Grade 7 Mathematics extends the number system to include integers and the introduction of formal algebra. The CAPS curriculum covers five content areas: Numbers, Operations and Relationships, Patterns, Functions and Algebra, Space and Shape (Geometry), Measurement and Data Handling. Learners begin working with algebraic expressions and equations, geometric proofs about angles and triangles, and more sophisticated data analysis. Grade 7 Maths is a crucial year — the foundations built here underpin all of FET Mathematics.
- Integers: order, compare, add, subtract, multiply, divide negative numbers
- Number lines extending in both directions
- Properties of integers: commutative, associative, distributive
- Exponents: squares and cubes, square roots and cube roots
- Prime factorisation using exponent notation
- LCM and HCF using prime factorisation
- Multiples and factors — revision and extension
- Order of operations (BODMAS) with integers and exponents
- Common fractions: add, subtract, multiply, divide — mixed numbers
- Equivalent fractions, simplifying, comparing
- Decimal fractions: all four operations to 3 decimal places
- Convert between fractions, decimals and percentages
- Percentage increase and decrease: calculate and apply
- Ratio: simplify, use in real contexts (recipes, maps, scale)
- Rate: unit rate and comparison
- Proportion: direct proportion — solve proportional problems
- Algebraic expressions: identify terms, like terms, coefficients, constants
- Simplify algebraic expressions: collect like terms
- Substitute values into algebraic expressions
- Solve one-step and two-step linear equations
- Geometric figures: classify triangles (sides and angles) and quadrilaterals
- Angle relationships: supplementary, complementary, vertically opposite, co-interior, alternate
- Parallel lines cut by a transversal — angle relationships
- Construct geometric figures using compass and protractor
- Area and perimeter: triangles, quadrilaterals and composite figures
- Volume and surface area of rectangular and triangular prisms
- Transformation geometry: reflection, rotation, translation, enlargement
- Cartesian plane: plotting and reading coordinates in all four quadrants
- Data: mean, median, mode, range of ungrouped data
- Represent data: bar graphs, histograms, line graphs, pie charts
- Interpret and analyse data: draw conclusions, identify trends
- Probability: theoretical probability — list outcomes, calculate probability
Integers need direction, not just size. When multiplying or dividing: same signs = positive, different signs = negative. Learn this rule and apply it every time.
Show all working for full marks. Method marks are awarded even if your final answer is wrong.
Algebra is just arithmetic with letters. When you see 3x + 5 = 17, ask: what number × 3 + 5 = 17? Then formalise it.
BODMAS is non-negotiable. Brackets → Orders → Division/Multiplication → Addition/Subtraction. Always.
Know your times tables to 12 × 12. Almost every Grade 7 Maths topic requires fast, accurate multiplication. No shortcuts here.