Program of our Math classes

Table of Contents

Math Level 0
Math Level 1
Math Level 2
Math Level 3
Math Level 4
Math Level 5
Math Level 6
Math Level 7
Math Level 8
Math Level 9
Math Level 10

Math Level 0

Please see the attached document: Curriculum PreK-K


Math Level 1

  • Different types of word problems involving addition and subtraction up to 20.
  • Place value: ones, tens. The graphic form of numbers larger than 10.
  • Addition and subscription for numbers more than 20 without regrouping.
  • Introduction to multiplication and division. Pyphagore table. Simple word problems involving multiplication.
  • Introduction to simple equations of the form x-a=b, x+a=b, a-x=b. Balance. Parts of a whole.
  • Time and units.
  • Geometry. 2D geometry.
  • Challenge analogies and patterns.
  • Combinatorics problems.
  • Logic problems.
  • Games. Blocks. Tangram puzzle.

Math Level 2

  • Place value: ones, tens, hundreds.
  • Addition and subscription with regrouping and borrowing.
  • Different types of word problems involving several steps of addition and subscription. Expressions with variables - putting the basic word problems into expression form.
  • Multiplication and division. Word problems involving multiplication.
  • Simple equations of the form x-a=b, x+a=b, a-x=b, ax=b
  • Order of operations
  • Properties of addition and multiplication
  • Introduction to sets.
  • 2D Geometry: a plane, a point, a line. Line segment, ray, parallel lines. Curves. Polygonal chains.
  • 2D shapes, perimeter and ares
  • Measurements - length, capacity and weight, units
  • Logic problems.
  • Extras

  • Introduction to Algorithms.
  • Combinatorics problems.
  • Zoom

Math Level 3

Algebra

  • Sets. Union, intersection. Venn diagram. Word problems with Venn diagram.
  • Order of arithmetic operations with parentheses.
  • Division with remainder. Multiples and divisors.
  • Long multiplication ( up to n digits to 2 digits). Long division with one or simple 2 digit divisor)
  • Negative numbers. Negative and fractional numbers on the number line. Operations with negative numbers (addition and subtraction).
  • Proper and improper fractions. Mixed numbers. Addition and subtraction of fractions; comparing fractions. Word problems and equations with fractions.
  • Money as a model for decimals. Addition and subtraction. Word problems with money.

Geometry

  • Lines. Segments. Rays. Parallel and perpendicular lines.
  • Measuring lengths and angles. Complementary and supplementary angels. Introduction to compass
  • Circle. Circumference
  • Triangles: acute, etc. Sum of angles of a triangle.
  • Special quadrilaterals: parallelogram, rhombus, trapezoid. Perimeter and area of figures with can be split in quadrilateral with right angels.
  • 3D geometry. Nets.

Extras

Logic ( The Lady or the Tiger level)


Math 4

Main topics studied in Math 4

  • Order of operations
  • Equation. Expression. Variable. Constant. Coefficient.
  • Prime numbers, divisibility tests
  • Combinatorics. Factorials. Permutations.
  • Fractions. Equivalent fractions.Addition, multiplication and division of fractions
  • Reciprocal fractions. Complex fractions.
  • Negative numbers and operations with them
  • Exponents
  • Geometry: a coordinate plane, circle, symmetries
  • Angles. Measuring with protractor.
  • Special quadrilaterals
  • Factorization. Prime numbers. LCM, GCD
  • Sets. Venn diagram.

Math 5

Main topics studied in Math 5

  • Overview of prime factorization
  • LCM and GCD
  • Fractions with large denominators
  • Algebraic laws. Distributivity (opening parentheses)
  • Negative numbers. Multiplication. Absolute value
  • Algebraic expressions and word problems (big topic!)
  • Powers. Negative power
  • Difference of squares. Roots. Pythogorean theorem
  • Probability
  • Binary numbers and operations with them
  • Parallel lines, transversal lines, corresponding angles etc.
  • Congruence tests for triangles

Math 6

Main topics studied in Math 6

  • Basic logic (knights and knaves, logic operations)
  • Set theory basics (basic operations and Venn diagrams)
  • Linear equations continued. Simple inequalities (Review)
  • Powers: an am=an+m . Multiplication and division by powers of 10 (Review)
  • Square roots. Rational and irrational numbers
  • Arithmetic and Geometric Progressions
  • Probability. Basic combinatorics: permutations
  • Similarity; relation with areas and volumes
  • Constructions with ruler and compass: Bisector, a circle inscribed in an angle, central angle, diameter perpendicular to a chord.
  • Coordinate plane and graphs of simple functions
  • System linear equation

Math 7

Main topics studied in Math 7

  • Combinatorics: choosing with and without repetitions. Pascal triangle; formual for nCk (no proof, and no binomial theorem)
  • Quadratic equation. Quadratic formula, Vieta formula. Parabola.
  • Coordinate System. Line. Circle. Parabola
  • Vectors and operations with them (in coordinates).
  • Transformation of the plane. Reflections, rotations, and their compositions.
  • Arithmetic sequence. Geometric progression.
  • Solving inequalities using interval method.
  • Fibonacci numbers
  • Basic trigonometry (definition of sin, cos). Law of sines.

Optional topics

  • Plane patterns and symmetries.
  • Introduction to Calculus

Math 8

Main topics studied in Math 8

  • Overview of combinatorics. Pascal triangle and binomial formula.
  • Divisibility, Euclid's algorithm, arithmetic of remainders, congruences. Application: check digits
    Fundamental theorem of arithmetic
  • Euclidean geometry (following Kiselev). First postulates, congruence tests for triangles, alternate interior angle theorem, properties of sepcial quadrialterals, similar triangles, Thales theorem, inscribed angles.
  • Logic and Truth tables
  • Chinese Remainder Theorem
  • Fermat's Little Theorem

Math 9

Main topics studied in Math 9

  • Elements of mathematical logic and set theory. Quantifiers. Bijection and injection. Infinite sets and cardinality.
  • Functions and graphs. Even, odd, periodic, monotonic functions. Graphs of basic functions (power function, roots, sin, cos,) and their transformations. Inverse function.
  • Equations of ellipse, hyperbola, parabola. Conic sections
  • Exponential function. Logarithm. Equations and inequalities with exponents and logarithms.
  • Polynomials; division of polynomials. Vieta formulas
  • Complex numbers
  • Mathematical induction

Optional topics

  • Trigonometry. Trigonometric equations and formulas.
  • Advanced geometry with vectors: Ceva theorem, Ptolemey theorem, nine point circle.

Math 10

Main topics studied in Math 10

  • Systems of Linear Equations, Matrices
  • Vectors, Dot Product, Cross Product
  • Metric Spaces, Open and Closed Sets
  • Sequences, Limits
  • Series, Convergence Tests
  • Continuous Functions, Intermediate Value Theorem, Topology
  • Groups, Subgroups, Lagrange's Theorem

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