8 Pythagoras Lesson Activities for GCSE Students

Written by: Jamie Wood

Reviewed by: Roger B

Published

26 June 2025

Contents

There are so many effective, interesting, and fun activities available for your students when teaching them about Pythagoras’ Theorem within GCSE Maths. Trying to decide which to use can end up wasting your precious planning time!

I have hand-selected a range of activities for teaching Pythagoras that fulfil different needs in the classroom, informed by my eight years of teaching experience. This means I know that these activities will benefit your students in the classroom, and benefit teachers like yourself by reducing their planning and research time.

To help you find what you need for your students, I have separated the activities into Introducing Pythagoras, Practising using Pythagoras, and Extending Pythagoras.

Introducing Pythagoras

Pythagorean Theorem water demo video

This video visually demonstrates how the sum of the squares of the two shorter sides is exactly equal to the square of the longer side.

You can choose how you use this video in your lesson, and at what point in their learning to show it to your students, but in my experience I have found it can be a great hook near the start of a lesson.

Students in a GCSE maths lesson will have some ideas about Pythagoras already, so showing them this video and asking “how does this link to Pythagoras?” can lead to some interesting responses to share or explore further.

Investigating areas and triangles

As a teacher I have tried quite a few different “Pythagoras investigations” with mixed success. Anything which avoids the students drawing their own squares on the sides of triangles tends to be a good idea in my experience! This activity by Paul Rowlandson on his blog Pondering Planning is excellent, as is his rationale for creating it.

There is a selection of pre-drawn squares with known areas which can be cut out and then put together to form triangles. Students then note if the largest angle of the triangle formed is a right angle, obtuse, or acute. Students can then start to think about how the areas relate to the type of angle formed, leading them to notice that if the sum of the smaller areas is exactly equal to the larger area, a right angle is formed.

The blog post also includes some further activities that involve deciding “is this triangle right-angled?”, and eventually going on to find missing areas when given two of the three areas involved. This is then only one step away from solving a standard Pythagoras question.

I really like this activity because it is well constructed, and embeds an understanding of what Pythagoras’ Theorem means, rather than just being a formula to remember.

Practising using Pythagoras

Save My Exams exam questions

We have exam style questions for Pythagoras & Trigonometry available, sorted into Easy, Medium, Hard, and Very Hard difficulties. Every question has a student-friendly model answer created by our team of experts, and you can download a PDF of the questions, or the questions and the answers.

As this pack does include trigonometry questions too, you could use our test builder feature to put together your own collection of Pythagoras-only questions.

Increasingly difficult questions

@TaylorDA01’s increasingly difficult questions are a fantastic resource for many GCSE Maths topics. They do what they say on the tin: they start with the basics and then every question becomes one step more difficult, introducing more problem-solving aspects.

The Pythagoras set of questions is one of my favourite activities as every question brings a meaningful amount of progression from the last. The answers are also available. I would recommend printing out the questions so students can annotate the shapes to help them solve the problems.

MEP practice book questions

The Centre for Innovation in Mathematics Teaching (CIMT) has all of their MEP resources generously available for free online. In Practice Book 9B you will find unit 15 on trigonometry which includes some excellent, clear questions on Pythagoras.

These questions have a clear progression from the simplest cases, up to geometric problems requiring more problem solving skills. I particularly like the questions about “which of the triangles below contains a right angle?” which flips the students’ idea of what Pythagoras is about on its head!

Extending Pythagoras

3D Pythagoras

Applying Pythagoras in 3D always feels like a natural extension of “regular” Pythagoras, especially if you can get your students to break the 3D problem down into several 2D problems. One of the most relatable problems that can be solved using 3D Pythagoras is to calculate the length of the diagonal of your (roughly) cuboid-shaped classroom.

This works best if you measure the length, width, and height of your classroom first in advance, and you can then pose the problem of “given these dimensions, what is the length of the diagonal?”. A class discussion or discussion in pairs is usually the next natural step, followed by trying to solve the problem on paper. If you can try and steer the class towards sketching the relevant 2D triangles, this is usually enough to help students who are finding it more difficult.

Finally, a nice conclusion is to use some string and a tape measure to see what the real length of the diagonal is.

At Save My Exams we also have a collection of 3D Pythagoras & Trigonometry exam questions, at three levels of difficulty.

The spider and the fly problem

This is a great problem solving question involving nets of 3D shapes and Pythagoras. It is listed on Underground Mathematics, and it also appears on NRICH. Whilst the final calculation is a relatively simple application of Pythagoras, it is the problem solving along the way, and thinking about 3D space which will really benefit your students. This is a fairly open problem and you can choose how much help and guidance you give your class with this one. The final solutions with clear diagrams are also included on NRICH and Underground Mathematics.

Don Steward’s triple triangle lengths

This is a collection of problems from the late Don Steward which all involve multiple triangles within the same diagram. His blog post includes a link to a powerpoint which I would suggest you print off so your students can annotate them with their workings. The problems are quite similar to some exam questions, where a problem-solving aspect appears and students have to decide which length to find next to help them.

Some of the problems also introduce algebraic terms to find, which is also similar to some exam questions. I personally enjoy setting these problems because they always seem to prompt a lot of discussion between students who are keen to show off how they found their solution.

Improve Student Outcomes with Save My Exams

Here at Save My Exams, we have many different types of resources to help you and your students in GCSE Maths. We have concise revision notes to help your students when revising, as well as differentiated exam-style questions that could be used for homework. Our questions have student-friendly model answers to allow for easy self or peer assessment.

Why not try out our test builder feature too? Test builder lets you put together your own tests or quizzes using questions from our site, downloadable as a PDF.

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