Mathematics

The Kumon mathematics programme was the first one written by the Founder, Mr Toru Kumon, himself a high school maths teacher.

Although the programme has been considerably refined over the years, it still retains the same clear linear structure and overall objectives that have made it Kumon's most popular programme. In short, students develop advanced calculation ability progressing from counting to calculus.

Carefully organised to systemically train students' logical-thinking ability, the worksheets include a variety of curriculum, from simple line drawing, primary level simple equations, to secondary school levels factorisation, calculus, functions, and other advanced mathematics.

The ease with which Kumon students routinely learn to perform basic operations and solve problems is perhaps the most dramatic testament to the effectiveness of the Kumon Method.

Programme Samples

Worksheet Level Outline

7A Preparation Students read and recite numbers up to ten and recognise patterns of up to ten dots without counting. Example 1

6A Preparation Students read and recite numbers up to 30 and recognise patterns of up to twenty dots without counting. Example 1

5A Preparation Students improve writing skills by developing the skill of correct writing pressure, writing ability, work skills and concentration power; become proficient at reciting numbers up to 30. Example 1

4A Preparation Students learn number writing, dot counting, the sequence of numbers from 1 – 20 (and how to write numbers up to 120); develop number sense and work skills. Example 1

3A Arithmetic Students use the reciting and number writing skills developed in the previous level to master +1 to +5. Example 1

2A Arithmetic Students use their adding skills developed in the previous level to master +6 to +10; study basic subtraction from numbers up to 10. Example 1

A Arithmetic Students use the skills developed in the previous level to improve their mental addition and subtraction skills to produce instant answers. Example 1

B Arithmetic Students use the mental addition and subtraction abilities developed in Level A to acquire skills in vertical addition and subtraction. Example 1

C Arithmetic Students use the abilities developed in Level B to acquire the fundamental multiplication and division skills required for Level D. Example 1

D Arithmetic Students further develop the multiplication and division skills they acquired in Level C; learn to divide by 2-digit numbers; become familiar with fractions in order to gain skills necessary for Level E. Example 1

E Arithmetic Students acquire the ability to perform the four operations with fractions in order to gain the skills necessary for Level F. Example 1

F Arithmetic Students further develop the computational skills with fractions acquired in Level C to smoothly calculate the mixed four operations in order to consolidate the general arithmetical skills. Example 1

G Algebra Students develop their skills in working with introductory algebra, e.g. operations with positive and negative numbers; simplifying algebraic expressions and solving linear equations in one variable. Example 1

H Algebra Students operate algebraic expressions and solve equations by learning literal equations and simultaneous linear equations, inequalities, linear functions and operations with monomials and polynomials. Example 1

I Algebra Students master operations mainly with quadratic polynomials, equations and functions, e.g. multiplication of polynomials, factorisation, calculation with square roots, quadratic equations, quadratic functions and the Pythagorean Theorem. Example 1

J Analysis Students develop their ability to work with algebraic expressions, factorisations, irrational numbers, quadratic equations, simultaneous equations, the Remainder Theorem, the Factor Theorem and the proof of identities and inequalities. Example 1

K Analysis Students acquire knowledge of the basic properties of functions through a thorough study of quadratic functions; apply these skills while working with higher degree, fractional, irrational and exponential functions and graphs. Example 1

L Analysis Students learn to calculate and manipulate logarithms, graph logarithmic functions and solve logarithmic equations and inequalities; learn the beginning of calculus, studying basic differentiation and integration; strengthen skills in graphing functions, obtaining relative maxima and relative minima and maxima and minima, solving equations and inequalities and analysing applications of integration. Example 1

M Analysis Students develop an ability to work with trigonometric functions and equations of straight lines and circles. Example 1

N Analysis Students develop an ability to work with loci, quadratic inequalities, sequences, series, limits and differentiation. Example 1

O Analysis Students develop an ability to work with advanced differentiation, applications of differential calculus, indefinite and definite integrals, and differential equations. Example 1

Other Kumon programmes include English and Japanese.