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 and exercises for practice …

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: Distance, Number Line: Integers, and Number Line: Operations. All 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.

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I’ll mention the ‘sign rules’ here as they cause much confusion and many misconceptions, we need to word these so carefully. In fact, we need some more examples to stress we are talking about adjacent like signs.
Look at -4−-3 and -4−-6 for example.     

From Jonathan Hall, on MathsBot, generate all the addition and subtraction multiple-choice questions you want with his brilliant Directed Number MCQ Generator. I really like the option to have questions using counters of varying relative sizes.

Also from Jonathan Hall, try his Directed Number.

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On Chris McGrane’s Starting Points Maths, check the Negative Numbers category. Several tasks are available.

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We can use Graspable Math to check calculations.

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We have numerous activities from Nrich.

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From Don Steward we have many wonderful resources, see

• directed number (16)
• directed number add/take (24)
• directed number multiplication (4)

Check this excellent post of his suggestions.

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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.

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From the brilliant Standards Unit, N8, Using directed numbers in context and N9, Evaluating directed number statements.

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Colin Foster’s KS3 Instant Maths Ideas (3 books) are freely available online; these contain a wealth of ideas to try in the classroom. 1.13 in Number and Algebra is on Negative Numbers.

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Transum has several activities including basic practice in the four operations.

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Try the interactive tutorials on CIMT for these quizzes where students can check answers, Addition and Subtraction and Multiplication and Division.

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Corbett Maths provides us, as always, with videos and many practice examples. Scroll down the list to Negatives for a set of resources.

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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.

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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’ll mention the ‘sign rules’ here as they cause much confusion and many misconceptions, we need to word these so carefully. In fact, we need some more examples to stress we are talking about adjacent like signs.
Look at -4−-3 and -4−-6 for example.     

I like the wording here, students are often confused with sign rules when adding and subtracting positive and negative numbers.