Why count up instead of subtracting?

Because counting up avoids borrowing entirely and breaks the problem into two easy hops instead of one awkward calculation. Change from a dollar on sixty-three cents is seven to reach seventy and thirty more to reach a hundred, which most children can do in their head, while the written subtraction invites a regrouping mistake. The method is also the one used at a real counter.

Does my child need to know the coin values for this game?

Not to play it, because the amount paid is stated in words and the coins on screen are always quarters. What they do need is that a dollar is one hundred cents, since that is the destination for every question that involves paying with a dollar. Knowing the other coin values matters at the shop, so practice that with a real handful of change.

When do children learn to make change?

Counting money starts in second grade and making change runs through third and fourth, once subtraction within a hundred is reasonably solid. The reason it is worth more time than it looks is the strategy underneath: finding a difference by bridging to a friendly number is how mental subtraction of larger numbers gets done for the rest of school.

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Making Change

How much money comes back?

Grades 2-4 · Subtracting money and counting change

How to play

1You pay with coins for something that costs less.
2Choose the change you should get back.
3Count up from the price to what you paid. It is easier than subtracting.
4Keep a streak of correct change.

Try a few

You pay 50c for something that costs 35c
Answer: 15c
Do not subtract, count up. Start at the price, thirty-five, and go to the nearest friendly number: five more reaches forty. Then forty to fifty is ten more. Five and ten make fifteen, so the change is 15c. The two hops both land somewhere easy, which is why this beats writing fifty take away thirty-five in a column and hoping the borrowing goes right. It is also what a shopkeeper counting coins into your hand is doing out loud.
You pay $1.00 with four quarters for something that costs 63c
Answer: 37c
Sixty-three needs seven to reach seventy, and seventy needs thirty more to reach a hundred, so the change is seven and thirty, which is 37c. Bridging to seventy first keeps both steps inside numbers your child can hold. A dollar being one hundred cents is the fact the whole problem turns on, so if the second hop stalls, that is the thing to rehearse rather than the subtraction.
You pay 25c for something that costs 18c
Answer: 7c
Eighteen up to twenty is two, and twenty up to twenty-five is five, so the change is 7c. This is the smallest kind of question the game asks and the best one for establishing the method, because both hops are tiny and the answer can be checked on fingers. Once counting up feels natural on numbers this size it transfers without any new explanation to change from fifty cents and from a dollar.

Why this game helps

Change is subtraction with a reason to care, and it is also the place where counting up beats taking away for almost everyone. Working out the change from fifty cents on a thirty-five cent item by counting five to forty and ten more to fifty is quicker and less error-prone than a written subtraction, and it is what shopkeepers actually did for centuries. The skill underneath, finding a difference by bridging to a friendly number, transfers straight to mental subtraction of larger numbers, which is the real payoff.

If your child finds this hard

The wrong answer to watch for is one of the numbers from the question handed straight back, so a child asked for the change from fifty cents on a thirty-five cent item answers thirty-five, or answers fifty. This is the response recorded most often when children are asked how much more is needed to reach an amount, and it usually means the question has been heard as what is the price rather than what is left over. Ask them to say what they are looking for in their own words first, that it is the money coming back, not the money going out.

The second error is overshooting the landmark. Counting up from sixty-three towards a dollar, a child carries on past a hundred to a hundred and ten because counting in tens has its own momentum and nothing stopped it. Name the destination out loud before starting to count, and say it again as a target: we are going to one hundred and stopping there. Counting up is only faster than subtracting when the child knows where the counting ends, so the destination has to be fixed before the first hop.

Real coins on a real table sort this out quicker than anything on screen. Price a few things around the kitchen, hand over a fifty cent piece or a dollar, and make your child count the change into your palm out loud, from the price upwards, the way a till-free shopkeeper does. One thing to notice about this game while you play: it always pays with quarters, so the amount handed over is only ever twenty-five cents, fifty cents or a dollar. Those three landmarks are worth knowing cold, because every question here is a journey up to one of them.

Common questions

Why count up instead of subtracting?: Because counting up avoids borrowing entirely and breaks the problem into two easy hops instead of one awkward calculation. Change from a dollar on sixty-three cents is seven to reach seventy and thirty more to reach a hundred, which most children can do in their head, while the written subtraction invites a regrouping mistake. The method is also the one used at a real counter.
Does my child need to know the coin values for this game?: Not to play it, because the amount paid is stated in words and the coins on screen are always quarters. What they do need is that a dollar is one hundred cents, since that is the destination for every question that involves paying with a dollar. Knowing the other coin values matters at the shop, so practice that with a real handful of change.
When do children learn to make change?: Counting money starts in second grade and making change runs through third and fourth, once subtraction within a hundred is reasonably solid. The reason it is worth more time than it looks is the strategy underneath: finding a difference by bridging to a friendly number is how mental subtraction of larger numbers gets done for the rest of school.

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