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Overview
The Math Program consists of 26 Levels, numbered 7A through O. Each Level consists of 200 pages 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 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 calculus.
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.
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 concentration skills and learn to recite numbers up to 50.
Level 4A
Students learn to write numbers up to 120 independently and also work with patterns of up to 20 dots. By learning to recognize the number of dots in a group without counting, students become better prepared for the addition exercises in later levels.
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 +3 individually. The last 20 sheets of this Level are dedicated to random addition questions from +1 to +3.
Level 2A
In this Level, students learn to add up to +10 automatically. 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 is also the Level where they learn subtraction, subtracting up to -9 by the end of the level. This important level develops the mental calculation skills. 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 the level, students encounter the first word problems in Kumon. This Level draws on the advanced mental calculation skills learned in previous levels when students "carry" in addition and "borrow" in 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 progress 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 skills 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 a student's ability to work with all 4 arithmetic operations is confirmed, he or she begins 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 this level. The level concludes with advanced topics in geometry, including the Pythagorean Theorem.
Level J
Concepts learned through Level I are expanded and reinforced. Students are introduced to irrational numbers and advanced factoring methods.
Level K
Level K introduces students to advanced functions, such as exponential and trigonometric, and their corresponding graphics. The skills developed here help ease students into the calculus exercises of Level M.
Levels L
In Level L, Students continue their study of functions and are introduced to advanced trigonometry topics and analytic geometry.
Level M
Level M marks the beginning of the calculus levels. Students begin by studying series and sequences and continue on to basic differentiation and definite and indefinite integration. Level M concludes with an analysis of the applications of integration.
Level N
In Level N, students move beyond basic calculus applications learned in Level M to topics in vector analysis and linear algebra. To complete the level, students study mappings and transformations.
Level O
Level O builds upon topics learned in Level M 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 minima and maxima.
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