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South Africa Grade 5 Mathematics Syllabus

This outlines the topics covered in the Grade 5 Mathematics curriculum in South Africa, aligned with the Curriculum and Assessment Policy Statement (CAPS).

1. Numbers, Operations, and Relationships

Whole Numbers:

Mental calculations (addition, subtraction, multiplication) involving units, multiples of 10, 100, 1 000, and 10 000.

Counting, ordering, comparing, and representing numbers up to 6 digits.

Place value of digits in whole numbers up to 6 digits.

Rounding off to the nearest 5, 10, 100, and 1000.

Addition and subtraction of whole numbers up to 5 digits.

Multiplication of 3-digit by 2-digit numbers.

Division of 3-digit by 2-digit numbers.

Calculation techniques: estimation, column addition/subtraction, building up/breaking down numbers, number lines, rounding off and compensating, doubling and halving, inverse operations (addition/subtraction, multiplication/division).

Multiples and factors of 2-digit numbers up to 100.

Properties of whole numbers: commutative, associative, distributive, additive property of 0, multiplicative property of 1.

Problem-solving in financial and measurement contexts, including ratio, rate, and grouping/equal sharing with remainders.

Common Fractions:

Counting forwards and backwards in fractions.

Comparing and ordering common fractions up to twelfths.

Addition and subtraction of common fractions with the same denominators and mixed numbers.

Fractions of whole numbers resulting in whole numbers.

Equivalence of division and fractions.

Problem-solving in contexts involving common fractions, including grouping and sharing.

Equivalent forms of common fractions.

Decimal Fractions:

Converting between fractions and decimals.

2. Patterns, Functions, and Algebra

Numeric Patterns: Investigating and extending numeric patterns, determining input/output values and rules using flow diagrams and tables, and determining equivalence of different descriptions of the same relationship.
Geometric Patterns: Investigating and extending geometric patterns, determining input/output values and rules using flow diagrams, and determining equivalence of different descriptions of the same relationship.
Number Sentences: Writing number sentences to describe problem situations, solving and completing number sentences by inspection and trial and improvement, and checking solutions by substitution.

3. Space and Shape (Geometry)

2-D Shapes: Recognizing, visualizing, and naming 2-D shapes (regular/irregular polygons, circles), describing, sorting, and comparing 2-D shapes based on sides and angles, drawing 2-D shapes, and recognizing and describing angles (right, smaller than right, greater than right).
3-D Objects: Recognizing, visualizing, and naming 3-D objects (prisms, cubes, cylinders, cones, pyramids), describing, sorting, and comparing 3-D objects based on faces and surfaces, making 3-D models, and cutting open boxes to trace and describe nets.
Symmetry: Recognizing, drawing, and describing lines of symmetry in 2-D shapes.
Transformations: Making composite 2-D shapes and tessellated patterns using rotation, translation, and reflection, and describing patterns in nature, modern life, and cultural heritage.
Viewing of Objects: Linking the position of the viewer to views of single and collections of everyday objects.
Position and Movement: Locating positions on grids and maps using alpha-numeric grid references and following directions to trace paths on maps.

4. Measurement

Length: Practical measuring (estimating, measuring, recording, comparing, ordering) of 2-D shapes and 3-D objects using rulers, metre sticks, tape measures, and trundle wheels. Units: mm, cm, m, km. Problem-solving and conversions involving length.
Mass: Practical measuring (estimating, measuring, recording, comparing, ordering) of 3-D objects using bathroom scales, kitchen scales, and balances. Units: g, kg. Problem-solving and conversions involving mass.
Capacity/Volume: Practical measuring (estimating, measuring, recording, comparing, ordering) of 3-D objects using measuring spoons, cups, and jugs. Units: ml, l. Problem-solving and conversions involving capacity/volume.
Time: Reading time in 12-hour and 24-hour formats on analogue and digital instruments (clocks, watches, stopwatches), reading calendars, calculating time intervals, and understanding the history of time measurement.
Temperature: Practical measuring (estimating, measuring, recording, comparing, ordering) of temperature using thermometers. Unit: degrees Celsius. Problem-solving and calculating temperature differences.
Perimeter, Surface Area, and Volume: Measuring perimeter, finding areas of shapes by counting squares on grids, and finding volume/capacity by packing or filling objects.
History of Measurement: Understanding historical methods of measurement.

5. Data Handling

Collecting and Organizing Data: Collecting data using tally marks and tables, and ordering data.
Representing Data: Drawing pictographs, bar graphs, and pie charts to display and interpret data.
Analyzing, Interpreting, and Reporting Data: Critically reading and interpreting data, analyzing data by answering questions related to categories, sources, and contexts, summarizing data verbally and in writing, and examining ungrouped numerical data to determine the mode.
Probability: Performing simple repeated events (tossing a coin, rolling a die, spinning a spinner), listing possible outcomes, and counting and comparing the frequency of actual outcomes.

Additional resources and worksheets can be found on websites such as Twinkl, Math Mammoth, and the WCED ePortal. Examples of worksheets include: and