📚 Grade 8 lessons(41)
Every lesson is one focused sub-topic, worked in full, with a printable worksheet and an exam paper with its memo.
Term 1
Adding & Subtracting DecimalsThe one rule that makes decimal addition and subtraction reliable — line up the decimal points — plus filling gaps with zeros and money problems, with worked examples, a worksheet with memo and a quiz.6min read · lesson, worksheet & exam paperAdding & Subtracting FractionsAdding and subtracting fractions with the same denominator, with different denominators using the LCD, and with mixed numbers — shown with a bar diagram, exam-style worked examples, a worksheet with memo and a quiz.9min read · lesson, worksheet & exam paperAdding and Subtracting IntegersOrdering integers on a number line, then the two adding rules and the 'add the opposite' trick for subtracting — with a number-line diagram, exam-style worked examples, a worksheet with memo and a quick quiz.9min read · lesson, worksheet & exam paperDecimals: Place Value, Ordering & RoundingWhat each digit after the decimal point is worth, how to compare and order decimals correctly, and how to round off to a given number of decimal places — with a place-value chart, worked examples, a worksheet with memo and a quiz.8min read · lesson, worksheet & exam paperEquivalent Fractions & SimplifyingWhat the top and bottom of a fraction actually mean, how to build equivalent fractions, and how to simplify to lowest terms using the HCF — with a bar diagram, worked examples, a worksheet with memo and a quiz.7min read · lesson, worksheet & exam paperExtending Numeric & Geometric PatternsSpotting what a pattern is doing — a constant difference, a constant ratio, or something else entirely — and extending it, including patterns given as diagrams or tables, with worked examples, a worksheet with memo and a quiz.8min read · lesson, worksheet & exam paperFactors, Multiples & Prime FactorisationWhat factors and multiples really are (and how never to mix them up), what makes a number prime, and how to break any number into its prime factors with a factor tree — worked examples, a clear diagram and an exam-style worksheet with memo.8min read · lesson, worksheet & exam paperFractions of Quantities, Grouping & SharingFinding a fraction of an amount, working backwards from a fraction to the whole, and the grouping and sharing word problems that carry the marks in exams — worked examples, a worksheet with memo and a quiz.8min read · lesson, worksheet & exam paperHCF and LCM (Highest Common Factor & Lowest Common Multiple)Highest Common Factor and Lowest Common Multiple made simple by reading them straight off the prime factors — with a Venn-diagram picture, exam-style worked examples and word problems, plus a worksheet with memo.9min read · lesson, worksheet & exam paperIntegers: Squares, Cubes, Roots & Mixed OperationsSquares, cubes, square roots and cube roots of integers, the crucial difference between (−3)^2 and −3^2, and how to run BODMAS through a calculation containing negatives — worked examples, worksheet with memo and a quiz.8min read · lesson, worksheet & exam paperMultiplying & Dividing DecimalsCounting decimal places when multiplying, the shift trick for dividing by a decimal, multiplying and dividing by 10, 100 and 1000, and estimating the answer first — worked examples, a worksheet with memo and a quiz.9min read · lesson, worksheet & exam paperMultiplying & Dividing FractionsMultiplying straight across, the reciprocal, and why dividing by a fraction means multiplying by its flip — including mixed numbers and dividing whole numbers by fractions, with worked examples, a worksheet with memo and a quiz.9min read · lesson, worksheet & exam paperMultiplying and Dividing IntegersThe one sign rule that covers both × and ÷ — same signs give a positive, different signs give a negative — shown as a grid, with exam-style worked examples, a worksheet with memo and a quick quiz.7min read · lesson, worksheet & exam paperOrder of Operations: Getting BODMAS RightDo calculations in the wrong order and you get the wrong answer, even with perfect arithmetic. BODMAS is the rule that fixes that.5min read · lesson, worksheet & exam paperPattern Rules: In Words and in AlgebraTurning a pattern into a general rule — first described in words, then written algebraically as Tₙ = dn + c — and using that rule to find far-off terms or to work backwards, with worked examples, a worksheet with memo and a quiz.9min read · lesson, worksheet & exam paperProperties of Integers & InversesThe commutative, associative and distributive properties applied to integers, plus additive and multiplicative inverses — what they are, how exams ask for them, with worked examples, a worksheet with memo and a quiz.7min read · lesson, worksheet & exam paperProperties of Whole NumbersThe commutative, associative and distributive properties, the identity roles of 0 and 1, and why dividing by 0 is undefined — the rules that let you rearrange any calculation, with a diagram, worked examples and an exam-style worksheet with memo.8min read · lesson, worksheet & exam paperSquares, Cubes & Roots of DecimalsSquaring and cubing decimals, and finding square and cube roots of decimals, using the decimal-place count or by converting to fractions — with worked examples, a worksheet with memo and a quiz.6min read · lesson, worksheet & exam paperSquares, Cubes & Roots of FractionsSquaring and cubing fractions, and finding square roots and cube roots of fractions — the rule is simply 'do it to the top and to the bottom', with worked examples, a worksheet with memo and a quiz.6min read · lesson, worksheet & exam paper
Term 2
Algebraic Language: Terms, Coefficients & Like TermsThe vocabulary of algebra — variables, constants, terms, coefficients and exponents — how to spot like terms, and how to add and subtract them correctly, with worked examples and a quiz.8min read · lesson, worksheet & exam paperExpanding & Simplifying Algebraic ExpressionsMultiplying a monomial into brackets, dividing expressions by a monomial, and substituting values to find the numerical value of an expression — the core Grade 8 algebra skills, with worked examples and a quiz.9min read · lesson, worksheet & exam paperExponents: Notation, Squares, Cubes & RootsWhat exponential notation actually means, how to read and write it, squares, cubes, square roots and cube roots, and scientific notation — with a labelled diagram, worked examples and a quiz.9min read · lesson, worksheet & exam paperFunctions & Relationships: Flow Diagrams, Tables and FormulaeInput values, output values and rules — how the same relationship can be shown as a flow diagram, a table or a formula, and how to find a missing input, output or rule, with a clear diagram and a quiz.8min read · lesson, worksheet & exam paperInterpreting & Drawing GraphsReading global graphs — increasing, decreasing and constant sections, linear versus non-linear, maximum and minimum points, and discrete versus continuous data — plus plotting points on the Cartesian plane, with diagrams and a quiz.9min read · lesson, worksheet & exam paperSolving Algebraic Equations (Grade 8)Solving equations by inspection and by using inverse operations — one-step, two-step, brackets and equations with exponents — plus setting up equations from word problems, with worked examples and a quiz.10min read · lesson, worksheet & exam paperThe Laws of Exponents (Grade 8)The five exponent laws in the Grade 8 CAPS syllabus — multiplying, dividing, a power of a power, a power of a product, and the zero exponent — each explained from first principles with worked examples, a worksheet and a quiz.10min read · lesson, worksheet & exam paper
Term 3
Angle Relationships: Straight, Intersecting & Perpendicular LinesAngles on a straight line, angles round a point, vertically opposite angles and perpendicular lines — the four relationships every geometry rider is built from, with a diagram, worked examples and a quiz.8min read · lesson, worksheet & exam paperAngles in Triangles and Quadrilaterals: Full GuideFind any missing angle in triangles and quadrilaterals — including isosceles, right-angled, the exterior-angle rule, solving for x, and the special quadrilaterals — each worked in full, with a worksheet.13min read · lesson, worksheet & exam paperAngles on Parallel Lines: The Complete Exam GuideEvery angle relationship a parallel-lines question uses — corresponding, alternate, co-interior, plus straight-line and vertically-opposite angles — with worked examples for finding angles, solving for x, and multi-step reasoning, and a full worksheet.13min read · lesson, worksheet & exam paperCollecting & Organising DataHow a statistics investigation actually works — asking a good question, samples versus populations, questionnaires, and organising results with tally tables, stem-and-leaf displays and grouped intervals, with a worked diagram and a quiz.9min read · lesson, worksheet & exam paperCongruent & Similar 2D ShapesThe difference between congruent shapes (identical) and similar shapes (same shape, different size), how to spot each, and how to use proportion to find missing sides — with a clear diagram, worked examples and a quiz.8min read · lesson, worksheet & exam paperConstruction of Geometric FiguresUsing only a compass and ruler to bisect a line, bisect an angle, construct 60° and 90°, and build a triangle from given sides — the constructions that appear as their own exam question, with step-by-step diagrams.9min read · lesson, worksheet & exam paperMean, Median, Mode and Range: Complete GuideThe four everyday statistics, and every twist an exam adds — odd and even data sets, the median between two middle values, finding a missing value from the mean, and working back from a total — each worked in full, with a worksheet.13min read · lesson, worksheet & exam paperPercentages: The Complete Money-Maths GuideEvery percentage question in the Grade 8–9 syllabus — finding a percentage, increase and decrease, one number as a percentage of another, percentage change, VAT, profit and loss, and reverse percentages — each worked in full, with a worksheet.15min read · lesson, worksheet & exam paperProbability: The Complete Grade 8–9 GuideEvery probability question in the Grade 8–9 syllabus — single events, the complement (not happening), relative frequency, and simple two-event experiments — each worked in full, with a worksheet.13min read · lesson, worksheet & exam paperRatio and Rate: Every Exam Question TypeAll the ratio and rate skills a Grade 8–9 exam tests — simplifying, sharing in a ratio, finding a missing part, equivalent ratios, increasing/decreasing in a ratio, and unit rates — each worked in full, with a worksheet.14min read · lesson, worksheet & exam paperSimple Interest & Budgets (Grade 8)Working out simple interest on savings and loans, finding the total amount owed or saved, and drawing up a monthly budget that balances.10min read · lesson, worksheet & exam paperTransformation Geometry: All Four TransformationsEvery transformation an exam sets — reflection in the axes and y = x, translation, rotation about the origin, and enlargement — with the coordinate rule for each, worked examples and a worksheet.13min read · lesson, worksheet & exam paper
Term 4
Area and Perimeter: Every Shape (Complete Guide)Perimeter and area for every shape in the Grade 8–9 syllabus — rectangles, squares, triangles, circles (and half-circles), plus composite shapes and working backwards from the area — each worked in full, with a worksheet.14min read · lesson, worksheet & exam paperSurface Area and Volume: Complete GuideVolume and surface area for every 3D object in the syllabus — cubes, rectangular prisms and triangular prisms — plus capacity, unit conversions and working backwards, each worked in full, with a worksheet.14min read · lesson, worksheet & exam paperThe Theorem of Pythagoras (Grade 8)The relationship between the three sides of a right-angled triangle — finding the hypotenuse, finding a shorter side, leaving answers in surd form, and testing whether a triangle is right-angled — with a labelled diagram, worked examples and a quiz.9min read · lesson, worksheet & exam paper
📖Grade 8 Mathematics: curriculum guide & study tipsRead more ▾Show less ▴
Grade 8 is the first year of the Senior Phase and the foundation for everything that follows in high school mathematics. The CAPS curriculum moves learners from arithmetic into real algebra for the first time: working with integers, exponents and algebraic expressions, and solving equations. Learners who master Grade 8 algebra find Grades 9–12 dramatically easier, which is why most of the papers and worksheets on this page focus on building fluency with the basics.
Topics by term (CAPS)
Term 1
Whole numbers (properties, calculations, ratio and rate, finance), integers, exponents, and numeric and geometric patterns.
Term 2
Functions and relationships, algebraic expressions, algebraic equations, and the June (mid-year) examination.
Term 3
Geometry of straight lines and 2D shapes, angle relationships, construction of geometric figures, area and perimeter of 2D shapes.
Term 4
Surface area and volume of 3D objects, transformation geometry, data handling (collecting, organising and summarising data), probability, and the November examination.
How you'll be assessed
Grade 8 learners typically write class tests each term, a mid-year examination in June and a final examination in November. Papers usually run out of 50–100 marks depending on the school. The papers on this page come from provincial departments and Danemathics class tests, each paired with its memorandum where available.
Study tips from the classroom
- Master integer rules (adding, subtracting, multiplying negatives) until they are automatic — most Grade 8 marks are lost on sign errors.
- Practise exponent laws with numbers before applying them to variables.
- When solving equations, write every step; skipping steps is the main source of errors in June and November papers.
- Work through at least two past papers before each test, then mark yourself with the memo and redo every question you got wrong.