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Algebraic Expressions

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

8 ready-made resources for teaching Algebraic Expressions, 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

Add and subtract like terms, and evaluate an algebraic expression by substituting given values in for its variables (the groundwork this topic's own "combining unlike terms" misconception depends on).
Use the commutative, associative and distributive laws to classify algebraic terms as like or unlike terms.
Multiply a monomial by a monomial, a binomial, or a trinomial.
Divide a multi-term expression (a binomial or trinomial) by a monomial: note the direction: CAPS never asks a learner to divide a monomial by a binomial or trinomial, since that generally isn't simplifiable at this level.
Simplify a bracketed expression that combines at most two different operations across one or two bracket pairs.

Grade 9, in addition

Multiply two binomials together (e.g. (x + 4)(x + 7)), applying the distributive law and the bracket-expansion skill built in Grade 8 to a two-bracket product rather than a single one.
Divide a polynomial by a monomial (extending Grade 8's binomial/trinomial-by-monomial division to longer expressions).
Simplify algebraic expressions using the laws of exponents, and using factorisation.
Factorise algebraic expressions by: finding a common factor; recognising and factorising a difference of two squares; and factorising trinomials of the form x² + bx + c, and ax² + bx + c where a is a common factor.

Where learners go wrong

Combining unlike terms as though they were like terms (e.g. treating 3x + 2x² as 5x³ or 5x).
Making a sign error when expanding a bracket with a negative term outside it.
Multiplying only some of the terms inside a bracket when expanding, rather than every term.
At Grade 9, factorising incompletely: leaving a common factor still inside the bracket, or stopping after finding one factor of a trinomial rather than checking the factorisation is complete.
Confusing a difference of two squares (a² - b², which factorises) with a sum of two squares (a² + b², which generally does not factorise over rational numbers).
Attempting to divide a monomial by a longer expression (a binomial or trinomial): this isn't the direction division questions are ever asked in at this level, and it's a sign a learner has the numerator/denominator the wrong way round.

How it gets asked in the exam

"Simplify ...", "Expand and simplify ...", "Determine the product of ... and ...", "Factorise ...", "Classify the terms in ... as like or unlike terms".

Key vocabulary

Term, like terms, unlike terms, monomial, binomial, trinomial, expand, simplify, factorise, common factor, difference of two squares.

Assumed prior knowledge

Representing a pattern or relationship algebraically (previous topic).
The commutative, associative and distributive properties of operations on rational numbers (Number strand).
Multiplication and division facts, and confident work with signed numbers.

How Speca scaffolds this topic

Use a consistent "expand checklist", an arrow from the term outside a bracket to every term inside it, with a dedicated sign-tracking box, so no term is missed and no sign is dropped, especially once double-bracket products are introduced at Grade 9.
A colour-coded like/unlike terms sorting activity, using the same colour for matching term types, builds the classification skill concretely before it's needed for simplifying expressions.
Provide a factor-pair grid/box method as the default visual for factorising trinomials, consistent with the same technique's use in other algebra content.
South African decimal convention: use a comma as the decimal separator wherever a decimal value appears (e.g. 2,5, not 2.5).

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