| 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 number dots in a group without counting, students become better prepared for the additional exercise in later levels. By the end of the Level, students learn to count up to 220.
Numbers up to 10
Numbers up to 30-220
| 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 to +5 individually. The last 20 sheets of this Level are dedicated to random addition questions from +1 to +5.
Numbers up to 120
| 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.
Review up to 3A
Adding 6 -10
Subtracting up to 5
Subtracting up to 7
Subtracting up to 9
| 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 number as big as 20.
Review up to 2A
Addition up to 200+200
Subtraction from numbers up to 20
Review Addition and Subtraction
| 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. Master of Level B greatly reduces errors in multiplication and division in Levels C and D.
Review up to A
Addition up to 200+200
Addition of 2 digit numbers
Subtraction of 2 digit numbers
| 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 diversion by one digit is introduced. Students who have developed good mental calculation ability will not have to write division steps.
Review up to B
Multiplication up to 9
Multiplication 2 digits
Introduction to Division
Division with remainders 1-4
Division 2 digits
Division 3 digits
| 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.
Review up to C
Multiplication 2 & 3 digits
Addition & Subtractions
Multiplication & Division
Division 2+ digits
| 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.
Review up to D
Addition of Fractions
Subtraction of Fractions
Multiplication of Fractions
Division of Fractions
Fractions & Decimals
| 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.
Review up to E
Multiplication & Division of 3 fractions
Addition & subtraction of 3 fractions
Value of X
Solving Word Problems
| LEVEL: G
Students are introduced to positive and negative numbers, as well as to basic algebra. Students use their previously learned operation skills to master linear equations. A word problem set rounds off the Level, allowing students to apply everything they have learned in Level G.
Review up to F
Addition & Subtraction of Positive & Negative Numbers
Multiplication of Positive & Negative Numbers
Division of Positive & Negative Numbers
Values of Algebraic Expressions
Simplifying Algebraic Expressions
Application of Equations
| LEVEL: H
Students will learn to solve simultaneous linear equations in two to four variable. Concepts of numerical and algebraic value are strengthened. Students are introduced to transforming equations, inequalities, functions and graphs.
Simultaneous Linear Equations up to 4 variables
Application of Equations
Functions and Graphs
Simplifying Monomials & Polynomials
| 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.
Multiplication of Polynomials
Multiplication Using Formulas
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 Level J, students conduct proofs or algebraic equalities and inequalities.
Expansion of Polynomial Products
Quadratic Equations & Complex Numbers
Proof of Identities & Equalities
Proof of Inequalities & Equalities
| LEVEL: K
Students acquire the basic properties of functions, through a thorough study of quadratic functions. Level K introduces higher degree, fractional, irrational and exponential functions and their corresponding graphs. The skills developed here will help ease students into the calculus exercises of Level L.
Review Linear Functions
Quadratic Functions & Graphs
Determining Equations of Quadratic Functions
Maxima & Minima
Higher Degree Functions
Graphs of Functions
Graphs of Irrational Functions
Graphs of Exponential Functions
| LEVEL: L
Students begin Level L by studying logarithmic functions, and are led into the beginning of calculus. Students study basic differentiation and definite and indefinite integrals. The Level concludes with an analysis of the applications of integration, including areas, volumes, velocity and distance.
Graphs of Logarithmic Functions
Limits and Derivatives
Velocity & Distance
| LEVEL: M
In Level M, students begin studying the basics of trigonometric functions. Students are then introduced to more advanced trigonometry topics and analytic geometry.
Sine and Cosine Theorem
Coordinates of a Point
Equations of Straight Lines
Equations of Circles
Tangent Lines of Circles
| LEVEL: N
Level N begins with the advanced calculus topics of vector analysis. The Level expands on quadratic regions and concludes with the study of series and sequences.
Coordinates in Space
Inner Products of Vectors
Equations of Lines and Planes
Mathematical Introduction & Recursion Formula
| LEVEL: O
Level O builds upon the 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.
Infinite Geometric Progressions
Limits of Functions
Continuous & Discontinuous Functions
Higher Degree Derived Functions
| 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.
Applications of Integrals
| 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.
Introduction to Permutations
Independent Trials and Expectations