## ABSTRACT

Explaining and Exploring Mathematics is designed to help you teach key mathematical concepts in a fun and engaging way by developing the confidence that is vital for teachers. This practical guide focuses on improving students’ mathematical understanding, rather than just training them for exams. Covering many aspects of the secondary mathematics curriculum for ages 11-18, it explains how to build on students’ current knowledge to help them make sense of new concepts and avoid common misconceptions.

Focusing on two main principles to improve students’ understanding: spotting patterns and extending them to something new, and relating the topic being taught to something that the pupils already understand, this book helps you to explore mathematics with your class and establish a successful teacher-student relationship.

Structured into a series of lessons, Explaining and Exploring Mathematics is packed full of practical advice and examples of the best way to answer frequently asked questions such as:

• Do two minuses really make a plus?
• Why doesn’t 3a + 4b equal 7ab?
• How do you get the area of a circle?
• Why do the angles of a triangle add up to 180°?
• How can you integrate 1/x and calculate the value of e?

This book will be essential reading for all trainee and practising teachers who want to make mathematics relevant and engaging for their students.

### chapter 6|7 pages

#### Use hundreds and thousands, not apples and bananas!

Helping beginners make sense of algebra

### chapter 15|6 pages

#### Number museum

How many factors?

### chapter 17|6 pages

#### The m,d method

An alternative approach to quadratics

### chapter 30|5 pages

#### Farey sequences

Fractions in order of size

### chapter 34|7 pages

#### d why? by dx

Or what is differentiation for?

### chapter 37|5 pages

#### Summing series

Using differencing instead of induction