What you need
- The bundles of ten from The Bundle of Ten, plus loose sticks
- Nothing else
How to play
- 1
Ask for a number
Say a two-digit number — 52 — and ask him to build it. He makes five bundles and two loose sticks. Easy, and he should feel that it is easy.
- 2
Ask for it again, differently
Now say: show me 52 again, but a different way. Do not explain what you mean. Let the puzzle sit. Most children go quiet here, and that quiet is the activity working.
- 3
Let him find the untie
If he is stuck after a while, pick up a bundle and turn it over in your hand without saying anything. If he is still stuck, untie one yourself and ask how many sticks are on the floor now. Four bundles and twelve loose — still 52.
- 4
Count it back
Have him count the new arrangement to prove it is still 52. Ten, twenty, thirty, forty, then twelve more. The number did not change; only its shape did.
- 5
Go one more
Ask for a third way. Three bundles and twenty-two. Then a fourth. Children usually start enjoying this once they see the pattern — each untie moves ten from one side to the other.
- 6
Say the sentence
Finish by saying it plainly, and have him say it back: I exchanged one ten for ten ones. Not borrowed. Exchanged. That word will do a lot of work in a year's time.
What your child is learning
Honestly stated — this is what the activity actually builds, not a list of everything it might touch.
- That the same number can be split more than one way
- The exact flexibility that borrowing and carrying depend on
- That untying a ten changes the arrangement, not the amount
The two minutes that decide subtraction
Almost every child who fails at column subtraction fails in the same place: the top digit is smaller than the bottom one, and they do not know what to do. The textbook says borrow. The child, having no idea what that means, does the thing that looks sensible — takes the smaller from the larger and writes 52 − 28 = 36.
That mistake is not carelessness. It is a reasonable rule applied by someone who was never shown the alternative.
The alternative is this activity. A child who can turn five bundles and two into four bundles and twelve, with his hands, on demand, already knows what regrouping is. The written procedure becomes a description of something familiar rather than a spell.
Do it before the subtraction, not during
The instinct is to introduce this at the moment he gets stuck on a sum. That is the worst moment — he is already frustrated, and the new idea arrives as a rescue rather than as knowledge.
Play it as a game for a week with no arithmetic anywhere near it. Then bring out the sums.
Make it harder without making it longer
Once the untie is easy, reverse it. Put out three bundles and twenty-two loose sticks and ask him to tidy it up. He should tie two new bundles and be left with five and two. That is carrying, met from the other direction, and it costs nothing extra to teach.
The word to avoid
Not borrow. Nothing is ever given back, so the word describes an action that does not happen, and children notice. Exchange is accurate, it matches what his hands are doing, and it will still be accurate when he meets decimals.
Published 17 August 2026 · Suitable for Early schooler, Big kid