• NATIONAL STEM LEARNING CENTRE

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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Maths Subject Knowledge: Graphs, Functions and Solving Equations Graphically

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.

Syllabus

  • Week 1

    Introducing straight line graphs

    • Function machines and plotting graphs

      In this course we will explore linear and quadratic graphs, the algebra behind them, their key features and how we can use them. We start with function machines, inputs and outputs, and how these can be represented graphically.

    • Understanding gradients

      How would you explain what a gradient is? In this part of the course we look at how an understanding of gradients helps to define straight lines and solve a famous shape problem.

    • The equation of a straight line

      With an understanding of what a gradient is, you can now define a straight line using the general equation y=mx+c. But what do each of these letters mean?

    • Straight line graphs and proportionality

      How does a straight line describe a proportional relationship between two variables? In this section you'll see how straight line graphs have applications in science.

  • Week 2

    Linear graphs and equations

    • Parallel and perpendicular lines

      This week we'll look at linear graphs and equations. We start by exploring parallel and perpendicular lines. What will you notice about equations of these lines?

    • Sketching graphs

      Sketching graphs is a fundamental skill students will need to develop. In these two videos we go through the process and help you understand the link between an equation and what you see graphically.

    • Finding the equation

      How can you use limited information to find the equation of a line? In these examples we look at how you can use points on a graph and an understanding of parallel and perpendicular lines.

    • Solving linear equations graphically

      In this part of the course we look at how equations can be solved using graphs. Where might you use these techniques?

  • Week 3

    Quadratic graphs

    • Properties of quadratic graphs

      This week we look at quadratic graphs, how to sketch them and where they are found. We start by defining quadratic sequences.

    • Plotting quadratics and the general equation

      With an understanding of what a quadratic graph is, you'll now look at the general equation of a quadratic graph.

    • Changing the shape

      In this section you’ll use graphing tools to explore how the shape of a quadratic graph can be changed and how to find the line of symmetry of a quadratic graph.

    • Finding roots

      The final part of this week explores the roots of quadratic graphs and their link with solving quadratic equations graphically.

  • Week 4

    Transformations of graphs

    • Transformations of graphs

      Welcome to the final week of the course. This week we look at how we can change the shape of graphs by changing their equations. First we look at the different types of 'transformations'.

    • Reflections

      What happens to the equation of a graph when it is reflected? In this section we look at reflections in a straight line, such as an axis.

    • Translations

      Translation is moving a graph up, down, left or right. How would a translation change the equation of a graph?

    • Stretching

      The third type of transformation we'll explore is stretching. We look at stretching vertically and horizontally.

    • Summary of this week: transformations

      This week you've looked at transformations. We look at further examples here of everything you've learnt across the course.

    • Completing your professional development

      This final part of the course provides a test to certify your understanding from this course and direction for your next professional development.

When would you like to start?

Start straight away and learn at your own pace. If the course hasn’t started yet you’ll see the future date listed below.

Learning on this course

You can take this self-guided course and learn at your own pace. 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?

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.

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

Who developed the course?

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.

Learning on FutureLearn

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  • Complete 90% of course steps and all of the assessments to earn your certificate

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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.

  • Unlimited access to this course
  • 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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