Square Pairs

A Maths Starter Of The Day

Numbered trees
Consider each pair
Adjacent sums
Must be square



Topics: Starter | Arithmetic | Number | Problem Solving | Puzzles

  • Transum,
  • Could you do this activity with trees numbered 1 to 16?
    ...trees numbered 1 to 17?
    ...trees numbered 1 to 18?
  • Jemma, Elmrise, Bournemouth
  • Ive noticed that the totals make a pattern that goes, 16,9,16,25 repeated.
    Would this continue if you used numbers 1-16?
  • Miss Moa, St Helens
  • Great Activity. Thanks :).
  • Mr Kavanagh's Fifth Class, Cork, Ireland
  • At first we got it wrong and struggled to find the correct answer or even what was required. however once we figured out what to do we really enjoyed this one. Bayley and Cormac were the first to get the correct answer.
  • Transum,
  • There are some similar challenges you can do with a pack of playing cards. You can find them and other playing card mathematical activities on the newly created Playing Card Maths pages.
  • Clive, Southampton
  • This could be played as a two-player game. The first player plants a tree in one of the centre holes. The second player has to plant one of the remaining trees next to it so that the pair sum is a square number. The game continues until one player can't plant a tree that obeys the 'pair sum is square' rule. The other player is the winner.

    [Transum: Thanks for that idea Clive. You can play the Transum interactive version of that here: Square Pairs Game.]

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.
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Laptops In Lessons

Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments:


However it would be better to assign one of the student interactive activities below.

Laptops In Lessons

Here is the URL which will take them to a similar activity.


Here is the URL which will take them to another activity involving square numbers.


Student Activity

Here is the URL which will take them to the interactive version of this activity called Square Pairs Game


Student Activity



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