How Many Squares? 1

How Many Squares?

Can you work out how many squares can be found in this diagram? Can you be sure you haven't missed any? Can you be sure you haven't counted any twice?

A Mathematics Lesson Starter Of The Day


Topics: Starter | Puzzles | Shape

  • Quinetta, NH
  • My fiance and I just did this puzzle; me on paper and him in head. I got 44 and he got 46. Very fun though.
  • Class 5G, Derby
  • We think that Mrs Green is the cleverest teacher in the world as she got all 42!! 5G are quite celever too... :).
  • Mrs Hill's Marvellous Maths Group - Form 5, Eversfield Preparatory School, Solihull
  • We found all 42 squares easily. We went on to look at the chess board and found lots of squares...204 in total. What's more, we noticed lots of other really interesting patterns. Square numbers are clever things...and so are we!
    Mrs Hill's last ever maths lesson at Eversfield. :-(.
  • Mr Cansdale, Wintringham Grimsby
  • The majority of 8X2 of Wintringham believe it is 44! (HA).
  • Mr Cansdale 8A4, Oasis Wintringham
  • 7 out of 21 think 34.
  • Mr Jing-Hao, Japan School
  • Extremely easy starter the pupil in my top set found 42 in a matter of seconds.
  • Purab, Noida
  • Quinetta can you tell me how you got 46 or 44 I only got 40.
  • Mary And Class 3, Class 3
  • Class 3 at Frettenham Primary (Year 4/5/6) all agree there are 42 squares.

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There is a printable worksheet to go with this activity.



The important thing is not the answer but the method you used to arrive at the answer. Did you have a structured approach? Were you sure that you had the right answer? Can you make up a puzzle like this for others to solve?

Extension Challenge

How many squares are there on a chess board?

Chess Board

A more difficult extension challenge would be to work out how many rectangles are on a chess board. The use of a spreadsheet might be useful when working on this problem.

Other shape counting starters:

How Many Squares 1? | How Many Squares 2?
How Many Triangles 1? | How Many Triangles 2? | How Many Triangles 3?
How Many Rectangles? | Rectangles Investigation | Icosahedron | Mystic Rose

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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...

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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 another systematic listing activity.

Student Activity


Extension Answers


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