Madison Country Day School has adopted the Singapore National Curriculum for its Mathematics Program.  The curriculum is internationally respected for turning out the best math students in the world according to the Third International Math and Science Study (TIMSS).  The philosophical approach of this program is to move all learners through very specific stages of math development.

Each topic is introduced from CONCRETE » PICTORIAL » ABSTRACT. Students are provided with the necessary learning experiences in the concrete and pictorial stages, followed by the introduction of algorithms in the abstract stage, to enable them to learn mathematics meaningfully.  The program encourages active thinking processes and flexible computation strategies.  Emphasis is given to the communication of mathematical ideas, problem solving, and mathematical investigations, while requiring mastery of basic computational skills in the early grades.

Program Goals

• To acquire the necessary skills and understanding of mathematics to ensure practical application
• To develop proficiency in the basic mathematical operations
• To encourage the vocabulary of mathematics in everyday life
• To develop problem solving skills
• To nurture a respect for and an independent approach to mathematical thinking

Program Curriculum
The Singapore math program continually reinforces the basic four operations while incorporating these skills into higher level mathematical problems. Assessment is frequent and thorough (quizzes and tests) and examines both the computation and problem-solving skills.  The School's carefully constructed, sequential mathematics curriculum is designed to prepare each student for calculus in the Upper School (ninth through twelfth grade).

Through practical activities, the mathematics curriculum helps students acquire the necessary skills and understanding in arithmetic, geometry, algebra, and data handling, and helps them learn to use these mathematical skills as tools in everyday situations. Emphasis is given to communication of mathematical ideas, problem solving, and mathematical investigation including:

Grade 5
Fifth grade mathematics uses the Singapore national curriculum. Guided by their understanding of place value, students practice whole number and decimal arithmetic. Arithmetic with fractions includes addition and subtraction of fractions of unlike denominators, the product of fractions, and division of a fraction by a whole number. In reducing fractions and computing their product, students learn to see a number as a product of its factors. Students work with ratio, percentage, average, rate, and line graphs. They apply the unique method of Singapore bar diagrams to word problems that play an essential role in each topic’s development. Students study the geometry of angles, the triangle, parallelogram, rhombus, trapezoid, cubes, and cuboids. They find the area of triangles and the volumes of cuboids.

Grade 6
Sixth grade mathematics uses the Singapore national curriculum. Students divide a fraction by a fraction. Working word problems, students apply the arithmetic learned in previous years to the study of ratio, proportion, percentage, and average speed. The challenge and subtlety of these problems gradually increases until students work complex problems involving speed and problems in which the ratio changes. Using the unique device of Singapore bars, students graphically represent these problems and their solutions in a way that ties the concrete work of their earliest mathematics to the symbolic mathematics of years to come. In geometry, students study the triangle, various quadrilaterals, and the circle. They apply basic principles about vertical angles and parallel lines to find unknown angles in figures composed of triangles and quadrilaterals. After learning to compute the area and circumference of a circle, students figure out the areas of regions composed of sectors of circles and other plane figures; they determine the length of curves consisting of parts of several circles. Students learn to find the volume of a cuboid, then work many problems including those in which a fluid is displaced by an irregular solid, and those in which a container is being drained or filled at a certain rate. This year emphasizes problem solving and critical thinking developed through written work and lively class discussion.

Grade 7
Study of the integers includes prime numbers, prime factorization, divisors, multiples, the divisor theorem, positive and negative integers, absolute value, and order. Students practice the basic principles of algebraic manipulation by solving equations of one unknown. Students learn about the coordinate plane. The idea of a function is informally introduced when direct and inverse variation are discussed in the context of word problems. Students work with functions represented by tables, graphs, and equations. The correspondence of a function’s algebraic and graphic representations is emphasized. Geometry includes the straight line, Euclidean constructions, the circle, sectors, chords, and arc length; relations between straight lines and planes, polyhedra, solids of revolution, surface area and volume of pyramids, cones, and spheres.

Grade 8
Students learn about polynomials including combining like terms and finding the product and quotient of a monomial and polynomial. They solve linear inequalities, simultaneous linear inequalities, and pairs of simultaneous equations. Students consider the linear function in the coordinate plane. The correspondence of the line’s algebraic and graphic representations is emphasized. Students practice finding the equation of a line, given two points or given a point and a slope; they write the equation of the line through a specific point and parallel or perpendicular to a given line. In geometry, students continue their study from previous years of angles, parallel lines, triangles, and parallelograms, though they now prove the theorems that they use. Congruence and similarity, particularly of triangles, is a principal area of study and students create many proofs that depend on demonstrating that a pair of triangles is congruent or similar.