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.

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 3.8 out of 5 based on 572 votes.

Previous Day | This starter is for 27 December | Next Day


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

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.


Texas Instruments Nspire Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a gift for a special occasion but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

Apple iPad Pro

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent gift for anyone.

The redesigned Retina display is as stunning to look at as it is to touch. It all comes with iOS, the world's most advanced mobile operating system. iPad Pro. Everything you want modern computing to be. more...

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

Click the images above to see all the details of these items and to buy them online.

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


©1997-2020 WWW.TRANSUM.ORG