The Night 13 Minus 5 Ended in Tears
I'll tell you exactly where we were when subtraction broke my daughter: page 42 of a P1 practice book, question three, 13 − 5. She had been fine — genuinely fine — with 9 − 4 and 8 − 3 for weeks. Then the numbers crossed into the teens, and suddenly a child who liked maths was rubbing holes in the paper with her eraser and telling me she was "bad at subtraction".
She wasn't bad at subtraction. She was standing at the exact spot where subtraction within 20 trips almost every P1 child — the crossing-ten problem — with a parent (me) who kept saying "just count backwards" as if repetition would make it helpful. It took us a few wrong turns and one very good conversation with her teacher to find the way through. This post is everything I wish I'd known on that first night.
Addition Comes Easy, Subtraction Comes Sideways
First, some reassurance: if your P1 child sailed through addition and then stalled at subtraction, that is the normal order of things. Addition matches how young children naturally think — more things, count them all, bigger number, done. Subtraction asks them to imagine things disappearing, to hold in mind both what was there and what's left, and often to run their number line in reverse — and counting backwards is genuinely harder than counting forwards at this age.
So expect subtraction to lag addition by a good stretch, and don't read the lag as a warning sign. What matters is how your child is finding answers, not just whether the answers are right. Two children can both correctly answer 13 − 5: one counts back five numbers on her fingers hoping not to slip; the other thinks "5 plus what makes 13?" The second child has a strategy that will still be working in P3. The whole game of P1 subtraction is moving your child from the first kind of answer to the second — gently, and in the right order.
Number Bonds: The Foundation Everything Sits On
If your child's school follows the standard local approach, you've met number bonds: those little diagrams with one number splitting into two parts. 8 branches into 5 and 3. 10 branches into 6 and 4. Parents sometimes treat the bond diagrams as a warm-up ritual before "real maths" starts. They are not a warm-up. They are the entire foundation.
Here's why. A number bond says 8 is made of 5 and 3 — one fact, three faces: 5 + 3 = 8, 8 − 3 = 5, 8 − 5 = 3. A child who truly owns the bond doesn't experience subtraction as a new operation to learn. Asked 8 − 5, they aren't computing anything; they're recalling the missing part of a whole they already know. Subtraction becomes memory, not machinery.
Which bonds matter most? In my experience, in order:
- Bonds of 10 — 1+9, 2+8, 3+7, 4+6, 5+5. These are the crown jewels. Everything about crossing ten (coming soon) depends on them being instant, not worked out.
- Bonds within 10 — all the ways to make 5, 6, 7, 8, 9.
- Ten-plus facts — 10+3=13, 10+6=16. Sounds trivial; quietly essential, because it's how a child sees that 13 is 10 and 3.
The Two Strategies: Count Back vs Think Addition
P1 children are generally shown two mental routes to an answer like 9 − 3, and it helps enormously when the parent at home knows both and uses their names.
Count back. Start at 9, step backwards three: 8, 7, 6. Answer 6. This is the beginner strategy, and it's the right one when you're only removing a little — subtracting 1, 2, or 3. Beyond that it collapses: watch a child do 13 − 9 by counting back nine steps and you'll see fingers, lost count, a re-start, and a fifty-fifty answer. The strategy isn't wrong; it's just being asked to do too much.
Think addition. For 13 − 9, don't go backwards at all. Ask: "9 plus what makes 13?" Count up — 10, 11, 12, 13 — four steps. Answer 4. Same problem, four small forward hops instead of nine shaky backward ones, and forward counting is the direction children are strong in.
The rule of thumb we landed on, which matched what her teacher taught: when the numbers are close together, think addition; when you're only taking away a small amount, count back. 15 − 13? The numbers are practically neighbours — count up, answer 2, done in a second. 15 − 2? Just step back twice. A child who can look at a question and choose the route is doing real mathematics, even at seven.
One warning from our house: if your child is a determined counter-backer, don't ban the old strategy — outlaw it and you get tears plus secret finger-counting under the table. Instead, race the strategies side by side on a question like 12 − 9, let them feel think-addition winning, and let them switch because it's obviously better. Children abandon slow strategies the moment the fast one belongs to them.
Why Crossing Ten Trips Everyone Up
Now the boss level. 13 − 5. Why is this so much harder than 8 − 5?
Because the answer lives on the other side of ten. The child starts in the teens and must end below ten, and somewhere in the middle sits the ten-boundary like a monsoon drain to jump. Counting back across it is exactly where little working memories drop things — somewhere around "...11, 10, 9..." they lose count of how many steps they've taken, and out comes 7, or 9, or a shrug.
The method schools teach for this — often called making ten, and worth knowing by name — goes like this for 13 − 5:
- Split 13 into 10 and 3 (that ten-plus fact again).
- You want to take away 5. First take the 3, using up part of the five: 13 − 3 = 10. Now you're standing exactly on ten.
- You've still got 2 more to take away (because 5 splits into 3 and 2 — a number bond). 10 − 2 = 8.
If the paper method looks laborious when your child does it, one honest note: it's slower than counting at first. It wins later, when the same structure carries them through 43 − 5 and beyond in P2. You're not teaching a trick for this year's questions; you're installing the plumbing for the next four years.
Concrete → Pictorial → Abstract, at the Dinner Table
The sequence local teachers use — concrete objects first, then pictures, then symbols — isn't just classroom procedure. It's a map of how understanding actually forms, and it works even better at home because home has better objects.
Concrete. Real things, physically moved. Thirteen grapes on the table; eat five (the most popular subtraction in our flat); count what's left. Toy cars driving away from a car park of 15. Ten-and-three fingers between parent and child. The crucial move: say the number sentence while the objects move — "thirteen take away five... is eight" — so the symbols and the physical truth get wired together. For crossing ten specifically, two egg trays or an ice-cube tray with ten hollows is gold: fill ten, put three beside, and the "take three to get to ten, then two more" step becomes something the child can see.
Pictorial. Draw 13 circles, cross out 5, count the survivors. Yes, it's slow. Slow is fine; crossing-out is the bridge between the grapes and the bare digits, and children linger on it for exactly as long as they need. This is also where those simple part-whole pictures earn their keep: whole 13 at the top, one part 5, mystery part — the child sees what kind of question subtraction is, not just how to grind it.
Abstract. Only now, 13 − 5 = 8 in naked symbols. If your child falters here, don't push harder at this level — step back a layer. The fix for an abstract stumble is nearly always one floor down, in pictures or objects. And a caution I needed personally: don't rush the tower. I once skipped ahead because the grapes felt babyish for a P1 child, and I bought myself a week of guessing. The concrete stage isn't the remedial stage; it's the load-bearing one.
Ten minutes after dinner, three questions with real things, done. Little and often, always. And when you want variety without another assessment book, a handful of well-made digital questions — the counting and puzzle corner in BrightBit, in our case, which also has reasoning puzzles in its Genius Lab that sneak the same part-whole thinking in sideways — fills the gap on the days you're too tired to be the fun parent.
The Mistakes You'll Actually See — and What to Say
A field guide from our dining table. You will meet most of these; none of them is alarming.
- Off-by-one errors: 13 − 5 = 9 (or 7). The child counted "13, 12, 11..." starting the count on 13 — counting the starting number itself as the first step — or lost track mid-flight. Say: "Show me on your fingers how you counted." The bug reveals itself out loud, and the child usually catches it themselves. That habit — check by re-doing it a different way — is worth more than the correct answer.
- Subtracting the wrong way: reading 3 − 13 out of a bond picture, or announcing that "you can't take 5 from 3, so the answer is 0". This child needs more part-whole time: the whole is the big number, the parts are inside it. Back to concrete, no shame attached.
- Always counting back, whatever the question. Not an error — a habit that will silently cap their speed. Run the strategy race from earlier; let think-addition win on the child's own clock.
- Knows it with objects, collapses on the bare sum. The bridge between layers is missing a plank. Do the same question both ways in one sitting — grapes first, then the written sum, and point at how they match.
- Fine all week, blank at the weekend. Not forgetting — consolidating. New skills wobble before they set. Two-minute refreshers across many days beat any amount of Saturday drilling.
What "Good" Looks Like by Year's End
Rough and unofficial, but a fair target by the end of P1: subtraction within 10 is quick and mostly known by heart; subtraction within 20 is reliably correct with a sensible strategy, even if it isn't fast yet. Fast comes in P2. Understanding has to come first, because speed built on counting fingers collapses exactly when the numbers grow.
And the emotional target matters just as much as the mathematical one: a child who ends P1 saying "subtraction is okay" is set up better than a drilled child who ends it saying "I hate maths". 13 − 5 stopped being a monster in our house the week it became grapes, then a picture, then a bond she already knew. Without tears — eventually, and truly. Yours will get there too.