Package 3-1 Factor squares

In this task students will investigate factors to solve a problem.

Things you need

Have these things available so your child can complete this task.


  • 24 toothpicks

Back up

  • 24 pencils or sticks

Before you start

You will need a large table or floor space to spread the toothpicks out.

3 rows of toothpicks, each row contains 4 bundles of 2 toothpicks.

What your child needs to know and do

Students will need to know how to count to 24 and the properties of a square.

What to do next

  1. Make 1 large square.

Toothpicks laid out in a square shape - 6 toothpicks in each side.

  1. Make 2 squares.

  2. Make 3 squares.

  3. Make 4 squares. Hint: A square can share a side of another square.

  4. Can you make 5 squares? Hint: Squares don’t all have to be the same size.

  5. Can you make 6 squares?

  6. Can you make 7 squares?

  7. Now make 8 squares?

  8. Can you make 9 squares? Why or why not?

  9. Can you make 10 squares? Why or why not?

  10. Why can we make some squares and not others?

Options for your child

Activity too hard?

Use 12 toothpicks instead of 24 and make 1 square, 2 squares, 3 squares and 4 squares.

Activity too easy?

Follow the same instructions as above but use 48 toothpicks.

Can you make more squares?

Extension/additional activity

Try this activity with a triangle and pick a number which is divisible by 3.

E.g 27 toothpicks.

Does this work as successfully as an even number? Why?

What happens when you halve the number?

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