What you need
- About 40 identical small objects — rajma, chana, buttons, bottle caps or coins
- A tray, a thali or a clean patch of floor
- Paper and pencil to record what he finds
How to play
- 1
Count out twelve
Give him exactly 12 beans. Ask him to arrange all 12 into a neat rectangle — equal rows, no leftovers, nothing sticking out.
- 2
Find every rectangle
Once he makes one, ask for a different one. Twelve gives 2 × 6, 6 × 2, 3 × 4, 4 × 3, 1 × 12 and 12 × 1. Let him hunt for all of them himself rather than telling him how many there are.
- 3
Write them down
Each rectangle he finds gets written on the paper as a sum: 3 × 4 = 12. By the end he has built his own list of the factors of 12, which is the same list he will be asked for in school.
- 4
Try a stubborn number
Now give him 13 beans and ask for a rectangle. He will fail, and he should — 13 only makes a single line. That is what a prime number is, and he just met one with his hands.
- 5
Hunt the squares
Ask him to find numbers that make a perfect square: 4 makes 2 × 2, 9 makes 3 × 3, 16 makes 4 × 4, 25 makes 5 × 5. Line the squares up in a row and let him see the pattern in the answers.
What your child is learning
Honestly stated — this is what the activity actually builds, not a list of everything it might touch.
- That multiplication is rows and columns, not a list to be recited
- That 3 × 8 and 8 × 3 are the same rectangle turned sideways
- Factors, square numbers and prime numbers — found by hand, before the words arrive at school
Why rectangles and not counting
Most children are first taught multiplication as repeated addition — three fours is 4 + 4 + 4. That is true, and it is also the reason so many children get stuck counting. Addition is a line: you start at the beginning and move along it. There is no way into the middle.
A rectangle is not a line. You can see the whole of it at once, you can split it, you can turn it. When a child has spent twenty minutes making rectangles, “three eights” stops being a journey he has to walk from the start and becomes a shape he can picture. That is the shift this activity is for.
The bit that surprises them
Ask him to guess, before he starts, how many different rectangles 16 will make. Then let him find out — 1 × 16, 2 × 8, 4 × 4 and their flips. Then ask him about 17, which makes none at all except a line. Children find this genuinely interesting, because it looks like the numbers are behaving unfairly, and “why does 17 refuse?” is a much better question than anything a worksheet asks.
If you have squared paper
Drawing the rectangles on squared exercise-book paper works just as well and leaves a record he can keep. Beans are better for the first few goes, because he can push them around and change his mind, and being able to change your mind is most of what thinking is.
Take it to division
When the rectangles are made, point at one and ask the question backwards: “Twenty beans, four rows — how many in each row?” It is the same rectangle he just built, read the other way. Division and multiplication are one idea, and a child who meets them together on the same tray has a much easier time than one who meets them as separate chapters months apart.
Published 16 August 2026 · Suitable for Early schooler, Big kid