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In this lesson there are eight calculator based problems for students aiming at, or trying to consolidate a grade 4 at GCSE mathematics.

The eight grade 4 calculator problems cover the following topics:

- Error Intervals
- Angles in parallel lines
- Substitution into formulae
- Similar shapes
- Equations and inequalities
- Problem solving with triangles
- Scatter graphs
- Frequency polygons

Here is a sample of three questions.

The key to this problem is to work out the length scale factor of the two shapes to find the width of the larger rectangle.

I encourage students to think about how the word similar describes the relationship between the two rectangles. The purpose being to identify that one is an enlargement of the other.

When students work out the length scale factor everyone is able to correctly find the perimeter of the larger shape.

This question connects the properties of angles in parallel lines with angles in a triangle.

Nearly all students work out angle ABD using angles on a straight line but often struggle to go further.

I encourage students to use angles in parallel lines to work out BCE, and angles in a triangle to find ADB.

With BCE and ADB found all students go on to solve the problem correctly.

This question connects the area of a triangle with Pythagoras’ Theorem. You can watch the video here.

I encourage students to draw a sketch of the red triangle so it is separated from the rectangle. With the base of 18 cm given I ask them consider what else they need to know about the triangle.

Most of the class realise the need to Pythagoras’ Theorem to find the perpendicular height, AE of the triangle.

My name is Jonathan Robinson and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

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