Botswana

The Mathematics Curriculum in Primary and Lower Secondary Grades

The mathematics syllabus in the primary grades is divided into a lower primary syllabus⁹ (Grades 1 to 4) and an upper primary syllabus¹⁰ (Grades 5 to 7). In Grade 4, students take national achievement tests in three subjects, including mathematics.

The lower primary school mathematics syllabus (Grades 1 to 4) is organized around modules, which are divided into topics and then subdivided into general and specific objectives. The specific objectives outline the breadth and depth of teaching required in a particular topic. Five modules are covered in the lower primary syllabus:

• Numbers and Operations—This module helps students understand the concept and use of numbers. Students practice counting, sorting, and classifying numbers, as well as matching objects and numbers. These concepts lay a foundation for addition and subtraction. By the end of Grade 4, students should be able to add and subtract three-digit numbers vertically and horizontally. They should be able to multiply using one-digit to three-digit numbers and do simple division. Students also should understand money, local currency denominations, and monetary units and be able to add, subtract, multiply, and divide with money.
• Geometry—Students are introduced to geometry with the study of shapes and solids. Students identify shapes such as rectangles and triangles, and solids such as cubes and cylinders. By the end of Grade 4, students should be able to describe shapes by the number of sides and number of angles and be able to name solids.
• Measures—The intention of this module is to develop measuring skills. Students start by comparing lengths and weights in Grade 1, and gradually begin using standard measuring instruments. By the end of Grade 4, students should be able to use formulas to calculate area and perimeter. They should be able to use instruments to measure volume and mass, and to convert units of length, time, and mass.
• Problem Solving—This module introduces students to practical problem solving skills. Skills are developed through mathematical games, simple puzzles, and simple investigations involving numbers and shapes. By the end of Grade 4, students should be able to conduct simple research projects.
• Statistics—This module introduces simple methods of data collection and simple statistical presentations, such as pictographs. By the end of Grade 4, students should be able to interpret information and draw simple statistical conclusions, such as finding the mode.

The upper primary mathematics syllabus (Grades 5 to 7) is designed to help students develop further numeracy and computational skills as well as problem solving skills. The upper primary syllabus covers the same five modules covered in the lower primary grades:

• Numbers and Operations—The aim of this module is to teach students to read whole numbers up to 10,000 and write these numbers in words. By the end of upper primary school, students should be able to apply the basic arithmetic operations (addition, subtraction, multiplication, and division) in the correct order when working with whole numbers, fractions, and decimals and be able to use percentages to increase, decrease, and compare quantities.
• Geometry—In this module, students learn to name two- and three-dimensional geometric shapes and recognize their properties. Students differentiate straight lines from curves and use rulers, compasses, and squares to draw perpendicular and parallel lines, angles, and shapes. They work with Cartesian coordinates in the first quadrant and carry out simple transformations (translations, reflections, and enlargements).
• Measures—The curriculum is designed to help students appreciate measurement, use measuring devices, and estimate quantities. Students use instruments to measure length and determine the perimeter of regular and irregular shapes. Students calculate the area of shapes and the volume of objects, and they measure the volume of various objects using displacement methods.
• Algebra—Students are introduced to algebra as a method of communicating mathematics through symbols. Students generate number patterns and complete arithmetic sequences, replace missing numbers in boxes that later are represented by letters, simplify linear expressions, and translate simple statements into algebraic expressions and equations. By the end of Grade 7, students should be able to solve equations of the form ax+by=c through systematic trial and error using whole numbers. They also should be able to use substitution to evaluate simple expressions.
• Statistics—This module helps students develop skills in collecting, organizing, and analyzing data, as well as understanding the basic concepts of probability. Students should be able to read and interpret data; collect and organize data by tabulation; draw pictographs, charts, and other graphs; and find the mode, median, and mean. Students are expected to know the meaning of probability and be able to describe probability in terms such as “likely,” “unlikely,” “never,” and “certain.” Students should be able to explore the likelihood that an event may occur through simple games and experiments.

When students complete Grade 7, they proceed to Grade 8 and begin studying toward the Junior Certificate Examinations (JCE). At the end of the JCE curriculum, students should be able to apply computational skills in everyday life for commercial and social purposes.

The JCE, or lower secondary school mathematics syllabus¹¹ (Grades 8 to 10), has the same organizational structure as the primary school syllabus. Generally, lower secondary school extends primary school learning and students are expected to begin applying concepts to solving practical problems. The following topics are covered in the lower secondary school mathematics syllabus:

• Numbers—Students apply arithmetic operations (addition, subtraction, multiplication, and division) to whole numbers, decimals, fractions, and integers; solve problems involving percentages, money, ratio, and proportion; approximate and estimate using significant figures and round numbers to specified accuracies; square, cube, and find square and cube roots of real numbers, including fractions; derive laws of exponents by investigation and apply laws of integer exponents in problem solving; solve problems using numbers in scientific notation; understand simple money and non-money bank transactions; calculate labor costs, material costs, and overhead costs of basic projects; understand and solve problems involving insurance policies, simple interest, contracts, income tax, and duty charges; and add and subtract matrices and multiply matrices by scalars
• Measures—Students investigate the relationship between the circumference of a circle, the related diameter, and π (pi); calculate the length of arcs and the perimeter and area of composite shapes, as well as the volume of cubes, cuboids, and cylinders, including composite cross sections; solve problems that involve time, distance, and speed, and use and interpret distance-time graphs; and calculate speed in kilometers per hour, meters per second, and other metric units
• Algebra—Students simplify linear expressions and use substitution to solve equations for one variable; expand and factor binomial expressions of the form (a±b)² and factor expressions of the form ax³±bx²±cx±d; use graphical methods to solve simultaneous equations; and solve linear simultaneous equations in two unknowns by Gaussian elimination and by substitution
• Geometry—Students construct geometrical elements, such as line segments, parallel lines, perpendicular lines, and angle and perpendicular bisectors; construct triangles and quadrilaterals; understand and use properties of angles to solve problems and calculate unknown angles using angle properties, such as corresponding angles, alternate angles, interior angles, and complementary and supplementary angles; describe line and rotational symmetries, and solve problems involving angle properties of triangles and quadrilaterals; plot points in all four quadrants of the Cartesian plane and join them to form shapes; and draw graphs of functions of the form y=mx+c and y=ax²+bx+c
• Statistics and Probability—Students collect, process, and tabulate grouped and ungrouped data; use grouped and ungrouped data to draw and interpret bar graphs, pie charts, and line graphs; calculate and interpret the mean, median, and mode of ungrouped data; interpret scatterplots for given data or situations using the line of best fit; interpret basic concepts of probability; distinguish theoretical probability from experimental probability; and calculate probabilities of single events for up to 12 outcomes