# Creating and Manipulating Linear and Quadratic Expressions - Key Stage 4

This is a second collection of resources to support the teaching of Creating amd Manipulating Linear and Quadratic Expressions.

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

- Pair Products Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
- Factorising with Multilink Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
- What’s Possible? Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
- Pythagoras Perimeters If you know the perimeter of a right angled triangle, what can you say about the area?

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.

### Equations

**Quadratic Equations** has a set of questions where students are given the sum and product of two numbers which they need to find. There are also similar questions where the difference and product are given.

### Algebraic Structure

**Pack 2** has three relevant sections.

Smile card 1665 describes an investigation of the expansion of (x+1)^{2}. This starts on page 5 of the pdf.

Smile card 0876 is a short investigation involving the expansion of brackets. This is on page 7 of the pdf.

Smile card 0818 is an investigation into the difference of two squares. This begins on page 8 of the pdf. It starts with a practical approach which becomes more algebraic.

### Quadratic Functions

Quadratic functions has a section which explains how to use a grid method to factorise quadratic expressions. This begins on page 8 of the pdf.

Overhead slides has a page showing three examples of this grid method of factorising. This can be used to aid whole class discussion.

### Nuffield National Curriculum Mathematics 5

The relevant section begins on page 57 of this pdf.

This section has examples and sets of problems which require the use of algebra. This includes the expansion of brackets, factorising expressions and collecting like terms. Diagrams show the expansion of (x+a)(x+b) and there is a section on the difference of two squares.

### Quadratics

**Quadratics Solving** is an interactive spreadsheet which shows how to use the formula to solve quadratic equations. New equations can be generated and the substitution and subsequent steps can be revealed.