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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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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