The Kumon Maths Programme

Levels 3A to D deepen number sequence understanding before introducing the main operations of addition, subtraction, multiplication and division. Each operation is introduced with smaller numbers and single digits at first, increasing to larger numbers and double digits and so on. The methodology is also gradually advanced, from horizontal to vertical addition and subtraction, as well as multiplication and division, through small steps and half-worked questions to help children progress. 

In levels E and F, students get to grips with fractions, enabling them to complete addition, subtraction, multiplication and division of fractions through examples and introductory problems. As their confidence and speed grows they move on to more complex problems, learning the correct order of steps to work out the solution, finding the Least Common Denominators and Least Common Multiples, working up to three fractions and four operations. Learners will also start to become more familiar with decimals. 

Levels G to I aim to help students master positive and negative numbers using the four operations, as well as algebraic expressions and equations. Students are encouraged to write out the steps that they make to get to the solution until they are familiar with the process. Algebraic complexity increases, completing operations with monomials and then polynomials before moving on to factorisation, square roots, quadratic equations and functions and Pythagorean Theorem. Students build the skills to solve problems accurately, writing down appropriate intermediate steps. 

Level J fully develops student’s algebraic skills before the next level moves on to tackle the basic properties of functions. Students gradually increase their understanding of functions by tackling problems of greater complexity, before moving on to logarithms, limits, differentiation and integration. Students then develop the skills to work with trigonometric functions and equations of straight lines and circles. 

Levels N and O build the skills needed for advanced integration and differential equations after improving their understanding on limits. Skills that children have built up throughout the maths programme culminate at this point in their ability to complete high school mathematical problems based on their calculation skills developed so far and a sense for graphs. They will also have developed the necessary skills to progress further through self-learning as they will be used to using examples, hints and solution books to understand and execute complex mathematical concepts.