Togo Collège (Lower Secondary) Subjects - Mathematics

The Togolese lower secondary mathematics curriculum, following the HPM (Harmonisation du Programme de Mathématiques) framework, aims to improve the quality of mathematics education and make it accessible to more students. The curriculum emphasizes active pedagogical methods that promote knowledge transfer and concrete experiences, helping students refine their vocation and orientation. It prioritizes a pedagogy of animation that contributes to students' intellectual development, enabling them to understand and adapt to the world around them.

The following outlines the yearly plan for each grade level:

Sixième (Grade 6)

First Trimester:

• Geometry: Lines in the plane (points, intersecting lines, perpendicular lines, parallel lines, half-lines); Segments (measuring segments, midpoint of a segment, perpendicular bisector of a segment); Angles (measuring angles, constructing angles, angle bisector).
• Numeracy: Arithmetic (natural numbers, multiples and divisors, divisibility rules); Arithmetic decimal numbers (comparing decimals, operations with decimals); Calculation program (order of operations, introduction to literal calculation).

Second Trimester:

• Geometry: Circle (radius, diameter, chord, arc, circumference, area of a disc); Triangle (vocabulary, constructing triangles, special triangles, altitudes, perimeter, area); Symmetric figures with respect to a point (symmetric points, properties of symmetric figures, figures with a center of symmetry); Parallelogram (definition, properties, rhombus, rectangle, square, perimeter, area); Symmetric figures with respect to a line (symmetric figures, construction, properties of symmetric figures, figures with a center of symmetry).
• Numeracy: Division (division of natural numbers, calculations with powers of 10, division of decimals); Fractions (different forms of fractions, operations with fractions); Organizing data (proportionality, proportionality tables, coefficient of proportionality, scales).

Third Trimester:

• Geometry: Rectangular prism and right cylinder, cube (observation and description, net, position of edges and faces, volume and area); Cylinder (observation and description, net, volume and area).
• Numeracy: Relative decimal numbers (introduction to sets, sum of relative integers, sum of relative decimals).

Cinquième (Grade 7)

First Trimester:

• Geometry: Distance between two points (properties of distance, perpendicular bisector of a segment, dividing the plane with a perpendicular bisector); Angles (complementary angles, supplementary angles, vertical angles, angles formed by two parallel lines and a secant); Symmetric figures with respect to a line and a point (using properties of conservation, constructing symmetric figures).
• Numeracy: Relative decimal numbers (representation, number line, opposites, comparison); Operations with relative decimal numbers (addition, subtraction, algebraic sum, equations); Powers (powers of relative decimals, calculations with powers).

Second Trimester:

• Geometry: Triangles (characterizing special triangles, constructing angle bisectors with ruler and compass); Circles (regions of a plane, interior and exterior of a circle, circumscribed circle of a right triangle); Quadrilaterals (parallelogram, rectangle, rhombus, square, trapezoid); Regular polygons (definition, equilateral triangle, hexagon).
• Numeracy: Division (Euclidean division, prime numbers, least common multiple); Fractions (simplifying fractions, greatest common divisor, addition and subtraction, comparison); Proportionality (coefficient of proportionality, speed, flow rate, density, scale, percentage, graphical representation).

Third Trimester:

• Geometry: Regular polygons (square, octagon); Right prism (description, vocabulary, properties, net, volume, area).
• Numeracy: Revisions.

Quatrième (Grade 8)

First Trimester:

• Geometry: Problem-solving (proofs, constructions); Orthogonal and central symmetries (concept of application, properties of symmetries); Distance (distance from a point to a line, distance between two parallel lines, characterization of angle bisector, circles and lines, tangent).
• Numeracy: Calculations with algebraic expressions (sums, products, powers, literal calculation, expanding and simplifying, notable products, factorization); Decimal numbers (powers of 10, scientific notation); Rational numbers (fractions, least common multiple, greatest common divisor, operations with rational numbers, approximating rational numbers).

Second Trimester:

• Geometry: Right triangle (Pythagorean theorem, metric properties); Translations - Vectors (translations, vectors, vector addition, characterizing the midpoint of a segment, vector characterization of translation); Projection - Coordinates (projection, coordinates on a number line, coordinates in the plane).
• Numeracy: Equations and inequalities (equations of the first degree, inequalities of the first degree, problem-solving); Proportionality (situations of proportionality).

Third Trimester:

• Geometry: Angles (central angle, chords and arcs of a circle); Cavalier perspective (representing objects in space, representing solids, sphere).
• Numeracy: Lines and planes in space (lines and planes, relative positions of lines and planes, relative positions of two planes, relative positions of two lines); Statistics (organizing data, mean, diagrams).

Troisième (Grade 9)

First Trimester:

• Geometry: Thales' theorem (direct and reciprocal theorem, applications); Right triangle (calculations in a right triangle, trigonometry, using trigonometric tables and calculators); Vectors (product of a vector by a real number, vectors and configurations, collinear vectors, orthogonal vectors).
• Numeracy: Literal calculation (quotients, powers with relative integer exponents, expanding and simplifying, notable identities, factorization, monomials, polynomials, rational fractions); Square root; Real numbers (square root, comparing real numbers, operations with radicals); Numerical calculation (absolute value, inequalities, intervals, comparing real numbers, approximating real numbers).

Second Trimester:

• Geometry: Coordinates of a vector (definition, coordinates of a sum of vectors, coordinates of a product of a vector by a real number, collinear vectors, orthogonal vectors, calculations in a coordinate system); Equations of lines (Cartesian equation of a line, coordinates of a direction vector, slope, relative positions of two lines); Inscribed angles in a circle (definition and vocabulary, measure of an inscribed angle, inscribed angles intercepting the same arc); Regular polygon (definition, inscribed regular polygon); Symmetries and translations (orthogonal symmetries, central symmetries, translations, using symmetries and translations for proofs and constructions).
• Numeracy: Equations and inequalities (equations of the first degree, systems of equations, inequalities of the first degree, systems of inequalities); Equations and inequalities with absolute value; Affine applications (concept of affine application, graphical representation, sense of variation, linear applications, examples of affine applications).

Third Trimester:

• Geometry: Homothety (definitions, properties, image of simple figures); Pyramids and cones (observation and description, vocabulary and properties, regular pyramid, net, volume and area, sections of a pyramid, frustum of a pyramid, cone of revolution, sections of a cone, frustum of a cone).
• Numeracy: Statistics (grouping into classes, histograms).