Interesting teaching ideas for introducing and revising Pythagoras’ theorem and trigonometry

Pythagoras’ theorem and trigonometry are two of those classic topics that pupils revisit year-on-year. This is partly because these topics come in many forms and interesting contexts, from basic Pythagoras and Soh-Cah-Toa, to graphs of trigonometric functions and calculus.

With the increased emphasis on ratio in the new GCSE specification, trigonometry is likely to start appearing in non-calculator papers as well. As such, it is more important than ever for students to get to grips with this crucial and fascinating area of mathematics.

Fortunately, TES Maths is here to help!

Below is a selection of 15 top Pythagoras and trigonometry resources, all uploaded by the talented members of the TES Maths community. Why not use them to give you some new ideas for teaching these topics across all year groups?

Craig Barton, TES Maths adviser

1. Perigal’s dissection
   Encourage pupils to stumble upon Pythagoras’ theorem by themselves by first introducing them to Perigal’s cut-and-shift proof.
2. Introduction to Pythagoras’ theorem
   This well-differentiated lesson neatly introduces the famous theorem and the correct use of the calculator in solving Pythagoras-related problems.
3. Interactive Pythagoras lesson
   Culminating in a treasure hunt, this action-packed lesson starts with an element of discovery before progressing on to using Pythagoras in real-life contexts.
4. Have I got hypotenuse for you?
   Revise the key aspects of Pythagoras in a fun and effective way with this select-and-reveal starter and plenary activity.
5. Trigonometry investigation
   Give your students the opportunity to discover the relationship between trigonometry and ratio in this fully-resourced investigation.
6. Introduction to trigonometry
   Introduce sin, cos and tan for the first time with this clear, well-structured lesson, which can be easily adapted to suit your class’ needs.
7. Soh-Cah-Toa
   Crammed full of differentiated activities, this complete lesson on trigonometry uses Bloom’s taxonomy questioning to challenge pupils.
8. Batman-themed word problems
   Help Gotham City’s Police Commissioner catch criminals while recapping existing learning on trigonometry with these engaging problems.
9. Pirate problem-solving
   Revise trigonometry, Pythagoras’ theorem and even geometry in this themed activity, in which pupils are tasked with finding Admiral Angle’s buried treasure.
10. Pythagoras or trigonometry?
    Clarify the process of deciding whether a question requires the use of Pythagoras or Soh-Cah-Toa with this handy flow chart.
11. 3D trigonometry
    Stretch more able learners with this innovative task, which is ideal for pair work and contains plenty of opportunities for peer and self-assessment.
12. Finding exact trigonometric values
    Use these clear worksheets to encourage students to become familiar with ‘special triangles’, in order to be able to calculate exact trigonometric values without a calculator.
13. Sine and cosine rule lesson
    This step-by-step lesson plan with precise explanations and well-worked examples is ideal for KS4 classes.
14. Sine and cosine sorting exercise
    Put your pupils’ understanding of when to use the sine and cosine rule to the test with this versatile resource, with plenty of AfL opportunities.
15. Pythagoras and trigonometry revision booklet
    Containing lots of exam-style questions, this comprehensive workbook has plenty of space for students to show their working and explain their reasoning.