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Lengths in Right-angled triangles

- 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.

October 22, 2017

When factorising algebraic expressions with powers students often struggle to identify the highest common factor when it involves an algebraic term. For example, factorising 3h + 12 as 3(h + 4) is attempted correctly much more often than factorising 3h2 + 12h as 3h(h + 4). In this lesson students learn how to identify the […]

August 14, 2017

While I was teaching a higher GCSE class about Reflections, Rotations and Translations I wanted to explore extending transformations beyond shapes on a grid to include transforming straight line graphs. About forty minutes into the lesson on reflections the majority of the students were quietly working their way through the activities. The class were well […]

June 4, 2017

Here is a list of what I consider to be the best secondary school maths websites that I use every week. Best secondary school maths websites are ... UK Maths Challenge Geogebra http://prethomework.weebly.com/ This website has a good range of homework tasks for key stage 3 classes. Every worksheet includes a skill, challenge, literacy, research […]