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Maths Extension through Breadth and Depth

Maths Extension through Breadth and Depth

High challenge maths activities for KS4 students


Key stage 4 maths students.

Maths Extension through Breadth


Maths Extension through Breadth uses key stage 4 maths topics as jumping-off points for exploring fresh and exciting mathematical ideas that students won't have seen before. It aims to give students a new sense of the scope and power of the subject and its applications.


These resources were jointly developed by London Gifted & Talented, the London Borough of Harrow and the maths department at Imperial College.

There are four topics to explore. Each topic has a teacher's guide and student worksheets which are available to download.

1. Loopy Logic

This is about iterative and recursive processes, and the strange objects and phenomena they give rise to, like chaos and fractals.

2. So Solid

This invites students to use their geometrical knowledge to explore the third dimension.

3. Get Connected

This is about networks and graphs: it introduces the idea of an algorithm, and gets students thinking about what it means to say that a maths problem is 'hard'.

4. Prove It!

This is about why mathematicians need to be careful when they make statements, and how they make sure they don't make claims that are false.

Maths Extension through Depth


Maths Extension through Depth aims to give students a deepened appreciation of the key stage 4 curriculum in mathematics and of the power of mathematical rigour.


These resources pool the best of tried-and-trusted classroom practice in the London boroughs of Camden and Haringey, further developed by London Gifted & Talented.

There are three topics to explore. Each topic has a series student worksheets which are available to download.

1. Geometrical reasoning

This gets students thinking deeply about shapes in two and three dimensions, and how mathematics can help us understand them.

2. Statistical reasoning

This is all about the mathematical study of the random, and making decisions on the basis of partial knowledge.

3. Algebraic and numerical reasoning

This deals with numerical structures and the symbolisms mathematicians use to help explore them.