The Mathematics Curriculum in Primary and Lower Secondary Grades
A brief overview of the mathematics curriculum for Grades 1 to 10 follows.
The first sentence of the curriculum states, “Mathematics is part of our global cultural heritage.”8 After presenting mathematics as a possible source of joy, the curriculum emphasizes the broad range of mathematics applications and utilities. It goes on to introduce certain concrete and practical as well as abstract and theoretical aspects of mathematics, which have an essential place in the teaching and learning of the subject.
The mathematics curriculum is organized under subject domains. The domains for Grades 1 to 4 are Numbers, Geometry, Measuring, and Statistics. The domains for Grades 5 to 7 are Numbers and Algebra, Geometry, Measuring, and Statistics and Probability. The domains for Grades 8 to 10 are Numbers and Algebra; Geometry; Measuring; Statistics, Probability, and Combinatorics; and Functions.
The curriculum defines five basic areas of skill across all subjects and at all grade levels. For mathematics, these skill areas include the following:
- Oral skills—Creating meaning by listening, asking, speaking, reasoning, and discussing mathematics; developing communication skills, progressing from simple, informal language toward precise terminology and unambiguous conceptual language
- Writing skills—Expressing discoveries, ideas, lines of thought, and solutions; making suitable sketches, drawings, tables, graphs, and diagrams; and developing the ability to use formal, symbolic language and to formulate comprehensive arguments about complex relationships
- Reading skills—Understanding texts containing mathematical expressions, graphs, diagrams, tables, symbols, formulas, and logical reasoning; and understanding complex texts with advanced symbolic language and concepts
- Numeracy—Applying symbolic language, mathematical concepts, and a variety of strategies in problem solving and investigations in practical, everyday situations and in pure mathematical contexts; recognizing mathematical aspects of situations and problems, analyzing them, and evaluating the validity of solutions; progressing from a basic understanding of numbers toward analyzing and solving complex problems using a variety of strategies and methods; and learning to use various tools more in calculations, modeling, and communication
- Digital skills—Applying digital tools to calculation, investigation, visualization, simulation, modeling, and presentation; and critically evaluating sources, analyses, results, and utilities
Exhibit 1 presents a summary of the competencies that students are expected to attain in mathematics in Grades 1 to 4, Grades 5 to 7, and Grades 8 to 10, respectively. As a general indication, it might be expected that the most elementary third of the goals for Grades 5 to 7 should be attained in Grade 5, and that one-third and two-thirds of the goals for Grades 8 to 10 should be attained in Grade 8 and Grade 9, respectively.
Exhibit 1: Expected Competencies in Mathematics, Grades 1–10 (Abbreviated) 9
| Grade Range | Subject Domain | Expected Competencies |
| Grades 1–4 | Numbers | Use the number line, describe and use the place-value system for integers, and use positive and negative integers, simple fractions, and decimal numbers in practical contexts; estimate both mentally and on paper; develop and use different methods for addition, subtraction, multiplication, and division mentally and on paper, and apply them in practical contexts; find information in texts or practical situations, choose an arithmetic operation and provide a rationale for the choice, exploit relations between arithmetic operations, assess results, and present solutions; recognize, experiment with, describe, and develop simple number patterns; use mathematical symbols and expressions in problem solving |
| Geometry | Recognize, sort, and describe characteristics of geometric figures; recognize and use mirror symmetry and translation in practical situations; make, explore, and describe geometric patterns, with and without digital tools; read, place, and describe positions in grids, on maps, and in coordinate systems with and without digital tools | |
| Measuring | Estimate and measure length, area, volume, mass, temperature, time, and angles, and assess whether the results are reasonable; compare magnitude and convert units; solve practical tasks that involve buying and selling | |
| Statistics | Collect, sort, record, illustrate, and comment on data using tallies, tables, and bar charts with or without digital tools, and discuss the results | |
| Grades 5–7 | Numbers and algebra | Calculate with positive and negative integers, decimal numbers, fractions, and percentages; find common denominators; use a spreadsheet for simple calculations and presentations; justify solution methods; explore and describe structures and changes in numerical and geometrical patterns using figures, words, and formulas; formulate and solve simple equations; and simplify expressions with parentheses, addition, subtraction, and multiplication of numbers |
| Geometry | Analyze characteristics of two- and three-dimensional figures, build three-dimensional models, and draw simple three-dimensional figures in perspective; describe and perform reflection, rotation, and translation; describe position and movement in a coordinate system; and calculate distances parallel to the coordinate axes |
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| Measuring | Select suitable measurement tools, choose suitable units, and convert between units; explain the structure of measurements of length, area, and volume and calculate circumference, area, surface area, and volume of simple two- and three-dimensional figures; use a scale to calculate distances from a map and to make a scale drawing; use ratios in practical situations; calculate velocity; and convert currencies | |
| Statistics and probability | Collect data from observations, questionnaires, and experiments; represent data in tables and graphs digitally and manually; read, interpret, and assess data; find median, mode, and average for simple data sets, and assess them in relation to each other; assess and discuss probability in everyday contexts, games, and experiments; calculate probability in simple situations | |
| Grades 8–10 | Numbers and algebra | Compare and convert between integers, decimal numbers, fractions, percentages, and numbers in standard form, and assess the suitability of different representations in various situations; divide and reduce fractions; use factors, powers, square roots, and prime numbers in calculations; factor and simplify algebraic expressions, and relate such expressions to practical situations; manipulate formulas, parentheses, and simple rational expressions; solve linear equations and inequalities and simple systems of equations with two unknowns, and apply this to solve practical and theoretical problems; do calculations about consumption, use of credit cards, income, loans, and savings, and set up budgets and accounts using a spreadsheet; analyze complex problems, identify fixed and variable quantities, carry out calculations, and present the results in a suitable manner; use numbers and variables in investigation, experimentation, practical and theoretical problem solving, and technology and design projects |
| Geometry | Investigate and describe characteristics of two- and three-dimensional figures, and use them for constructions and calculations; carry out, describe, and explain constructions with a compass and a ruler, and with a dynamic geometry program; use and explain the use of congruence and the Pythagorean theorem to calculate unknown lengths and angles; make and interpret scale drawings and perspective drawings; use coordinates to represent and investigate geometric figures; formulate logical reasoning about geometrical ideas | |
| Measuring | Discuss precision and uncertainty of measurements; account for the number π, and use it in calculations of circumference, area, and volume | |
| Statistics, probability, and combinatorics | Carry out investigations and use databases to search for and analyze statistical data and demonstrate critical assessment of data sources; order and group data; find and discuss median, mode, average, and range; present data with and without digital tools, and discuss different ways of presenting data; find and discuss probabilities through experimentation, simulations, and calculations in everyday contexts and in games; describe sample spaces and represent probabilities as fractions, percentages, and decimal numbers; discuss and solve simple combinatorial problems | |
| Functions | Construct functions that describe numerical relationships and practical situations, with and without digital tools, describe and interpret the functions, and convert between various representations of functions, such as graphs, tables, formulas, and text; identify and apply properties of proportional, inversely proportional, linear, and quadratic functions, and provide examples of practical situations that may be described by these functions |