Students need to be confident in applying the four operations to positive and negative numbers; the image above shows the subject content included in GCSE (age 14-16) Maths specifications. KS3 (age 11-14) students too are required to be fluent with negative numbers.
A look at some resources to develop understanding of operations with positive and negative integers …
To use the number line as a model for ordering real numbers and also to illustrate operations with negative numbers we can use the excellent PhET simulations, Number Line: Integers and Number Line: Operations. Both are excellent for students to explore.
Create a free teacher account to access further help and information on any PhET resource including a very comprehensive guide to using the resource and suggested lesson activities. See Number Line: Integers and Number Line: Operations.
We can use Graspable Math to check calculations.
Some further resources follow.
We have numerous activities from Nrich.
From Don Steward we have many wonderful resources, see
Check this excellent post of his suggestions.
On Craig Barton’s Variation theory, you will find several negative number examples. Also from Craig Barton, try these two Maths Venns and of course Diagnostic Questions where we could search in several ways, but have a look for example at the collections including The Eedi Ultimate Scheme of Work.
Corbett Maths provides us, as always, with videos and many practice examples. Scroll down the list to Negatives for a set of resources.
On Dr Frost Maths, see the KS3 Negative Number resources, note that the downloadable resource (slides which cover the four operations) and the video can be accessed without signing in.
On Mathisfun you will find information on number lines including questions to try, examples and definitions for adding and subtracting positive and negative numbers and examples for multiplying and dividing negative numbers.
I like the wording here, students are often confused with sign rules when adding and subtracting positive and negative numbers.