to develop fluency, the ability to recall and apply number facts rapidly and flexibly. Fluency is not rote memorisation. A child who has memorised that 7 × 8 = 56 may panic when asked to work out 14 × 8. A child with genuine number sense will think “double 7 × 8” and arrive at 112 with confidence.
LearningMole’s approach to maths learning is grounded in this distinction. Rather than drilling isolated facts, our resources build the patterns and relationships that allow children to reason their way through unfamiliar problems — a skill that serves them well beyond the maths classroom.
These seven strategies form the toolkit that the UK National Curriculum builds across KS1 and KS2. Helping children understand and apply all seven, rather than defaulting to one, develops the flexible thinking that underpins genuine problem solving.
| Strategy | What It Means | Example |
|---|---|---|
| Partitioning | Split a number into tens and ones | 47 + 35 → (40 + 30) + (7 + 5) = 82 |
| Compensation | Round up, then adjust | 39 + 45 → 40 + 45 = 85, minus 1 = 84 |
| Bridging through 10 | Use 10 or 100 as a stepping stone | 8 + 7 → 8 + 2 = 10, + 5 = 15 |
| Doubling and halving | Use known doubles to find near-doubles | 13 + 14 → double 13 = 26, + 1 = 27 |
| Reordering | Change the order of numbers to make calculations easier | 3 + 17 + 7 → 3 + 7 + 17 = 10 + 17 = 27 |
| Using number bonds | Recall pairs that make 10, 20 or 100 | 64 + 36 = 100 (bond to 100) |
| Counting on and back | Use a number line mentally | 52 − 9 → count back 9 from 52 = 43 |
Partitioning is usually the first strategy children encounter in KS1 and remains essential throughout primary school. Compensation becomes particularly powerful for solving maths problems that involve numbers just below a round figure (like 39, 49, 99). Bridging through 10 is the mental equivalent of crossing a stepping stone; it teaches children to look for the nearest landmark number rather than calculating in a straight line.
Once children are comfortable naming the strategies, the next step is helping them choose the right strategy for a given problem, which is a reasoning skill, not just a maths skill.
Here is something that often surprises parents: a child can know all seven strategies above and still struggle with maths word problems. The reason is cognitive load.
Cognitive load refers to the amount of mental effort a task demands. When a child has to concentrate hard on working out 47 + 35, there is very little mental space left for understanding what the word problem is actually asking. The calculation itself becomes an obstacle.
This is why fluency matters so much. When simple calculations become automatic — when a child just knows that 7 + 8 = 15 without having to think — the brain’s working memory is freed up to focus on the logic of the problem. What is being asked? What information is relevant? What operation is needed?
Mental bar modelling is a powerful bridge between calculation and reasoning. Bar models are widely used in UK primary classrooms as a visual tool for structuring word problems. The mental version takes this further: children learn to picture the parts and wholes of a problem in their mind before writing anything down. For example, when solving “Amara has 34 stickers. She gives 17 to her friend. How many does she have left?”, a child with a mental bar model can instantly see that this is a part-whole subtraction problem, then apply compensation (17 is close to 20: 34 − 20 = 14, + 3 = 17).
This is the bridge competitors rarely explain: mental maths is not the destination. It is the engine that powers genuine problem-solving for kids.
The UK National Curriculum sets clear expectations for what children should be able to do mentally at each stage of primary school. This tracker helps parents and teachers see whether a child is on track and where to focus next.
| Year Group | Key Mental Maths Expectations |
|---|---|
| Year 1 | Number bonds to 10 (e.g. 3 + 7); count on and back within 20 |
| Year 2 | Number bonds to 20; add/subtract a 2-digit number and ones mentally; recall 2×, 5×, 10× tables |
| Year 3 | Add/subtract 3-digit numbers and hundreds mentally; recall 3×, 4×, 8× tables |
| Year 4 | Mental addition and subtraction of 4-digit numbers; recall all times tables up to 12 × 12 |
| Year 5 | Mental calculation with larger numbers, fractions and decimals; solve multi-step problems |
| Year 6 | Apply all strategies efficiently; solve two-step and multi-step word problems mentally where possible |
A few things are worth noting here. The Year 4 multiplication tables check, a national assessment taken by all Year 4 pupils, tests fluency up to 12 × 12 under time pressure. Children who have moved beyond rote memorisation to genuine number sense (using doubling, for example, to derive 8 × 7 from 4 × 7) will handle this with far more confidence than those who have only drilled isolated facts.
By Year 5 and 6, LearningMole’s maths resources increasingly focus on the multi-step reasoning that the curriculum demands — helping children practise applying their mental toolkit to problems they have not seen before.
The Year 6 SATs mathematics assessments include three papers: Paper 1 (Arithmetic) and Papers 2 and 3 (Reasoning). Most preparation focuses on Paper 1, but it is the Reasoning papers where mental maths makes the biggest difference.
As Michelle Connolly, founder of LearningMole and educational consultant with over 15 years of classroom experience, explains: “Mental fluency is the hidden key to the Reasoning papers. If a child spends all their working memory on the addition inside a word problem, they have nothing left for the reasoning itself — the step where they decide what to calculate and why.”
In the Reasoning papers, children face two-step and multi-step problems that require them to extract relevant information, choose the right operation, carry it out accurately, and then interpret the result. Children who are fluent mental mathematicians move through the calculation step almost invisibly — which means they have more time and more brain power for the logic.
Practical implication: When preparing for KS2 assessments, do not neglect the mental work. Timed daily practice on core number facts (five minutes per day is sufficient), combined with regular exposure to word problems, is the most effective approach.
Word problems are one of the most effective tools for developing problem-solving skills in children because they require maths and literacy to work together. A child must read carefully, understand what is being asked, identify the relevant numbers, choose an operation, carry it out, and then check whether the answer is reasonable.
The RUCSAC method gives children a reliable framework for approaching any word problem:
RUCSAC is particularly useful for children who rush through problems and make avoidable errors. Encouraging them to pause at the “Understand” stage — before picking up a pencil — builds the metacognitive habit of thinking about the problem before attempting to solve it.
Story problems are a creative variant that works well at home. A parent or guardian describes a situation in words, and the child must work out what calculation is needed. Reversing this — asking the child to invent a story that matches a given number sentence, such as 12 − 5 = ? — extends the skill further and develops mathematical vocabulary naturally. Words like “altogether,” “difference,” “share equally,” and “how many more” are the linguistic building blocks of number reasoning, and children who know them are better equipped when they encounter them in assessments.
For younger children in EYFS and KS1, linking numbers to shapes and pictures provides a concrete starting point. Asking a child to represent the number three by drawing, then adding two more shapes, then removing one, creates a visual story that connects naturally to addition and subtraction operations.
These activities require no special equipment and can be fitted around everyday life. The goal is not pressure or speed; it is pattern recognition and confidence.
1. If This Is the Answer: Tell your child that the answer is 18 (or any number appropriate to their age). Ask them to find as many ways as possible to make that number using any operation. Younger children might offer 10 + 8 or 20 − 2; older children can reach 3 × 6, 36 ÷ 2, or 19 − 1. This game builds flexible thinking and shows children that there is rarely only one route to a solution.
2. Supermarket Maths: Rounding prices and estimating totals while shopping is genuine maths in context. “We have three items at roughly £2 each — about how much is that?” connects estimation to real-world decision-making. For older children, calculating percentage discounts or comparing unit prices adds further challenge.
3. Estimation Station: Ask your child to estimate answers before calculating: “About how many?” or “Is it closer to 50 or 100?” This builds the number sense needed to catch errors. A child who estimates before calculating will immediately notice if their answer is wildly wrong.
4. The Human Number Line: Place numbered cards on the floor in a line. Call out a calculation and ask the child to jump to where they think the answer is. This movement-based activity is especially effective for teaching bridging through 10 — children physically step on the landmark number before moving to the answer.
5. Daily Five-Minute Drill: Five minutes of focused practice on number bonds or times tables — spoken aloud, not written — builds automaticity faster than longer written sessions. Keep it conversational rather than test-like. The goal is fluency, not pressure.
One of the most underrated KS2 skills is knowing when to use a mental method and when to use a written one. The National Curriculum expects children to make this judgement efficiently.
A useful decision tree:
Teaching children this judgment, rather than always defaulting to column addition, is itself a problem-solving skill. It tells a teacher or examiner that the child understands what they are doing, not just how to execute a procedure.
LearningMole provides a growing library of maths resources specifically designed to support UK primary children with problem-solving and mental maths. Parents working through these strategies at home will find our video library particularly useful — short, focused lessons that children can watch independently or alongside an adult.
Our mental maths video collection covers partitioning, doubling and halving, bridging through 10, and addition strategies in an accessible format built for KS1 and KS2 learners. Alongside the videos, LearningMole’s subscription gives access to over 2,100 educational resources covering numeracy, literacy, science, and more.
For teachers, our resources align with National Curriculum expectations at each year group and are designed to complement classroom teaching rather than replace it. Whether you are looking for a warm-up activity, a differentiated task, or a homework-friendly video, LearningMole’s platform has resources ready to use.
Subscribe to LearningMole for as little as £1.99 per month and access the full library — including all maths problem-solving resources, mental maths drills, and word problem activities.
The seven core strategies are: partitioning, compensation, bridging through 10, doubling and halving, reordering, using number bonds, and counting on and back. Together, these strategies give children a flexible toolkit for solving maths problems without relying on written methods.
Focus on number sense rather than speed. Daily five-minute practice on number bonds and times tables builds automaticity, while regular exposure to word problems develops the reasoning layer. LearningMole’s video resources provide short, engaging lessons that complement this daily practice effectively.
Mental maths and problem-solving are related but distinct. Mental maths is the tool — the ability to calculate efficiently in your head. Problem-solving is the process of applying a tool to a situation with an unknown answer. Strong mental maths reduces cognitive load, freeing the brain to focus on the reasoning required to actually solve the problem.
From the moment children begin counting. In EYFS, visual number bonds (two groups of objects that make five, for example) lay the foundations. By Year 1, the National Curriculum introduces formal number bonds to 10. The earlier children develop number sense through play and visual patterns, the more confident they become in KS1 and KS2.
Arithmetic is the calculation of adding, subtracting, multiplying, and dividing. Mental maths is the strategy used to carry out that calculation without pen and paper. A child doing arithmetic might count up in ones; a child using mental maths will choose the most efficient route — compensation, partitioning, or a number bond — to reach the answer.
RUCSAC stands for Read, Understand, Choose, Solve, Answer, and Check. It is a structured approach to tackling maths word problems that helps children slow down, identify what is being asked, and verify their answer before moving on. It is particularly effective for children who rush through problems or misread what is required.
LearningMole offers a selection of free maths videos and resources on our website and YouTube channel. Our subscription library, available from £1.99 per month, gives access to the full collection of over 2,100 resources, including mental maths activities, word problem guides, and KS1/KS2 number fact drills.
Mental maths strategies are not a shortcut — they are the long game. Children who develop a genuine toolkit of flexible calculation strategies in KS1 carry that fluency into KS2, into secondary school, and into everyday life. The goal is never to produce human calculators; it is to develop confident, efficient thinkers who know how to approach a problem, choose a strategy, and check whether their answer makes sense.
The activities, strategies, and curriculum milestones in this guide provide parents and teachers with a clear framework for systematically building that confidence. Start with number bonds, build through the seven strategies, and connect everything back to real-world problems and word problems. This is the progression that the UK National Curriculum is designed around, and it is the one that produces children who genuinely enjoy solving maths problems.
LearningMole is here to support every step of that journey. Whether you explore our free video resources on YouTube, subscribe to the full library, or simply use the activities in this guide as a starting point, the most important thing is consistent, low-pressure practice. Five minutes a day, every day, builds the kind of mental agility that transforms a child’s relationship with mathematics.
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