Pythagoras' theorem

AQA GCSE Maths

8 ready-made resources for teaching Pythagoras' theorem, written for AQA GCSE Maths. Slides, worksheets, mark schemes, homework, an assessment and retrieval quizzes, all with SEN-friendly scaffolding built in as standard. Below is what the topic requires and where students usually go wrong, free to read whether or not you sign up.

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What is in this bundle

Assessment mark schemeWord, editable
End-of-topic assessmentWord, editable
HomeworkWord, editable
Retrieval-practice quizzesWord, editable
SlidesPowerPoint, editable
Starter & exit ticketWord, editable
Tiered worksheetWord, editable
Worksheet mark schemeWord, editable

Foundation tier

State Pythagoras' theorem for right-angled triangles.
Calculate the length of the hypotenuse given the two shorter sides.
Calculate the length of a shorter side given the hypotenuse and one other side.
Apply Pythagoras' theorem in simple 2D contextual problems (e.g. ladders against a wall, the diagonal of a rectangle).

Higher tier, in addition

Apply Pythagoras' theorem in 3D contexts (e.g. the diagonal of a cuboid).
Combine Pythagoras' theorem with trigonometry in multi-step problems.
Determine whether a triangle is right-angled given three side lengths (the converse).
Give answers in exact (surd) form where side lengths do not simplify to integers.

Where students go wrong

Applying the theorem to a triangle that is not right-angled.
Misidentifying the hypotenuse (it is the side opposite the right angle, not necessarily the longest side as written in the question).
Adding the squares of the two shorter sides correctly, but subtracting incorrectly when solving for a shorter side instead of the hypotenuse.
Forgetting the final square-root step and leaving the answer as the squared value.

How it gets asked in the exam

"Calculate the length of...", "Work out the distance between...", "Show that the triangle is right-angled", "Give your answer to 1 decimal place / in surd form".

Key vocabulary

Hypotenuse, right angle, theorem, square, square root, surd (Higher), adjacent, opposite.

Assumed prior knowledge

Squaring and square-rooting numbers.
Rearranging simple formulae.
Basic awareness of 3D shapes (Higher only).

How Speca scaffolds this topic

Consistently mark the right angle and highlight the hypotenuse in the same colour on every diagram, so students build a reliable visual identification habit.
Provide a fill-in-the-blank formula template (a² + b² = c²) that students annotate directly onto the triangle before calculating, separating "identify" from "calculate."
For 3D problems, explicitly scaffold the step of extracting the relevant 2D right-angled triangle first: this is the main barrier, not the arithmetic that follows.

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