# Math

LEVEL: 7ADESCRIPTION: 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. ACTIVITY: Counting Number Number Dots |

LEVEL: 6ADESCRIPTION: 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. ACTIVITY: Number Cards Number Board Number Dots |

LEVEL: 5ADESCRIPTION: 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. ACTIVITY: Exercises Tracing Lines Tracing Numbers Number Puzzle |

LEVEL: 4ADESCRIPTION: 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. ACTIVITY: Number Writing Numbers up to 10 Number Dots Numbers up to 30-220 |

LEVEL: 3ADESCRIPTION: 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. ACTIVITY: Numbers up to 120 Adding 1 Adding 2 Adding 3 Adding 4 Adding 5 |

LEVEL: 2ADESCRIPTION: 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. ACTIVITY: Review up to 3A Adding 6 -10 Subtracting 1-3 Subtracting up to 5 Subtracting up to 7 Subtracting up to 9 |

LEVEL: ADESCRIPTION: 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. ACTIVITY: Review up to 2A Addition up to 200+200 Subtraction from numbers up to 20 Review Addition and Subtraction |

LEVEL: BDESCRIPTION: 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. ACTIVITY: Review up to A Addition up to 200+200 Addition of 2 digit numbers Subtraction of 2 digit numbers |

LEVEL: CDESCRIPTION: 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. ACTIVITY: 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: DDESCRIPTION: 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. ACTIVITY: Review up to C Multiplication 2 & 3 digits Addition & Subtractions Multiplication & Division Division 2+ digits Fractions Reduction |

LEVEL: EDESCRIPTION: 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. ACTIVITY: Review up to D Fractions Addition of Fractions Subtraction of Fractions Multiplication of Fractions Division of Fractions Fractions & Decimals |

LEVEL: FDESCRIPTION: 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. ACTIVITY: Review up to E Multiplication & Division of 3 fractions Addition & subtraction of 3 fractions Four Operations Value of X Solving Word Problems Decimals |

LEVEL: GDESCRIPTION: 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. ACTIVITY: 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 Equations Application of Equations |

LEVEL: HDESCRIPTION: 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. ACTIVITY: Transforming Equations Simultaneous Linear Equations up to 4 variables Application of Equations Inequalities Functions and Graphs Simplifying Monomials & Polynomials |

LEVEL: IDESCRIPTION: 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. ACTIVITY: Multiplication of Polynomials Multiplication Using Formulas Factorization Square Roots Quadratic Equations The Pythagorean Theorem |

LEVEL: JDESCRIPTION: 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. ACTIVITY: Expansion of Polynomial Products Factorization Fractional Expression Irrational Numbers Quadratic Equations Quadratic Equations & Complex Numbers Discriminant Root-Coefficient Relationship Simultaneous Equations Dividing Polynomials Remainder Theorem Factor Theorem Proof of Identities & Equalities Proof of Inequalities & Equalities |

LEVEL: KDESCRIPTION: 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. ACTIVITY: Review Linear Functions Quadratic Functions & Graphs Determining Equations of Quadratic Functions Maxima & Minima Higher Degree Functions Graphs of Functions Graphs of Irrational Functions Exponential Functions Graphs of Exponential Functions |

LEVEL: LDESCRIPTION: 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. ACTIVITY: Logarithmic Functions Graphs of Logarithmic Functions Modulus Functions Limits and Derivatives Tangent Lines Relative Maxima/Minima Definite Integrals Volumes Velocity & Distance |

LEVEL: MDESCRIPTION: In Level M, students begin studying the basics of trigonometric functions. Students are then introduced to more advanced trigonometry topics and analytic geometry. ACTIVITY: Trigonometric Functions Addition Theorem Sine and Cosine Theorem Triangles Coordinates of a Point Equations of Straight Lines Equations of Circles Tangent Lines of Circles Loci |

LEVEL: NDESCRIPTION: 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. ACTIVITY: Surface Vectors Coordinates in Space Inner Products of Vectors Equations of Lines and Planes Quadratic Curves Arithmetric Sequences Geometric Sequences Mathematical Introduction & Recursion Formula |

LEVEL: ODESCRIPTION: 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. ACTIVITY: Infinite Geometric Progressions Infinite Series Limits of Functions Continuous & Discontinuous Functions Differentiation Higher Degree Derived Functions Maxima/Minima |

LEVEL: PDESCRIPTION: 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. ACTIVITY: Indefinite Integrals Definite Integrals Applications of Integrals Differential Equations |

LEVEL: QDESCRIPTION: 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. ACTIVITY: Introduction to Permutations Combinations Binomial Theorem Conditional Probability Independent Trials and Expectations Statistics Matrix Definitions Mapping Linear Transformations |