Pythagoras' Theorem
This topic covers 5 learning steps, guiding your child from the basics through to confident problem-solving. Each step includes a worked example and adaptive practice questions.
What Your Child Will Learn
- Identify right triangles
Know which side is the hypotenuse - Find the hypotenuse
Calculate the longest side - Find a shorter side
Calculate a missing leg - Real-world problems
Apply Pythagoras to distances and diagonals - Pythagorean triples & proofs
Recognise triples and verify right angles
Before This Topic
Your child should be comfortable with:
- Area of Triangles (Year 6)
- Square & Cube Numbers (Year 5)
Common Mistakes
- Using the formula a² + b² = c² without checking which side is the hypotenuse (e.g. always adding the squares even when finding a shorter side)
c is ALWAYS the hypotenuse — the longest side, opposite the right angle. To find the hypotenuse, add the squares: c² = a² + b². To find a shorter side, subtract: a² = c² - b². Getting this wrong is the most common Pythagoras mistake. - Forgetting to square root at the end (e.g. getting c² = 25 and writing the answer as 25 instead of 5)
The formula gives you c SQUARED, not c. You must always take the square root as the final step. If c² = 25, then c = √25 = 5. Write "c² = ..." then "c = √... = ..." as two separate steps.
Tips for Parents
- Test it physically: cut a right-angled triangle from card, measure the sides, square them, and check that a² + b² = c². The hands-on proof is very convincing.
- Use real-world examples: "A ladder is 5 metres long and the base is 3 metres from the wall. How high up the wall does it reach?" (5² - 3² = 25 - 9 = 16, √16 = 4 metres).
- Learn the common Pythagorean triples: 3-4-5, 5-12-13, 8-15-17. Spotting these saves calculation time and helps check answers.
- Remind your child: Pythagoras ONLY works with right-angled triangles. If there is no right angle, they need a different method (trigonometry or the cosine rule later on).
Key Words
- Hypotenuse — The longest side of a right-angled triangle — always opposite the right angle.
- Right angle — An angle of exactly 90 degrees — shown by a small square in the corner of a triangle.
- Pythagorean triple — A set of three whole numbers that fit the rule a² + b² = c² — like 3, 4, 5.
- Square root (√) — The reverse of squaring — √25 = 5 because 5² = 25.
- Theorem — A mathematical rule that has been proven to be always true — Pythagoras' Theorem works for every right-angled triangle.
Where This Fits
Before this topic: Children should understand squaring numbers and square roots, be able to identify right-angled triangles, and know how to rearrange simple formulas.
After this topic: Pythagoras' Theorem leads directly to trigonometry (SOH-CAH-TOA), working in 3D with diagonal distances, and coordinate geometry at GCSE.
How MathCraft Teaches This
In MathCraft, Pythagoras' Theorem is taught through the Geometry & Shape adventure track. Your child follows guided lessons with friendly characters, works through examples step by step, then practises with questions that adapt to their level.
The adaptive engine tracks mastery across all 5 steps, revisiting concepts your child finds tricky and advancing when they're ready. Parents can see detailed progress in the Parent Dashboard.
Practise Pythagoras' Theorem with MathCraft
Step-by-step lessons, worked examples, and adaptive practice — all wrapped in an adventure game your child will love.
Try MathCraft Free No credit card required