# Maths Subject Knowledge: Graphs, Functions and Solving Equations Graphically

Discover effective methods to teach graphs and functions as part of the maths curriculum for students aged 10-16 years.

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## Enhance your knowledge of graphs and functions to teach the maths curriculum

In this course, designed as a subject knowledge enhancement (SKE) for teachers, you’ll explore the topics of graphs and functions as part of the algebra curriculum for mathematics.

Led by experienced teachers, you’ll make links between different mathematical topics and develop an understanding of how certain methods work and why they work.

## Improve your subject knowledge of graphs and functions to develop your teaching approaches

You’ll watch demonstrations of teaching approaches, unpick the underlying mathematics behind graphs and build your confidence in these topics.

You’ll appreciate why linear graphs and quadratic graphs are important in representing connections between variables, and will develop a fluency in the nature of these relationships.

## Discover how graphs can solve problems and understand the concept of function notation

You’ll apply the use of graphs to display specific situations, find connections and solve an extensive array of problems.

You’ll also investigate how function notation can be used to describe transformations of graphs.

Skip to 0 minutes and 3 seconds Hello, and welcome to this STEM Learning online course all about graphs. Over the course of four weeks we will explore linear and quadratic graphs; the algebra behind them, their key features and where they appear outside of the classroom. We will provide you with clear, classroom-based teaching approaches that will help you to develop a deeper understanding of the topics we explore. Each week will include videos, examples, worked solutions and questions to help you consolidate and incorporate your learning into your teaching. Worksheet solutions are available on the last step of each week. We’ll begin by looking at function machines, finding inputs and outputs, and the rules that connect them.

Skip to 0 minutes and 49 seconds We’ll explore straight lines- we’ll draw axes, plot points, find the gradient and discover the equation of a straight line. We’ll also look at parallel lines, perpendicular lines and the many methods for finding their equations. Later in the course we will introduce quadratic graphs. You’ll see what they look like, how to sketch them and how to plot them. We will meet the equation of a quadratic graph and discover lines of symmetry, maximum and minimum points and find out where the line crosses the axes. We will finish the course by looking at transformations. You’ll see what happens when we move the graph up, down, left and right and also when we reflect it in a mirror line and stretch it too.

Skip to 1 minute and 33 seconds We look forward to seeing you on the course.

## What topics will you cover?

• The link between displaying the input and output of a function machine, as a table of results, a mapping and a graph.
• The nature and qualities of a linear relationship and a quadratic relationship.
• The application of graphs to finding approximate solutions to equations.
• Function notation and its use in describing transformations of graphs.

## Learning on this course

On every step of the course you can meet other learners, share your ideas and join in with active discussions in the comments.

## What will you achieve?

By the end of the course, you‘ll be able to...

• Reflect upon your current understanding of the basics of graphs and appreciate why graphs are important in representing connections between variables.
• Develop fluency in the nature and qualities of a linear relationship.
• Develop fluency in the nature and qualities of a quadratic relationship.
• Apply the use of graphs to display situations, find connections and solve problems.
• Investigate how function notation can be used to describe transformations of graphs.

## Who is the course for?

This course is specifically designed for secondary school teachers and educators who are not specialised in maths, but who are wanting to learn mathematical methods and improve their understanding of the subject.

It’s particularly suitable for new teachers and those studying teaching as a profession. Primary school teachers may find this course useful to understand how the mathematics curriculum progresses further in secondary school.

## Who will you learn with?

### Stephen Lyon

I have taught mathematics for over 30 years, as a head of department, an advanced skills teacher and as maths lead at STEM Learning. I am the level 3 lead for the Yorkshire Ridings maths hub.

### Michael Anderson

Mathematics Subject Specialist at the National STEM Learning Centre, York.

### Paula Kelly

Secondary maths teacher.

## National STEM Learning Centre

The National STEM Learning Centre provides world-class professional development activities and resources to support the teaching of STEM (science, technology, engineering and mathematics) subjects.

## What's included?

This is a premium course. These courses are designed for professionals from specific industries looking to learn with a smaller group of like-minded individuals.

• Includes any articles, videos, peer reviews and quizzes
• Tests to validate your learning
• Certificate of Achievement to prove your success when you're eligible

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## Learning on FutureLearn

• Courses are split into weeks, activities, and steps to help you keep track of your learning
• Learn through a mix of bite-sized videos, long- and short-form articles, audio, and practical activities
• Stay motivated by using the Progress page to keep track of your step completion and assessment scores

### Join a global classroom

• Experience the power of social learning, and get inspired by an international network of learners
• Share ideas with your peers and course educators on every step of the course

• As you work through the course, use notifications and the Progress page to guide your learning
• Whenever you’re ready, mark each step as complete, you’re in control
• Complete 90% of course steps and all of the assessments to earn your certificate

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