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Math Level 10

Please see the attached document: Curriculum PreK-K

- 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.

- 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.
- Introduction to Algorithms.
- Combinatorics problems.
- Zoom

- 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.

- 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.

Logic ( The Lady or the Tiger level)

- 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.

- 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

- Basic logic (knights and knaves, logic operations)
- Set theory basics (basic operations and Venn diagrams)
- Linear equations continued. Simple inequalities (Review)
- Powers: a
^{n}a^{m}=a^{n+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

- 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.

- Plane patterns and symmetries.
- Introduction to Calculus

- 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

- 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

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

- 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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