The Math Program consists of 21 Levels.

Each Level consists of 200 work pages (with the exception of Level P) and is broken down by topic into sections.

Each section is broken down into twenty 10 page sets.

There is an additional optional level, level X which allows students to further work on more advanced maths such as statistics, differentiation and integration as, and differential equations.


Level 7A:

Students count up to 10 pictures and dots individually and as a group. Mastery is gradual and the eventual goal is for students to be able to say the total number of objects in each group without counting. Number sequencing is reinforced through the use of the Magnetic Number Board.


Level 6A:

Students count up to 30 using pictures and numbers. Gradually, students learn to recognize groups of up to 20 dots without counting them individually. Number sequencing is reinforced through the use of the Magnetic Number Board.


Level 5A:

Students learn to use a pencil through line tracing exercises, beginning with short lines and advancing to long curved lines. The curved lines gradually take the shape of large numbers. This develops the fine motor skills needed to trace and write numbers independently and teaches the natural stroke order required for number formation. Students also develop their concentration ability and learn to recite numbers up to 50.


Level 4A:

Students learn to write numbers up to 120 independently. Students also work with patterns of up to 20 dots. By learning to recognize the numbers of dots in a group without counting, students become better prepared for the addition exercises in later levels. By the end of the Level, students learn to count up to 220.


Level 3A:

Building on a strong sense of number sequencing from Level 4A, students are introduced to addition in Level 3A. At first, students master + 1, + 2, through + 5 individually. The last 20 sheets of this level are dedicated to random addition questions from + 1 to + 5.


Level 2A:

In this level, students learn to add through to + 10 automatically. This is also the level where they learn subtraction, subtracting up to - 9 by the end. It is very important that students master the contents of this level for smooth progress in subsequent levels. Level 2A greatly develops a student's speed and concentration.


Level A:

Level A continues horizontal addition and subtraction, but with larger numbers than in Level 2A. This important level develops the mental calculation ability of students. By the end of it, students will be able to add advanced questions like + 200 and subtract from numbers as big as 20.


Level B:

This level teaches vertical addition and subtraction. Throughout it, students will encounter their first word problems in Kumon. This level draws on the advanced mental calculation skills learned in previous levels when students "carry" in addition questions and "borrow" in questions involving subtraction. Mastery of Level B greatly reduces errors in multiplication and division in Levels C and D.


Level C:

Students master the multiplication tables by practicing until they can answer immediately. Next, students learn up to 4-digit by 1-digit multiplication with mental carryovers. Once multiplication is mastered, simple division by one digit is introduced. Students who have developed good mental calculation ability will not have to write division steps.


Level D:

Students learn double-digit multiplication before advancing to long division. In this challenging section, students develop estimation skills that will be necessary for future fraction work. Once students' ability to work with all 4 arithmetic operations is confirmed, they begin to study fractions, learning to reduce using the Greatest Common Factor.


Level E:

Students learn to add, subtract, multiply, and divide fractions. Proper intermediate steps are emphasized. At the end of the level, students learn basic fraction/decimal conversions.


Level F:

Students continue calculations with fractions, now employing the order of operations. Level F contains a challenging section of word problems, as well as more work with decimals.


Level G:

Students are introduced to positive and negative numbers, as well as to basic algebra. Students use their previously learned four operations skills to master linear equations. A word problem set rounds off the level, allowing students to apply everything they have learned in Level G.


Level H:

Students will learn to solve simultaneous linear equations in two to four variables. Concepts of numerical and algebraic value are strengthened. Students are introduced to transforming equations, inequalities, functions and graphs.


Level I:

This level thoroughly reviews Levels G and H and introduces factorization. Factorization is an essential skill to advance to square roots and quadratic equations, also covered in the level. The level concludes with advanced topics in geometry, specifically related to the Pythagorean Theorem.


Level J:

Concepts learned through Level I are expanded and reinforced. Students are introduced to advanced factoring methods, complex numbers, the discriminant, and the Factor and Remainder theorems. At the end of the level, students conduct proofs of algebraic equalities and inequalities.


Level K:

After a thorough study of quadratic functions, Level K introduces students to various types of functions including higher degree, fractional, irrational, and exponential, and their corresponding graphs. The skills developed here will help ease students into the calculus exercises of Level L.


Level L:

Level L marks the beginning of calculus. Students begin by studying logarithmic functions, followed by basic differentiation and definite and indefinite integration. The level concludes with an analysis of applications of integration, including areas, volumes, velocity and distance.


Level M:

In level M, students begin by studying the basics of trigonometric functions. Students are then introduced to more advanced trigonometry topics and analytic geometry.


Level N:

Level N begins with the advanced calculus topic of vector analysis. The level expands on quadratic regions and concludes with the study of series and sequences.


Level O:

Level O builds upon topics learned in Level L and introduces students to a more advanced study of series and sequences, limits and differentiation. Students also experience the applications of differential calculus, specifically with regard to maxima and minima.


Level P:

In Level P, students continue their study of calculus by studying advanced integration (definite and indefinite) and applications of integration. Students are also introduced to differential equations.


Level Q:

Level Q introduces students to the study of probability and statistics. Students study combinations, permutations, trials, the binomial theorem, and distributions. To complete the level, students study matrices, mappings and transformations.















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