Working with Negative Numbers

Students learn how to use written methods to order and calculate with negative numbers.  Learning progress from performing arithmetic on a number line to multiplying and dividing with negatives.

This topic takes place in Term 2 of Year 9 and follows Properties of Numbers.


Working with Negative Numbers Lessons

Revision Lessons



Prerequisite Knowledge

  • count backwards through zero to include negative numbers
  • interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero
  • use negative numbers in context, and calculate intervals across zero

Success Criteria

  • order positive and negative integers
  • apply the four operations, including formal written methods, to integers, both positive and negative


Key Concepts

  • To order negative and positive numbers temperatures can be placed along a thermometer.
  • Use a number line to demonstrate how negative number is less than its positive counterpart but of equal magnitude.
  • Use a number line to demonstrate addition and subtraction involving negative and positive numbers.
  • Adding a negative is equivalent to a subtraction. ( 4 + -2 = 4 – 2)
  • Understanding why subtracting a negative results in an addition is vital to multiplying and dividing with negative numbers.

Common Misconceptions

  • Students often incorrectly consider negative numbers with a larger magnitude than positives to have a greater value. For example, -3 < 2.
  • Common incorrect answers to -4 + 6 are -2 (4 – 6) and -10 (-4 – 6)
  • Trying to remember multiplication rules for when to leave the answer as a positive or negative often results in confusion when adding and subtracting. Use a number line to demonstrate -3 x 2 = -3 + -3 = 6.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Getting Ready for a New School Year

When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way.  Mathematics Teaching and Learning Folder All teachers receive a folder […]

Mathematics OFSTED Inspection – The Deep Dive

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

How to Solve Quadratics by Factorising

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have.   Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]