Maths GCSE: Algebra and Negative Numbers

Negative numbers are made easy in this handy guide for maths GCSE students from Matt Parker, who breaks down his top five problems with negative numbers.

The mathematician and comedian uses this video to explain the sometimes confusing topic of negative numbers.

A mixture of graphics and jokes help break down negative numbers into Matt’s “Top Five” categories of negative number errors.

Matt also explains the history of negative numbers, including how Europeans didn’t use them until long after Chinese and Indian mathematicians.

He also reinforces the importance of order of operations when dealing with an equation and the use of acronyms such as BIDMAS and BODMAS in revision.

While the videos have been designed as revision tools for GCSE level students, they could also be used in part to introduce topics for earlier Key Stages.

This short film is from the BBC series, The Maths Show.

Teacher Notes

During the video:

  • As Matt sets up the various examples using brackets and powering negative numbers, pause before he answers and test your students on the questions. See if they can set up number lines correctly to solve equations that require adding and subtracting negative numbers.
  • Use Always/Sometimes/Never to elicit discussion of negative number ‘rules’ during the pausing of the video.
  • Students could use whiteboards or think pair share to encourage collaboration of checking methods that some students may already utilize.
  • A calculator emulator or similar would be useful to look at calculator skills.

After the video:

  • Look at other past exam questions that highlight the use of negative number skills. Use ‘spot the mistake’ questions to ensure use of appropriate checking skills. Explore different ways of creating number lines to use in a timely manner with sufficient but not excessive information.
  • Use a matching activity or similar to substitute negative values into formulae - ensure a mix of the four operations. For students that need negative number reinforcement before approaching algebra, a similar activity with sums alone will help students.
  • Students could create an odd one out activity where either two answers are the same and one is different, or two answers are correct, and one is wrong (breaking one of the top -5 rules).
  • Ask students to create a poster or display using their own examples for Matt’s “Top -5 mistakes with negative numbers”, including how to check that they haven’t made the errors. Students could start with a simpler substitution expression then slowly build it using various positive and negative terms.
  • Ask your pupils if they find any parts of negative numbers tricky that Matt didn’t mention?

Curriculum Notes

Suitable for teaching maths at GCSE in England, Wales and Northern Ireland and National 4/5 or Higher in Scotland.

More from The Maths Show

Algebra - Formulae and Graphs
Exam Techniques for GCSE Maths
Ratio and Proportion
Fractions, Decimals and Percentages