Magic Maths Tricks: Subtraction is where many children first run into trouble with maths. The moment numbers get bigger, the column method introduces exchanging, and suddenly, a child who was confident with addition is staring blankly at the page. What often helps is not more drilling but a different entry point.
Mental strategies and maths tricks give children a way to see numbers as flexible things they can move and adjust, which is exactly what the UK National Curriculum means when it talks about fluency and mathematical reasoning at Key Stage 1 and Key Stage 2.
The five strategies in this article are not shortcuts that bypass understanding. Each one works because of a genuine number property, and when children grasp why a trick works, they are building the kind of number sense that carries them through KS2 and beyond. LearningMole has produced curriculum-aligned maths videos and resources for primary children for over a decade, and the approach is always the same: make the concept visual and logical first, then let the speed follow naturally.
Michelle Connolly, who founded LearningMole after more than 15 years in primary classrooms, has seen this pattern repeat consistently: children who understand what they are doing become far more resilient when problems get harder.
This guide is for KS1 and KS2 teachers who want an engaging hook for a mental maths lesson, and for parents supporting subtraction homework at home. It covers five strategies, their classroom applications, how they map to National Curriculum year groups, and a step-by-step breakdown of the famous 1089 mystery trick that reliably produces a ‘wow’ moment in any primary classroom.
Every subtraction trick in this guide works because of the same underlying principle: numbers have structure, and you can use that structure to make calculations easier. This is not magic; it is place value in action. The UK National Curriculum introduces place value formally in Year 1 and builds on it through KS2, making these mental strategies a natural companion to formal written methods rather than an alternative to them.
One important distinction for UK teachers: where older textbooks and some international resources use the word ‘borrowing,’ current National Curriculum guidance uses ‘exchanging.’ This matters because ‘exchanging’ accurately reflects what happens: you are moving value between columns, not taking something that needs to be returned. When children understand this, the written column method and the mental strategies in this guide start to connect naturally.
Best used for mental work: the Compensation Method, the Shopkeeper’s Method, and the Constant Difference.
Best used for written support: the All from 9, Last from 10 method and the column method with understanding of exchanging.
This is the performance trick, the one that produces genuine amazement and works brilliantly as a lesson starter for Year 4 upwards. The child thinks of a 3-digit number, follows three steps, and always ends up at 1089. Here is how it works.
Why does it always equal 1089? The trick works because of the consistent algebraic structure of 3-digit subtraction when you reverse and add. For a number represented as (100a + 10b + c), the process always yields 99(a − c), and the only values of (a − c) that produce a 3-digit result add back to 1089 after reversal. It is not magic — it is arithmetic being consistent. Share this explanation with Year 5 and Year 6 children who ask why, and you have a natural extension task.
The trick works for any 3-digit number where the hundreds and units digits are not equal. If a child’s subtraction gives a 2-digit answer (for example, 80 instead of 080), remind them to treat it as 3 digits with a leading zero.
This is the most mathematically powerful mental strategy for subtraction, yet it appears in very few primary resources. The principle: if you move both numbers in a subtraction the same distance along the number line, the gap between them stays identical. This means you can slide an awkward calculation into one that requires no exchanging at all.
Example: 100 − 36. Exchanging across two columns is fiddly. Instead, subtract 1 from both numbers: 99 − 35 = 64. The answer is the same. Or take 62 − 37. Add 3 to both: 65 − 40 = 25. Instant answer, no pen required.
Classroom tip — The Subtraction Slide: Draw a number line on the board. Show children two points representing the two numbers in the subtraction. Slide both points the same amount left or right and ask: ‘Has the gap changed?’ This visual demonstration takes about two minutes and makes the Constant Difference principle concrete before you ask children to use it mentally.
Children who are confident in adding often struggle to subtract. The Shopkeeper’s Method uses that addition strength. Instead of taking away, you count up from the smaller number to the larger, bridging through the nearest ten or hundred on the way.
Example: 63 − 37. Start at 37. Add 3 to reach 40. Add 20 to reach 60. Add 3 to reach 63. Total added: 3 + 20 + 3 = 26. This method directly reflects how shopkeepers historically gave change, and it maps perfectly onto a number line. For children who find the column method confusing, it offers an alternative path to the same answer.
This strategy suits Year 2 upwards and works particularly well for children who find holding numbers in working memory difficult, as each bridge step can be written or shown on fingers.
When a number ends in 7, 8, or 9, it is almost always faster to round it up to the nearest ten, subtract that, then add the difference back. This is the Compensation Method, and it is one of the Year 3 and Year 4 mental strategies in the National Curriculum.
Example: 52 − 19. Round 19 up to 20. Subtract 20 from 52: 32. You subtracted 1 too many, so add it back: 33.
Example: 84 − 38. Round 38 to 40. 84 − 40 = 44. Add 2 back: 46.
Teaching note: Children often forget to add back after rounding up. A simple rule: if you rounded the subtracted number UP, add back the difference. Posting this as a classroom anchor chart alongside the compensation method significantly reduces errors.
This strategy handles subtractions from powers of ten — 10, 100, 1,000 — without any exchanging. The rule: subtract every digit of your number from 9, except the last non-zero digit, which you subtract from 10.
Example: 1,000 − 437. Apply the rule: 9 − 4 = 5, 9 − 3 = 6, 10 − 7 = 3. Answer: 563.
Example: 100 − 64. 9 − 6 = 3, 10 − 4 = 6. Answer: 36.
This trick has direct classroom value during SAT preparation, when children need fast, reliable ways to handle subtraction from round numbers without multi-column exchanging.
| The Problem | Column Method (Exchanging) | Mental Trick | Why It’s Faster |
|---|---|---|---|
| 1,000 − 437 | Exchange across three columns | All from 9, Last from 10: 563 | No exchanging needed |
| 100 − 36 | Exchange tens then ones column | Slide both: 99 − 35 = 64 | Avoids all exchanges |
| 63 − 37 | Exchange from tens column | Add up: 37+3+23 = 63, answer 26 | Intuitive bridging |
| 52 − 19 | Exchange from the tens column | Round: 52−20+1 = 33 | Exchange from the tens column |
| Year Group | Key Subtraction Focus | Recommended Tricks |
|---|---|---|
| Year 1 (KS1) | Subtracting single digits, counting back | Number Line, Make Ten |
| Year 2 (KS1) | Subtracting 2-digit numbers, mental methods | Number Line, Compensation |
| Year 3 (KS2) | The formal column method was introduced, exchanging | Compensation, Shopkeeper’s Method |
| Year 4 (KS2) | Subtracting up to 4-digit numbers | Constant Difference, 1089 Trick |
| Year 5–6 (KS2) | The formal column method was introduced, replacing | Multi-digit, decimal, reasoning problems |
The shift from KS1 to KS2 is from concrete and pictorial methods (number lines, objects, hundred squares) to increasingly abstract mental strategies and the formal column method. These tricks support children through that transition by giving them flexible, efficient mental tools.
“Children who can see that numbers move, that you can slide them, round them, and rearrange them, become flexible thinkers. Flexibility with numbers is the hallmark of a genuinely confident mathematician, not just someone who has memorised a procedure.”
Michelle Connolly, Founder of LearningMole and former teacher with over 15 years of classroom experience
One child uses a calculator; another uses a mental trick. Give both children the same subtraction problem. Race to see who gets the answer first. Children are consistently surprised to find the mental method beats the calculator — especially with the Compensation Method and the Constant Difference. This works as a starter activity, a fast-finisher challenge, or a maths enrichment task.
Place a number of buttons (or counters, cubes, or any small objects) on the table. State a subtraction sum aloud. Children physically remove the correct number and count what remains. This concrete method is ideal for Year 1 and Year 2 children who need tactile support before moving to mental methods, and it works equally well for home learning with household objects.
Draw a number line from 0 to 20 (or 0 to 100 for older children). Give a subtraction problem and ask children to ‘jump back’ to find the answer. Each jump can be counted aloud. This visual strategy is particularly effective for children who struggle to hold multi-step calculations in working memory, and it directly demonstrates the Shopkeeper’s Method on paper.
Before teaching the trick, show the answer — write 1089 on a sealed envelope at the start of the lesson. Tell the class you know what number they will end up with, no matter what 3-digit number they choose. Work through the steps on the board with a class-chosen number, then reveal the envelope. This sequence takes approximately ten minutes and provides a strong hook for a formal subtraction lesson.
SEND Adaptations: Use number fans or digit cards for the 1089 trick so the physical manipulation supports working memory. For the Compensation Method, provide a reference card showing the ’round, subtract, adjust’ steps. Number lines with moveable markers help with the Shopkeeper’s Method for children who struggle with abstract mental tracking.
LearningMole provides curriculum-aligned maths videos and primary teaching resources covering mental subtraction strategies, place value, and mathematical reasoning for KS1 and KS2. The video library includes step-by-step walkthroughs designed to be used on a classroom whiteboard or for independent home learning.
For parents: LearningMole’s maths resources explain subtraction strategies in straightforward language without assuming prior teaching knowledge. Children can watch explanations independently, pause and rewind as needed, and follow along at their own pace, making them useful for homework support as well as home education.
The Compensation Method is the most accessible starting point for children in Year 2 and Year 3. It works best when subtracting numbers ending in 7, 8, or 9, rounding up to the nearest ten, subtracting, then adding back the small difference. Children who can add single digits confidently can usually apply this method quickly. The Number Line/Shopkeeper’s Method is a good alternative for children who think more visually.
The term ‘exchanging’ reflects what actually happens in column subtraction: you are moving value from one column to another, for example, exchanging one ten for ten ones. Nothing is ‘borrowed’ because nothing gets returned. The UK National Curriculum moved to ‘exchanging’ because it reinforces place value understanding rather than treating subtraction as a mechanical procedure. LearningMole’s maths resources use ‘exchanging’ consistently to match what children hear in the classroom.
Use the All from 9, Last from 10 rule. For 1,000 − 437: subtract each digit from 9, except the last, which you subtract from 10. So 9−4=5, 9−3=6, 10−7=3, giving 563. This method works for any subtraction from a power of ten and eliminates multi-column exchanging completely. It is particularly useful in Year 5 and Year 6 mental arithmetic.
Yes. The Compensation Method and the Shopkeeper’s Method align directly with Year 3 and Year 4 National Curriculum mental fluency objectives. The Constant Difference is introduced well in Year 4. The 1089 trick works as a challenge activity for Year 4 upwards, but can be shown as a ‘magic’ demonstration to any year group. The All from 9, Last from 10 strategy is best introduced in Year 5.
Mental strategies are explicitly tested in KS2 SATs Paper 1 (Arithmetic), where children answer timed questions without a calculator. Using efficient mental methods, particularly the Compensation Method and the Constant Difference, can save significant time. For Papers 2 and 3 (Reasoning), children must often show their method, so the formal column method with correct exchanging is still essential. These tricks and the formal method work together, not in competition.
Start with the Compensation Method using real-world examples, ‘We had 52 minutes and spent 19 minutes watching a video; how long is left?’ Round 19 to 20, take that from 52, add 1 back: 33 minutes. Once children are comfortable with one trick, introduce the Shopkeeper’s Method using money calculations. LearningMole’s maths videos walk through each strategy visually, making them easy for parents to follow alongside their children without needing a maths background.
A mental maths strategy is a flexible approach for calculating in your head, choosing the method that suits the numbers in front of you. A formal written method (like column subtraction with exchanging) is a reliable procedure that works for any numbers, regardless of size. The National Curriculum expects children to develop both fluency with mental strategies for efficient everyday calculation and confidence with formal methods for more complex arithmetic. These five tricks build mental flexibility; the column method provides the written foundation.
Start with the Compensation Method for numbers ending in 7, 8, or 9 — it gives children an immediate, satisfying experience of mental subtraction being faster than reaching for a pencil. Follow with the Shopkeeper’s Method to address children who think additively. Introduce the Constant Difference once children are confident with the first two, as it requires understanding that both numbers change together. Save the All from 9 rule and the 1089 trick for Year 4 and above as extension and enrichment activities.
The five strategies in this guide are not about replacing the written column method. They are about building the number sense that makes formal methods feel logical rather than arbitrary. A child who has worked through the Constant Difference and understood why it works is a child who genuinely understands place value, and that understanding is what the National Curriculum’s mathematical fluency objectives are pointing towards.
For teachers, any one of these strategies can anchor a mental maths starter, a reasoning discussion, or an enrichment task. The 1089 trick in particular offers something rare in primary maths: a moment of genuine mystery that children want to understand rather than just repeat. That curiosity, the question ‘but why does it always work?’, is exactly the kind of mathematical thinking KS2 assessment increasingly rewards.
LearningMole’s curriculum-aligned maths videos cover subtraction strategies, place value, and arithmetic reasoning for every year group from Reception to Year 6. Whether you are a teacher planning a mental maths lesson, a parent working through homework with a frustrated child, or a home educator looking for structured support, the resources are designed to make maths visual, logical, and, occasionally, genuinely surprising.
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