PYTHAGORAS THEOREM & SURDS
OVERVIEW
During this half term students will be introduced to irrational numbers and work with surds. Students will then recap squares and square roots before moving on to investigate the relationship between the sides of a right-angled triangle. The converse of the theorem is emphasised so that students are aware that if the sides of a triangle satisfy the rule then the triangle must be right-angled. Students explore the theorem in context, including on coordinate axes and 3D shapes.
LESSON RESOURCES
Developed by BAA
Lesson 2 – Simplifying Surds (HIGHER)
Lesson 3 – Simplifying Surds using Prime Factorisation (HIGHER)
Lesson 4 – Adding Surds (HIGHER)
Lesson 5 – Expanding a single bracket with surds (HIGHER)
Lesson 6 – Expanding double brackets with surds (HIGHER)
Lesson 7 – Rationalising Surds (HIGHER)
Developed by LBA
Lesson 9 – What is Pythagoras Theorem?
Lesson 10 – Is the triangle right-angled?
Lesson 11 – Finding the hypotenuse
Lesson 12 – Applications of find the hypotenuse
Lesson 13 – Finding the shorter sides
Lesson 14 – Applications of finding shorter sides
Lesson 15 – Pythagoras Strategies
Lesson 16 – Further applications of Pythagoras
Updated April 2025
OLD LESSONS FOR THIS UNIT
| Lesson 1 | Tilted squares |
| Lesson 2 | Introduction to Pythagoras – finding the hypotenuse |
| Lesson | Pythagoras – finding a shorter side |
| Lesson 4 | Pythagoras problems |
| Lesson 5 | Introducing surds |
| Lesson 6 | Simplifying surds |
| Lesson 7 | Simplifying surds using prime factorisation |
| Lesson 8 | Manipulating surds |
| Lesson 9 | Expanding a single bracket containing surds |
| Lesson 10 | Expanding double brackets containing surds |
| Lesson 11 | Rationalising Surds |
| Lesson 12 | Visualising in 3D |
| Lesson 13 | Pythagoras in 3D |
| Lesson 14 | Solving 3D Pythagoras problems |
| Lesson 15 | Solving 3D Pythagoras in pyramids |
| Lesson 16 | Pyramids of Giza |
Updated April 2024