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Integers and Number Properties

CAPS Senior Phase Mathematics (South Africa): Grade 8–9

8 ready-made resources for teaching Integers and Number Properties, written for CAPS Senior Phase Mathematics. Slides, worksheets, mark schemes, homework, an assessment and retrieval quizzes, all with SEN-friendly scaffolding built in as standard. Below is what the topic requires and where learners usually go wrong, free to read whether or not you sign up.

Independently rechecked. These files were written to the specification from our own topic maps, then put through a separate recheck pass from the one that wrote them, which found and fixed real errors. A subject teacher has not signed them off individually, so give them your usual read before you teach from them.

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What is in this bundle

Assessment mark schemeWord, editable
End-of-topic assessmentWord, editable
HomeworkWord, editable
Retrieval-practice quizzesWord, editable
SlidesPowerPoint, editable
Starter & exit ticketWord, editable
Worksheet (Grade 8 & 9)Word, editable
Worksheet mark schemeWord, editable

Grade 8

Order and compare integers.
Add, subtract, multiply and divide integers (Grade 7 covered only addition and subtraction formally: multiplication and division of integers, and combining all four operations, is new at Grade 8).
Solve multiple-operation problems involving integers, applying the correct order of operations.
Understand and use additive inverses (that a number plus its additive inverse equals zero, e.g. -7 + 7 = 0).
Apply the commutative, associative, and distributive properties of operations across the full set of rational numbers, including negatives: Grade 7 restricted this to positive rational numbers and zero; the extension to negative numbers is what's new at Grade 8.
Solve problems in context involving all four operations with integers.

Grade 9, in addition

Revise multiple-operation calculations with integers.
Understand and use multiplicative inverses (that a number multiplied by its reciprocal equals one, e.g. 4 × ¼ = 1): a further new inverse alongside additive inverses, though note Grade 8's own equation-solving work already leans on both kinds of inverse informally (see the Algebraic Equations topic), so this isn't the learner's very first encounter with the idea.
Classify and consolidate the real number system: natural numbers, whole numbers, integers, rational numbers, and irrational numbers, and how these sets relate to one another (e.g. every integer is a rational number, but not every rational number is an integer).

Where learners go wrong

Sign errors when multiplying or dividing two negative integers (forgetting that a negative × a negative gives a positive).
Confusing an additive inverse (add to get zero) with a multiplicative inverse (multiply to get one).
Applying the distributive property incorrectly when a negative sign sits outside a bracket, losing the sign on the second term.
Assuming subtraction and division are commutative in the same way addition and multiplication are (e.g. treating 5 - 3 as equal to 3 - 5).
At Grade 9, assuming every rational number is an integer (or vice versa), rather than understanding integers as one subset within the larger set of rational numbers.

How it gets asked in the exam

"Calculate ...", "Determine the additive inverse of ...", "Determine the multiplicative inverse (reciprocal) of ...", "Use the distributive property to simplify ...", "Solve the problem in context involving ...".

Key vocabulary

Integer, additive inverse, multiplicative inverse, reciprocal, commutative, associative, distributive, natural number, whole number, rational number, irrational number, real number.

Assumed prior knowledge

Ordering and comparing integers, and addition/subtraction of integers (Grade 7 content).
Confident recall of multiplication and division facts.

How Speca scaffolds this topic

A number-line model for addition/subtraction of integers, and a "same sign / different sign" reference card for multiplication/division, are effective, low-abstraction anchors for the four-operations work.
Present additive and multiplicative inverses side by side once both are taught (Grade 9), explicitly contrasting "add to reach zero" against "multiply to reach one," rather than teaching them as two unrelated facts.
Colour-code each term when applying the distributive property, with an explicit sign-tracking box, matching the same scaffold already used for algebraic expressions elsewhere in the taxonomy.

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