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The Mathematics Curriculum in Primary and Lower Secondary Grades

Mathematics is one of the areas of knowledge that is taught in all six years of primary education (Grades 1 to 6) as well as all four years of compulsory secondary education (Grades 7 to 10). Mathematics is essential not only for the acquisition of knowledge that is useful in everyday life, but also for its role in the development of certain cognitive abilities.

At the primary level, mathematics learning must be essentially experiential; that is, instruction must contextualize the content in situations familiar to students, with a problem solving perspective that provides practical application. Problem solving is one of the basic features of the mathematics curriculum because it contributes to the acquisition of basic skills such as reading for comprehension, reflecting, establishing a working plan and modifying it if necessary, verifying the found solution, and communicating the results.

The mathematics curriculum incorporates spiral learning. It is organized into four blocks whose topics are covered throughout Grades 1 to 6: Numbers and Operations; Measurement; Geometry; and Information Processing, Chance, and Probability. The following summary relates both the topics students learn in each block of primary school and the skills they are expected to have acquired and practiced in problem solving contexts by the end of fourth grade:

  • Numbers and Operations
    • Topics—By the end of Grade 4, students should be familiar with the decimal number system; the meaning of operations; computations using standard algorithms and mental computation procedures; and estimation and determination of the most appropriate method of calculation for each estimate.
    • Skills—By the end of Grade 4, students should be able to read and write whole numbers up to six figures, know how to compare and order them, and be familiar with the structure of the decimal number system. They should have mastered the standard algorithms of multiplication and division (one-digit divisor) and be able to make reasonable estimates. Moreover, students should know the meaning of a fraction as part of a whole and be able to compare simple fractions.
  • Measurement
    • Topics—By the end of Grade 4, students should be familiar with estimation and calculation of magnitudes; familiarity with units of measurement and their equivalents; and selection of the most appropriate units and instruments to make reasonable estimates of measurements in the everyday environment.
    • Skills—By the end of Grade 4, students should know how to use the most common metric units of measurement of length, mass, and volume. They should be able to use the most common measurement instruments to estimate distance and measure familiar objects. In addition, students should know how to read and tell time (using both analog and digital watches or clocks) and manage the basic units of time. Finally, students should have begun to learn how to measure surface area by covering surfaces with geometric shapes (e.g., squares, rectangles) and nonstandard units (e.g., tiles).
  • Geometry
    • Topics—By the end of Grade 4, students should have acquired knowledge of geometric shapes and figures, and be able to use geometric knowledge to develop the ability to think, reason, and construct (e.g., build, draw, and model).
    • Skills—By the end of Grade 4, students should be able to identify and describe elementary geometric representations (e.g., planes and models), and have been introduced to types of angles, perpendicular and parallel lines, circles, and polygons up to six sides. Students should have begun to identify and classify two-dimensional shapes and three-dimensional figures according to their elements (e.g., sides, faces, and vertices), as well as to recognize these shapes and figures in everyday life.
  • Information Processing, Chance, and Probability
    • Topics—By the end of Grade 4, students should have developed understanding of information provided by the media; skills in presentation and organization of data using charts and graphs; and critical awareness about the use of information.
    • Skills—By the end of Grade 4, students should be able to collect and process basic data from everyday life, sort them into tables, display them in graphs (e.g., bar graphs, pictograms), and interpret tables and graphs relating to everyday phenomena. Students also will have been introduced to the language of chance and the random nature of some experiences.

In addition to these concepts and skills, the Grade 4 mathematics curriculum also covers attitudes such as the following: valuing a clear and orderly presentation of calculations, tables, and graphics; persevering in the search for solutions; having confidence in one’s own abilities to develop mental calculation strategies and make reasonable estimates; and explaining one’s problem solving process.

In compulsory secondary education, students follow a common mathematics curriculum in Grades 7 to 9. However, because they have different interest levels, motivation, and learning styles, students can choose between two curriculum options in Grade 10: Mathematics A and Mathematics B. Mathematics A focuses on more basic operational and practical subject knowledge, while Mathematics B focuses on deeper mathematical knowledge and requires a greater use of abstract symbolism, rigorous reasoning, and formal representations.

The compulsory secondary education mathematics curriculum is organized into six blocks whose topics are covered throughout Grades 7 to 10: Common Contents, Numbers, Algebra, Geometry, Functions and Graphs, and Statistics and Probability. The following relates the topics students learn in each block of compulsory secondary school and the skills they are expected to have acquired by the end of eighth grade:

  • Common Contents
    • Topics—By the end of Grade 8, students will have studied cross-curricular content in all areas, such as problem solving strategies, and attitudes such as persevering in the search for solutions and assessing completed work; and use of technological tools (e.g., calculators and computers) to facilitate calculations, representations, and geometric properties.
    • Skills—By the end of Grade 8, students will have studied problem solving strategies, and they should have become familiar with the analysis of problem statements, trial and error, splitting problems into parts, and testing obtained solutions.
  • Numbers
    • Topics—By the end of Grade 8, students will have studied numeracy concepts that began at the primary level extended to include all real numbers (e.g., integers, rational numbers, and irrational numbers) and new operations such as exponents (e.g., powers and roots) and logarithms; understanding of operations and practice using estimation skills and mental computation to control for possible errors in results; and numerical proportion.
    • Skills—By the end of Grade 8, students will have studied whole numbers, fractions and decimals, how to calculate percentages, increasing and decreasing powers of natural exponents and their operations, and scientific notation. Students also will have covered the use of the sexagesimal system for measuring time and angles. Their study of proportionality will have extended to inverse proportions.
  • Algebra
    • Topics—By the end of Grade 8, students will have studied yhe use of algebraic language (e.g., polynomials and equations).
    • Skills—By the end of Grade 8, students will have learned about first-degree binomials and should know how to solve linear equations and use linear equations to solve problems.
  • Geometry
    • Topics—By the end of Grade 8, students will have studied calculation of surface area and volume; description of geometric figures; and analysis, classification, and relationships between elements of geometric figures.
    • Skills—By the end of Grade 8, in plane geometry students will have studied the Pythagorean theorem, similarity (e.g., similarity ratio and scales), and Thales’ theorem. In solid geometry, students will have studied the basic elements: points, lines and planes, the relationships between them (e.g., incidence, parallelism, and perpendicularity between straight lines and planes), geometric figures, and the calculation of surface areas and volumes.
  • Functions and Graphs
    • Topics—By the end of Grade 8, students will have studied different types of functions (e.g., constant, linear and related, quadratic, exponential, and logarithmic) and their characteristics, with an emphasis on graphs (e.g., points of intersection with the axis, growth and decay, continuity, and symmetry).
    • Skills—By the end of Grade 8, students will have studied the characteristics of a function and its graph, as well as linear and inverse proportionality functions. Students also will have begun to use a graphing calculator and computer applications for drawing function graphs.
  • Statistics and Probability
    • Statistics topics—By the end of Grade 8, students will have studied basic concepts such as population, sample, discrete and continuous variable, organization of data in frequency tables and statistical graphs, and calculation of central tendency and dispersion measures to prepare students for critical analysis of statistical information.
    • Probability topics—By the end of Grade 8, students will have studied simple and compound probability, including randomized experiments, the assignment of probabilities by Laplace’s law, contingency tables, and tree diagrams. In Grade 10, Mathematics B topics also include combinatorics, applications to the calculation of probability, and conditional probability.
    • Skills—By the end of Grade 8, students will have studied various elements of statistics: absolute, relative, and cumulative frequency tables; statistical diagrams, including pictograms, population pyramids, and climate diagrams; and calculation of the mean, median, and mode. Students also should have learned how to use spreadsheets to organize data, perform calculations, and create graphs.