The Mathematics Curriculum in Primary and Lower Secondary Grades
The State Mandatory Standards of Education define the goals and objectives for mathematics education at the primary, basic secondary, and general secondary levels.9
Mathematics content and skill objectives for students in primary (Grades 1 to 4) and basic secondary (Grades 5 to 9) education are summarized as follows:
- Grades 1 to 4—Students develop number sense through counting and measurement and learn the principles of writing numbers; learn to perform arithmetic operations with numbers verbally and in writing, solving for unknowns; write and solve numerical expressions using rules of calculation; gain experience with solving arithmetic problems; gain familiarity with simple geometric shapes, values, and methods of calculation; learn arithmetic methods for solving word problems; learn methods of theoretical and practical problem solving that use mathematics; and learn to work with the algorithms of the arithmetic operations.
- Grades 5 to 6—Students develop familiarity with rational numbers and their properties, arithmetic operations with rational numbers, and common and decimal fractions; develop the ability to solve equations using their knowledge of arithmetic operations; learn to calculate using formulas; learn to solve problems involving proportion; learn to solve equations using the commutative and associative properties of addition; learn to solve linear inequalities with one variable; learn to solve simple one-variable equations and inequalities containing absolute value; learn to locate and plot points by their coordinates on coordinate axes and the coordinate plane; develop familiarity with the concept of functions and their properties (e.g., area and slope); learn to graph linear functions; learn to solve systems of linear equations with two variables; and develop familiarity with planes, balls, and spheres.
- Grades 7 to 9:
- Algebra—Students learn how to perform arithmetic operations with polynomials, factor polynomials, use formulas of abridged multiplication, perform operations on rational expressions, perform substitutions on rational equations, demonstrate that alternate forms of equations are identical, find absolute and relative error, learn to use substitution in solving equations containing square roots, quadratic equations, and rational equations, learn to solve quadratic inequalities using graphs of quadratic functions, and learn to solve rational inequalities using intervals.
- Geometry—Students develop familiarity with geometric shapes, including quantitative and qualitative relationships between components of one or several geometric shapes; develop deductive reasoning skills (direct proof, proof by contradiction), simple drawing and measurement skills, and the ability to imagine real objects in the form of one or several geometric shapes; expand and systematize theoretical knowledge of properties of plane figures; form and develop abilities and skills in solving geometric problems involving calculation, measurement, proof, and construction; expand abilities and skills in recognizing geometric shapes in drawings of different levels of complexity, using additional constructions and auxiliary drawings to solve problems; form and develop the ability to create images of plane figures using transformations and to solve geometric problems using algebraic methods; develop familiarity with space and spatial figures; develop familiarity with images of spatial figures and their components.
Basic mathematics programs typically include the following conceptual topics:10
- Numbers and Computation—Natural numbers, common and decimal fractions, percent and proportion, whole numbers, rational numbers, the concept of irrational numbers, real numbers, order of operations, exponents, finding roots, logarithms; sine, cosine, and tangent; and approximation and estimation
- Mathematical Expressions and Transformations—Variables, letter and number expressions, and identities and their use in the transformation of expressions; algebraic expressions (monomial terms, polynomial functions, and fractions) and arithmetic operations with integer and fractional algebraic expressions; and exponential, logarithmic, and trigonometric expressions
- Equations and Inequalities—Proofs of identity and inequality expressions; equivalence in equations and inequalities; identifying domains of equations and inequalities; equations and inequalities with one and two unknowns and their geometric interpretations; rational inequalities; systems of equations and inequalities; and general solution methods for equations and inequalities
- Functions—Numerical and elementary functions, and their properties and graphs; derivatives and anti-derivatives; integrals; and arithmetic and geometric progressions
- Geometric Figures and Measuring Geometric Variables—Geometric figures and their properties (points, segments, rays, straight lines, planes, subspaces, angles, polygons, circumference and circles, polyhedra, and solids of revolution); geometric relationships (transverse, intersection, tangency, parallelism, perpendicularity, equality, correspondence, and symmetry); geometric values (length of lines, value of angles, area, and volume); vectors and coordinates; and using analytical tools in geometry
- Elements of Probability Theory and Statistics—Ways of presenting statistical data (tables, diagrams, and histograms), calculation of descriptive statistics (mode, median, average, range, and standard deviation), graphs of real processes, calculation of variance, systematic enumeration, permutation, combinations, and geometric models of probability