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The aim of the Kumon Math program is to prepare students so that they can excel
The lower level Kumon worksheets are designed to build mastery of the four
operations, which are the basics of Mathematics.
Students with a mastery of addition, subtraction, multiplication and division
can easily learn more complex operations such as long division, fractions,
equation solving and factorization.
Students who are struggling with Math are most often those with poor foundation
skills. Kumon’s programs are structured in a linear fashion to ensure that
students master one concept before moving onto the next. Kumon students are able
to progress based on an assessment of their own needs and skills. This is one of
the major differences between Kumon and school-based learning.
The Math Program consists of 23 Levels, numbered Levels 7A through Level Q. Each
Level consists of 200 pages (with the exception of Level P) and is broken down
by topic into sections. Additionally, each section is broken down into sets of
10 pages each. Therefore, each level consists of 20 sets.
The Kumon Math Program begins with basic counting to reading numbers. It
proceeds to the four fundamental operations (addition, subtraction,
multiplication and division), then elevates to Algebra & Trigonometry. It then
graduates to higher Mathematics, such as Calculus, Statistics & Probabilities,
thus following a logical sequence. It is suitable for preschool children through
to senior high school students.
The main material of the program is the worksheets. The worksheets were designed
in minute steps to facilitate self-learning. The worksheets contain mostly
computational problems. As students study higher levels of Mathematics, the
percentage of calculations, both in school curriculum and textbooks, increases.
That is why, the worksheets will focus on developing the students´ computational
skills. The ability to calculate develops the ability to think and lead the way
to creativity. Whenever there are new lessons presented, examples are provided
to help students comprehend the concepts behind the exercises.
The Program begins with very basic number recognition and number counting. It
then progresses through addition, subtraction, multiplication, division and
fractions. Next, positive and negative numbers are introduced, followed by
algebra, factoring, functions, and finally, calculus. To reiterate, the Kumon
Math Program takes a very linear approach to learning math. Each concept that is
introduced builds on knowledge and skills learned from the previous concept. For
this reason, it is important that students completely master and understand
their current concept before advancing to the next.
||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.
||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.
||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.
||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.
||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 +
||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 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.
||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.
||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
||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.
||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.
||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.
||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.
||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.
||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.
||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.
||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 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.
||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 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 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.
||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
||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.
More info on the Kumon Math Program at our