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.
Click here to enter your comments.

If you don't have the time to provide feedback we'd really appreciate it if you could give this page a score! We are constantly improving and adding to these starters so it would be really helpful to know which ones are most useful. Simply click on a button below:

Excellent, I would like to see more like this
Good, achieved the results I required
Didn't really capture the interest of the students
Not for me! I wouldn't use this type of activity.

This starter has scored a mean of 3.1 out of 5 based on 397 votes.

Previous Day | This starter is for 20 March | Next Day



Sign in to your Transum subscription account to see the answers

Your access to the majority of the Transum resources continues to be free but you can help support the continued growth of the website by doing your Amazon shopping using the links on this page. Below is an Amazon search box and some items chosen and recommended by Transum Mathematics to get you started.


Have you read Craig's book yet?

Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more...

"How I wish I'd taught Maths" is an extraordinary and important book. Part guide to research, part memoir, part survival handbook, it’s a wonderfully accessible guide to the latest research on teaching mathematics, presented in a disarmingly honest and readable way. I know of no other book that presents as much usable research evidence on the dos and don’ts of mathematics teaching in such a clear and practical way. No matter how long you have been doing it, if you teach mathematics—from primary school to university—this book is for you." Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL.

The Craig Barton Book

Casio Classwiz Calculator

There is currently a lot of talk about this new calculator being the best in its price range for use in the Maths classroom. The new ClassWiz features a high-resolution display making it easier to view numerical formulas and symbols but it isn't a graphical calculator as such (it has the capacity to draw graphs on your smart phone or tablet, via a scannable QR code and an app).

As well as basic spreadsheet mode and an equation solving feature you also get the ability to solve quadratic, cubic or quartic polynomial inequalities and the answer is given just as it should be written down, using the correct inequality symbols!

This calculator has a high-performance processor and twice the memory of previous models ensuring speedy operation and superior computational power.more...

Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.


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



©1997-2020 WWW.TRANSUM.ORG