Teaching kids to make change

Making change is not subtraction. Cashiers do not calculate ten minus seven twenty — they count up from the total to the bill. Teach the subtraction first and your child will stall for months.

Updated: 2026-08-29

Ask an adult how to work out change from a ten-dollar bill on a $7.20 total and most will subtract: ten minus seven twenty is two eighty. Then they teach a seven-year-old to do the same, and are surprised when it goes nowhere.

Watch an experienced cashier without a screen and you will see something else entirely. They start at $7.20 and count up: a nickel makes $7.25, a quarter makes $7.50, two more quarters make $8, and two singles make $10. No subtraction anywhere — just addition, which your child already knows how to do.

That difference is the whole article.

Why counting up wins

Subtraction across a dollar boundary is one of the harder operations in early math. It requires borrowing, it requires holding two numbers in your head, and it goes wrong under pressure — which is precisely the situation at a register.

Counting up needs none of that. It moves in one direction, each step is small, and the coins in your hand tell you what the steps are. A child who can add to ten can make change.

There is a second, less obvious gain: counting up produces the coins as a by-product. When you subtract, you get “$2.80” and then still have to work out which coins make $2.80. When you count up, the coins are the answer.

The coin that trips up every seven-year-old

Before any of this works, your child has to recognise coins by value, not by size. American coins make that unusually hard.

A dime is worth ten cents and is physically smaller than a nickel, which is worth five. Children sort the world by size — bigger means more — and here the money contradicts them. It is the single most common sticking point, and it is not a sign of anything except that your child is being reasonable.

Two things help:

Sort by value, out loud, repeatedly. Lay out a handful and have your child put them in order of worth, not size. Do it until the dime stops being a surprise.

Name the ridge. A dime and a quarter have ridged edges; a nickel and a penny are smooth. That is a physical cue a child can use even without looking, and it splits the four coins into two pairs that are easy to tell apart by size within each pair.

Six stages, in order

1. Recognising coins (age 5–6). Name and value, out of order, until it is automatic. No arithmetic yet.

2. Counting same coins (age 6). Five dimes. Four quarters. Skip counting in disguise, and the foundation of everything after.

3. Mixed coins (age 6–7). A quarter, two dimes and a nickel. The rule that makes it work: start with the largest. Children left to themselves count in the order the coins happen to lie, and lose track.

4. Paying exactly (age 7). The total is $1.35 — build it. This is the first stage that feels like real shopping, and it is worth staying here longer than feels necessary.

5. Reading change back (age 7). You hand over the change; your child checks whether it is right. Verifying is easier than producing, and it teaches the same counting-up move from the safe side.

6. Making change (age 7–8). Your child is the cashier. Whole dollars first ($7 out of $10), then quarters ($7.50 out of $10), then anything ($6.35 out of $10).

Stage 6 is the one everybody wants to start at. Starting there is why it so often stops.

Amounts, in the order that keeps a child moving

• Whole dollars out of a whole bill. $7 out of $10.
• Halves and quarters. $7.50, then $7.25.
• Anything, once the quarters are automatic. $6.35 out of $10.

The jump from quarters to arbitrary cents is bigger than it looks and worth delaying by weeks rather than days. A child who is fluent to the quarter can improvise the rest; a child pushed there early goes back to guessing.

What breaks it

Correcting mid-count. Your child is at $7.50 and reaches for the wrong coin. Wait. An interrupted count has to restart from the total, and three restarts end the session.

Amounts that are too large. Change from a fifty is not a harder version of the same exercise — it is a different one, involving numbers your child cannot hold. Stay under ten dollars far longer than you think you need to.

Doing it in a real line. A queue behind you converts practice into pressure. Practise at home, then do it for real once, on a quiet afternoon — a first solo shopping trip is a separate exercise with its own preparation.

Digital-only practice. An app that totals everything for your child removes the part they are supposed to be doing. The app should check the answer, not produce it.

Practising without a real register

At home, the cheapest setup is real packaging, hand-written price tags and a handful of coins — that is playing store, and it costs nothing.

Where an app earns its place is the checking. KidRoles: Shop turns a tablet into the register: your child adds items, the app shows the total, your child enters what the customer handed over and then counts out the change — and finds out immediately whether it is right. You set the prices yourself, so you can hold the difficulty exactly at stage 4, 5 or 6 instead of whatever the app decided. It runs offline and collects no data.

The immediate feedback matters more than it sounds. Without it, a wrong answer waits for an adult to notice, and by then your child has moved on.

How to tell it has landed

Not by speed. By your child counting up out loud without being asked — “seven twenty… twenty-five… seven fifty… eight… nine, ten.” Once the method is audible, the arithmetic takes care of itself.

At that point the useful next step is not more counting but the math around the shelf: estimating, comparing prices, unit price. Change is a technique; the rest is judgment.

• Coins sorted by value, not size — dime versus nickel checked explicitly
• Counting up, never subtracting
• Whole dollars → quarters → arbitrary cents, in that order
• No corrections in the middle of a count
• Amounts under ten dollars for far longer than feels necessary

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