Pythagoras' theorem – Year 9 maths lesson
Lesson 13 of 38 in the Year 9 maths course
UK version. UK school years, UK spelling and pounds (£). · US Math Department
A complete 45-minute lesson for Year 9 (ages 13–14) that runs on this page – at school or at home. Every answer is marked straight away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Year
- Year 9 (ages 13–14)
- You need
- Paper, a pencil and this page
- Marked
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is marked straight away with a worked explanation, so you never have to mark anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “How can builders use a 3-4-5 triangle to check a right angle?”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Adding when finding a shorter side. If you want a short side, subtract from the hypotenuse squared.
- Forgetting to square root at the end. Check: the hypotenuse must be the longest side.
Tip for home: Work out the length of a ladder needed to reach a window.
What your child will learn
We are learning to use Pythagoras' theorem to find missing sides in right-angled triangles.
Success looks like
- I can find the hypotenuse.
- I can find a shorter side.
- I can use Pythagoras in problems.
Key words
- hypotenuse
- the longest side, opposite the right angle
- right angle
- an angle of 90°
- square root
- the number that squares to give the value
- converse
- if a² + b² = c², the angle is a right angle
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use a 3, 4, 5 triangle made from string to check right angles in the corner of a room.
The big ideas (for the adult)
In a right-angled triangle, a² + b² = c², where c is the hypotenuse, the longest side opposite the right angle.
To find the hypotenuse, square the two shorter sides, add, then square root. To find a shorter side, subtract instead.
Use it to find distances between points on a grid and to check whether a triangle has a right angle.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Marked by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, marked by Classfern |
| Independent practice | 15 min | Marked by Classfern |
| Plenary and exit ticket | 6 min | Marked by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are marked by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all marked instantly.
More practice
More Year 9 maths lessons
- Prime factors, HCF and LCM
- Rounding and estimation
- Bounds and error intervals
- Standard form
- Laws of indices
- Powers and roots
- Units and measures
- Area of triangles, parallelograms and trapeziums
- Circles: circumference, area, arcs and sectors
- Volume and surface area
- Angle facts and parallel lines
- Angles in polygons
- Trigonometry: SOH CAH TOA
- Transformations
- Similarity and congruence
- Quadrilaterals and symmetry
- Coordinate geometry
- 3-D shapes, plans and elevations
- Quartiles, box plots and spread
- Pie charts and time series graphs
- Sampling
- Relative frequency and expected outcomes
- Venn diagrams and conditional probability
- Algebraic notation
- Substitution
- Simplifying expressions
- Expanding brackets
- Solving linear equations
- Inequalities
- Rearranging formulae
- Sequences and the nth term
- Straight-line graphs
- Graphs of functions
- Ratio
- Percentages
- Speed, density and pressure
- Scale drawings and maps
Curriculum
National Curriculum for England, Year 9: “use Pythagoras’ Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles”
National Curriculum for England, Year 9: “apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras’ Theorem, and use known results to obtain simple proofs”
Contains public sector information licensed under the Open Government Licence v3.0.
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.