Learning Academy · Math
Taming subtraction (yes, it's genuinely harder)
Subtraction reliably lags addition, and the classic 'borrowing' errors have one root cause. Here's why it's harder, the strategies that tame it, and the fix for regrouping.
Written by Andreea Schwimmer, M.A. — credentialed elementary teacher, 13+ years in TK–5 classrooms · Reviewed by South Bay Peak Learning
Last updated July 11, 2026 · 8-minute read · This guide is written to support families and complements — never replaces — communication with your child's classroom teacher.
In this guide you'll learn
- Why subtraction is legitimately harder than addition (your child isn't imagining it)
- The two mental models — take-away and find-the-distance — and why the second is a superpower
- Fact families: turning every subtraction into an addition your child already knows
- The real cause of regrouping errors (34 − 18 = 24) and the concrete repair
Here's validation for every child who finds subtraction meaner than addition: it is. Counting backward strains young working memory; subtraction can't be reordered the way addition can (5 + 8 = 8 + 5, but 5 − 8 ≠ 8 − 5); and its written procedure — regrouping — is the first genuinely multi-step ritual most children meet. Subtraction lagging addition by months is the norm, not a red flag. What matters is equipping the right strategies, because the default one (counting backward on fingers) is the worst of the lot.
The two mental models
Take-away is the model everyone teaches: 13 − 5 means start with 13, remove 5. Fine for small numbers, but it locks children into counting backward. Find-the-distance is the sleeper superpower: 13 − 5 asks how far from 5 to 13? — count UP: "5… 10 is five more, plus 3 is eight." Counting up is easier, more accurate, and it's secretly how adults make change and do mental subtraction (83 − 68? "68 to 70 is 2, to 83 is 13 more — 15"). Children shown both models, with distance made physical on a number line, subtract better for life.
Fact families: the great shortcut
The fastest route to subtraction fluency runs straight through addition your child already owns. Teach facts as families: the trio 5, 8, 13 generates four facts (5+8, 8+5, 13−5, 13−8) that live together. Then every subtraction becomes a familiar question in disguise: 13 − 8? "8 plus what makes 13?" — an addition lookup. Triangle flashcards (three corners, cover one) and "family reunion" games (deal three cards, say all four facts) make this concrete. It halves the memorization and builds the inverse-operations understanding that algebra will eventually stand on.
Regrouping: the truth about 34 − 18 = 24
The most famous wrong answer in elementary math is not carelessness — it's a systematic error: the child subtracted smaller-from-bigger in each column (8 − 4 flipped to 4 from 8) because "borrowing" was learned as an incantation without the place-value picture underneath. The repair is always the same, and it's physical:
- Build 34 in base-ten blocks (3 tens, 4 ones). Try to take 8 ones away. You can't — there aren't enough. FEEL the problem
- Trade one ten for ten ones — now 2 tens, 14 ones. Nothing changed in value; everything changed in form. THIS is 'borrowing'
- Now remove 8 ones and 1 ten. Read the answer off the table: 16
- Do it with blocks until boring, then with drawings, then connect each written step to the trade it records — the algorithm is just the receipt
A week of this sequence fixes what a year of red-penned worksheets doesn't, because the worksheet corrects the answer while the blocks correct the model.
Suggested next reading
- Addition Strategies — the ladder this page's shortcuts climb on
- Number Sense, Explained — why the blocks work: place value as felt reality
- Multiplication Mastery — the next operation — and a fresh start
Questions parents ask
Why does my child know 8 + 5 but freeze on 13 − 5?
Because those live in different mental drawers until fact families connect them. Teaching '13 − 5 asks: 5 plus WHAT makes 13?' converts every subtraction into an addition lookup — the single most useful subtraction move there is.
Is counting backward a good subtraction strategy?
It's a weak one — counting backward is genuinely hard for young children and error-prone past small numbers. Counting UP from the smaller number ('9… 10, 11, 12, 13 — that's 4') is easier, more accurate, and scales beautifully.
My 2nd grader keeps getting 34 − 18 = 24. Careless?
Not careless — systematic. That answer comes from subtracting 'smaller from bigger in each column' (8−4 flipped), which means regrouping was learned as a ritual without the place-value picture. The fix is concrete: base-ten blocks, trading a ten for ones, until the WHY exists. Then the procedure holds.
Should subtraction facts be memorized separately from addition?
Mostly no — learn them AS fact families (5, 8, 13 is one family, four facts). It halves the memory load and builds the addition-subtraction connection algebra will lean on later.