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## Maths Extension through Breadth and Depth

### High challenge maths activities for KS4 students

#### Audience

Key stage 4 maths students.

### Maths Extension through Breadth

#### Purpose

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.

#### Content

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

#### Purpose

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.

#### Content

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.