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Students are guided through the discovery of Pythagoras’ Theorem and learn how to apply it to calculate an unknown side in a right-angled triangle. As learning progresses they are challenged to solve a range of problems using Pythagoras’ Theorem.

This unit takes place in Year 8 Term 6 and is follows finding the area of 2D and 3D shapes.

- Draw and measure line segments and angles in geometric figures, including interpreting scale drawings
- Apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles
- Derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon

- For a right-angled triangle, Pythagoras’ Theorem states that a
^{2}+b^{2}= c^{2}where c is the hypotenuse.

- A Pythagorean triple is a set of three integers that exactly fits the Pythagoras relationship.
- If the lengths of the three sides of a triangle obey Pythagoras’ Theorem the triangle is right-angled.
- Students should look for right-angled triangles in shapes with problem solving with Pythagoras’ Theorem.

Develop fluency

- Use language and properties precisely to analyse 2-D and 3-D shapes.
- Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
- Select and use appropriate calculation strategies to solve increasingly complex problems

Reason mathematically

- Make and test conjectures about patterns and relationships; look for proofs or counter-examples
- Begin to reason deductively in geometry, number and algebra, including using geometrical constructions

Solve problems

- Develop their mathematical knowledge, in part through solving problems and evaluating the outcomes, including multi-step problems
- Develop their use of formal mathematical knowledge to interpret and solve problems
- Begin to model situations mathematically and express the results using a range of formal mathematical representations
- Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems

Geometry and measures

- 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
- Use Pythagoras’ Theorem in similar triangles to solve problems involving right-angled triangles
- Interpret mathematical relationships both algebraically and geometrically.

July 3, 2020

Students are challenged to apply their understanding of the mean, mode, median and range to calculate datasets by setting up and solving equations.

June 30, 2020

Five, real-life and functional problem solving questions on compound percentage changes.