# Creating and Manipulating Linear and Quadratic Expressions - Key Stage 3

This collection of resources supports the teaching of Creating amd Manipulating Linear and Quadratic Expressions.

Here are some of the favourite activities selected by the NRICH team.

- Perimeter Expressions Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?
- Always a Multiple? Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
- Special Numbers My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
- Quadratic Patterns Surprising numerical patterns can be explained using algebra and diagrams...

These are just a few of the activities on Creating and Manipulating Linear and Quadratic Expressions that you can find on the NRICH curriculum pages.

The activities below, taken from the STEM Learning website, complement the NRICH activities above.

### Factorising Quadratics

Factorising Quadratics is a worksheet giving practice at finding the sum and product of two numbers and also finding the two numbers given their sum and product. Students are given two pieces of information and they need to find the other two.The questions progress to include negative numbers.

### Whole School Mathematics Projects

The Mathmagic problems can all be explained by using algebra, including multiplying out brackets. Students are shown a trick and then they need to use algebra to explain why the trick works.

Teacher's notes for the seven problems start on page 39 and the student resources start on page 45.

### Task Maths 2

Encourage students to explore different ways of writing the formulae including the use of brackets.

An example and a series of questions dealing with writing formulae involving lengths and areas can be found on pages 77-78. Students are encouraged to explore different ways of writing the formulae. They are especially encouraged to explore the use of brackets to get equivalent expressions.

### Number and Algebra 2

Exploring sequences through this set of structured questions and investigations that require students to use algebra to describe sequences.

The relevant section begins on page 118 of the pdf. It starts with an example of how to carry out an investigation showing various possible stages. Then there are a series of investigations and structured questions where students need to use algebra to describe patterns and sequences.