Applying Pythagoras' theorem
Apply Pythagoras’ Theorem (a² + b² = c²) to calculate unknown side lengths in right-angled triangles, including in real-world and coordinate-geometry contexts
Lesson
Set out your lesson
“Applying Pythagoras' theorem means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Grid paper or squared paper
- Ruler and pencil
Extra for the adult
Worked example. On grid paper, legs 3 and 4 give hypotenuse 5 because 9+16=25.
Optional challenge. For Applying Pythagoras' theorem, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Applying Pythagoras' theorem, not mastery.
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Teaching approaches
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1 approach
Applying Pythagoras' theorem means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Grid paper or squared paper; Ruler and pencil. 1. Say the goal of Applying Pythagoras' theorem in plain words once. 2. Adult marks a 3-4-5 right triangle and checks 3²+4²=5². 3. Child builds three right triangles on grid paper and checks a²+b² against c². 4. Fresh check: one fresh 3-4-5 (or similar) check. Record and stop. Done: three checked right triangles with a²+b² and c² recorded. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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Learning resources
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PhET Interactive Simulations · Practice link — not the full lesson
Area Builder
Before you open · source notes
Area Builder supports hands-on exploration for Applying Pythagoras' theorem. Not every lab worksheet.
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Source, access and review notes
Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Area Builder.” External page; Gakuva does not copy, host, embed, or redistribute materials.
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Check understanding
- Calculate the hypotenuse of a right-angled triangle given the two shorter sides
- Find a shorter side given the hypotenuse and the other short side
- Use Pythagoras’ Theorem to find the distance between two points on a coordinate grid
“If your child wants to check whether a shelf bracket makes a perfect right angle and the sides measure 30 cm, 40 cm, and 50 cm, can they use Pythagoras to verify?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Geometry
- Age range
- Ages 13–14
Standards