# Program of our Math classes

## 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.
• 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)
• 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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