Square Pairs
Years 5 - 10


Turn off your sound, then click the image to watch this 2min 15sec video.


Explaining The Video

  • What was the person doing with their hands?
  • What was the first way the person arranged the tiles?
  • What did the person do with the tiles after that?
  • Play the video again (without sound) and pause to look at the pairs. Why do you think the person thinks these pairs are special?
  • If you were this person what pair you would make next? Why?
  • Write and draw about the video in your journal.

Investigating Square Pairs

  • Print Square Pair Tiles and cut out 1 through to 20.
  • Open this Square Pairs Starter.
    You can read it on screen or print it.
  • Investigate Square Pairs using the questions on the Starter.
    You can work with a partner if you wish.
    They can cut their own tiles.
    This Square Line Paper can help you keep your lists neat. One number in each box.

    Take your time. The mathematicians who solved this problem took years. So it can't be easy.
    Record in your journal, then you know where you are up to if you stop and come back to it another time.

Have fun exploring Square Pairs.
  • Even if you find only one or two lists you have been a successful mathematician.
    Actually even if you don't find any lists, but you were interested in the problem, you were a successful mathematician.
Note: If your school is a member of Maths300, your teacher can provide software that will help you explore Square Pairs.

Just Before You Finish

For this part you need your maths journal and your Working Like A Mathematician page.
  • Read again what it means to work like a mathematician.
  • In your journal, finish this paragraph:
    Working with Square Pairs I was a successful mathematician because...


Answers & Discussion

These notes were originally written for teachers. We have included them to support parents to help their child learn from Square Pairs.

Send any comments or photos about this activity and we can start a gallery here.


Maths At Home is a division of Mathematics Centre