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The Mathematics Curriculum in Primary and Lower Secondary Grades

In 2000, the National Department of Education released the Revised National Curriculum Statement Grades R to 9, to streamline and strengthen the 2005 curriculum.6 The Revised National Curriculum Statement Grades R to 9 was approved in 2002 and implemented in 2004. In 2011, this curriculum was revised as the Curriculum and Assessment Policy Statement, and was subsequently implemented in 2012. The National Curriculum and Assessment Policy Statement is a single, comprehensive, and concise policy document that has replaced the Subject and Learning Area Statements, Learning Programme Guidelines, and Subject Assessment Guidelines for all the subjects listed in the National Curriculum Statement Grades R to 12.7 Students in Grade 9 during the 2014–2015 school year were taught according to this curriculum.

The mathematics curriculum for the General Education and Training Phase (Grades R to 9) consists of five sets of learning outcomes: Numbers, Operations, and Relationships; Patterns, Functions, and Algebra; Space and Shape (Geometry); Measurement; and Data Handling.8 Grade levels determine the focus of each learning outcome. The following is a summary of the learning outcomes and assessment standards that students are expected to have attained in mathematics in Grades R to 9.

  • Numbers, Operations, and Relationships―Students should be able to recognize, describe, and represent numbers and their relationships, and to count, estimate, calculate, and check with competence and confidence in solving problems
    • Foundation Phase (Grades R to 3)—Understand that there are different kinds of numbers, their relationships with one another, the relative sizes of numbers, multiple representations of numbers and meanings, and the effects of performing arithmetic operations on numbers; count reliably (forward and backward) in multiples of 1, 2, 5, 10, 20, 25, 50, and 100; know number names and symbols to 100, order and compare numbers using the words “more, less, and equal,” solve addition and subtraction problems with single-digit numbers orally, solve problems in groups, and explain solutions; represent even and odd numbers from zero to 10, recognize two-digit numbers and place values, do repeated addition with whole numbers, do mental calculations with numbers up to 20, and solve problems with numbers; compose, decompose, halve, and double numbers using concrete objects and number lines; recognize South African currency and solve currency problems; multiply two-digit numbers by single-digit numbers; and divide single-digit numbers by single-digit numbers
    • Intermediate Phase (Grades 4 to 6)—Represent numbers in multiple ways, including representations from different cultures (local and foreign) throughout history, in addition to all foundation phase concepts; recognize, represent, and know place value and compare whole numbers with at least nine digits (Grade 6); work with common fractions, equivalent fractions, and decimal fractions extending to two decimal places (Grade 6) and including measurements; demonstrate a sense of zero, additive inverse, and multiplicative inverse; know multiples of single-digit numbers to at least 100, including factors of three-digit numbers (Grade 6); recognize and use equivalent fractions, including common fractions with single-digit or two-digit denominators, decimal fractions to at least two decimal places, and percentages (Grade 6); perform mental calculations involving addition, subtraction, and multiplication (to 12×12); compose and decompose numbers mentally, and round, double, and halve numbers; use calculators; recognize the reciprocal relationship between multiplication and division, and divisibility rules for 2, 5, 10, 100, and 1,000 (Grade 6)
    • Senior Phase (Grades 7 to 9)—Count forward and backward in decimal intervals and in integers for any interval; describe and illustrate the historical and cultural development of numbers; recognize, classify, and represent integers, decimals, fractions, percentages, factors, prime factors, and numbers in exponential form in order to describe and compare them; recognize and use equivalent forms of rational numbers; solve problems in context including contexts that span areas of human rights, social, economic, and environmental issues, such as finances and measurement and technology; solve problems that include ratios and rates; estimate and calculate using appropriate operations; and perform mental calculations involving squares of natural numbers and exponents. (The above assessment standards are for the seventh and eighth grades.)
  • Patterns, Functions, and Algebra―Students are expected to recognize, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills
    • Foundation Phase (Grades R to 3)—Use physical objects and drawings to copy, extend, create, and describe geometric and numeric patterns; describe, identify, and copy observed patterns, including those from geometry, nature, and cultural artifacts; and use drawings to copy patterns (Grade 2) and extend number patterns from 100 to 200 (Grade 1) and to 1,000 (by Grade 3). (The expectations for the Foundation Phase (Grades R to 3) are based on laying a foundation for developing algebra skills.)
    • Intermediate Phase (Grades 4 to 6)—Study numeric and geometric patterns with a special focus on the relationships between terms in a sequence and between the number of the term and the term itself; investigate and extend numeric and geometric patterns represented in physical or diagram form, and not limited to sequences involving a constant difference or ratio, patterns found in natural and cultural contexts, and patterns of students’ own creation represented in tables (Grade 6); describe observed relationships and rules; determine output values from function rules; use tables to represent functions and flow charts to represent algorithms (Grade 6); write number sentences to describe problem situations representing social, economic, cultural, and environmental issues; solve or complete number sentences by inspection or trial and error and check solutions by substitution; and determine the equivalence of different descriptions of the same relationship or rule through verbal discussion, flow charts, number sentences, or tables (Grade 6)
    • Senior Phase (Grades 7 to 9)—Investigate and extend numeric and geometric patterns by investigating relationships, patterns, and rules represented in physical or diagrammatic form, not limited to sequences involving a constant difference or ratio, found in natural and cultural contexts or created by the students, or represented in tables or algebraically (Grade 8); describe, explain, and justify observed relationships, patterns, and rules; represent relationships between variables to determine input or output in multiple ways, including oral description, flow charts, and tables (Grade 8); use formulas and equations to represent functions; construct mathematical models to solve problems involving environmental issues, health issues, and issues in other contexts; complete number sentences using strategies such as inspection, trial and error, and substitution; use graphs to describe real world numerical situations and interpret situations from graphs; determine, analyze, and interpret the equivalence of different descriptions of the same relationship or rule using the most useful representation for a given situation; use algebraic vocabulary in context (e.g., term, expression, coefficient, exponent, base, constant, variable, equation, formula, or rule) (Grade 8); classify terms, multiply, divide, compare, simplify, and write algebraic expressions using conventions, commutative, associative, and distributive laws (Grade 8)
  • Space and Shape (Geometry)―Students should describe and represent characteristics and relationships between two-dimensional shapes and three-dimensional objects in a variety of orientations and positions
    • Foundation Phase (Grades R to 3)—Recognize, identify, name, describe, sort, compare, and build three-dimensional objects in their surrounding environment; recognize symmetry, and describe one three-dimensional object with respect to another and follow directions as individuals and within a group (Reception year); identify, describe, sort, and compare two-dimensional shapes and three-dimensional objects (Grade 1); and construct and explore two-dimensional and three-dimensional shapes and objects (Grades 2 to 3)
    • Intermediate Phase (Grades 4 to 6)—Recognize, visualize, name, describe, sort, and compare two-dimensional shapes and three-dimensional objects in the environment, according to their geometric properties; build or construct, draw, and investigate two-dimensional shapes and three-dimensional objects using drinking straws, cut-out polygons, graph paper, nets, and pairs of compasses; recognize and describe lines of symmetry in two-dimensional shapes; perform rotation, reflection, and translation of geometric figures and solids, and describe them using geometric vocabulary and properties; tessellate shapes and three-dimensional objects to make patterns, discover lines of symmetry, recognize, and describe natural and manmade two-dimensional shapes and three-dimensional objects; locate positions on a scaled grid and on maps; and recognize column-and-row structure
    • Senior Phase (Grades 7 to 9)—Identify similarities and differences among polyhedra and quadrilaterals; describe shapes in terms of sides, angles, and parallel and perpendicular sides; describe geometric figures in context, including faces, vertices, edges, sides, angles, and diagonals, with a focus on triangles and quadrilaterals; describe parallel lines cut by a transversal, perpendicular lines, intersecting lines, and triangles, with a focus on vertical angles and corresponding angles; use pairs of compasses, rulers, and protractors to construct geometric figures and investigate their properties, and create nets to make models of geometric solids; use transformations and symmetry to investigate properties of geometric figures; and locate positions using compass directions, ordered pairs, and slopes
  • Measurement―Students should be able to use appropriate measuring units, instruments, and formulas in a variety of contexts
    • Foundation Phase (Grades R to 3)—Describe time of day using vocabulary such as “early, late, morning, afternoon, and night,” read clock time in hours and minutes; order recurring events in daily life, comparing them using longer, shorter, faster, and slower as measurement units of events, sequence events within one day and extend the sequence to today, tomorrow, and yesterday; use appropriate vocabulary to describe mass, capacity, and length of concrete objects; estimate, measure, compare, and order objects using nonstandard measures; investigate distance, distance around, and area of two-dimensional shapes using strings and tiling
    • Intermediate Phase (Grades 4 to 6)—Read, tell, and write analog and digital 24-hour time to at least the nearest minute and second; solve time problems using time units, including time zones; use instruments to appropriate precision levels, including watches and stopwatches; illustrate and describe time in different cultures throughout history; estimate, measure, record, compare, and convert among appropriate units and order two-dimensional shapes and three-dimensional objects using the International System of Units (S.I. units) for mass, capacity, length, and temperature
    • Senior Phase (Grades 7 to 9)—Solve problems related to time, distance, speed, length, perimeter, area, and volume; estimate and calculate to two decimal places; convert among S.I. units; use appropriate formulas for perimeter and area of polygons and volumes of cylinders and prisms; and describe relationships between perimeter and area of geometric figures
  • Data Handling―Students learn to collect, summarize, display, and critically analyze data in order to draw conclusions, and interpret and determine chance variation
    • Foundation Phase (Grades R to 3)—Collect physical objects from the environment according to specified features, individually and within groups; sort and record collected objects as pictures or tallies, and respond to questions about the data (e.g., which is the least or most); construct pictographs and use stickers or stamps to represent individual elements in a collection of objects; describe collections of objects, explain the sorting scheme, and respond to questions about it; and use tables to present and interpret the lists of objects
    • Intermediate Phase (Grades 4 to 6)—Pose simple questions about the environment, school, and family, and identify appropriate data sources in order to address the questions; collect data individually and within a group; and organize and record data using tallies, tables, and graphs
    • Senior Phase (Grades 7 to 9)—Extend data collection to appropriate sources, use simple questionnaires to collect data, distinguish between samples and populations, and suggest appropriate samples for investigations; perform simple experiments using random samples, and organize and record data using tallies, tables, and stem-and-leaf plots; summarize grouped and ungrouped numerical data by measuring central tendency; and determine measures of dispersion, including range and extremes