## Why MathPlus?

We are raising the bar!- Our advanced program is for motivated students and parents.
- All teachers have a master degree or Ph.D in mathematics.
- We create a solid base for success in schools and Olympiads.
- Teaching math with a person-to-person interaction.

## Preschool Level Program

### Prerequisite: 4 years of age – this program is a prerequisite for the Kindergarten Level Program

- Name numbers, count 0-10
- Recognize the attributes of size, length, area, weight, and capacity of everyday objects
- Compare numbers. Understand addition and subtraction as putting together or taking away
- Identify colors
- Identify relative position of objects in space
- Sort, categorize, and classify objects
- Identify various two-dimensional shapes (squares, circles, triangles, rectangles)
- Time – put pictures in order. Before and after
- Compare three-dimensional shapes with the shapes of real objects
- Patterns
- Analogies
- Develop attention, memory and fine motor skills
- Simple logic problems
- Game and blocks

## Kindergarten Level Program

### Prerequisite: this program is a prerequisite for the Level 1 Program

- Count to 100 by ones and by tens
- Numbers name and counting up to 20. Number line. Zero
- Decompose numbers less than or equal to 10 into pairs in all possible ways (e.g., 5=5+0, 5=1+4, 5=2+3)
- Compare numbers
- Separate numbers 11-19 in groups of 10 and number from 1-9
- Solve addition and subtraction word problems, and add and subtract within 10. Use number line
- Compare objects by measurable attributes, such as length or weight
- Identify and describe shapes. Compare simple shapes to form larger shapes
- Sort, categorize, and classify objects. Introduction to set
- Name relative positions of objects
- Patterns
- Analogies
- Develop attention, memory and fine motor skills
- Simple logic problems
- Games. Blocks

## Level 1 Program

- Place value: ones, tens. Graphic form of numbers larger than 10
- Different types of word problems involving addition and subtraction up to 20
- Introduction to multiplication and division. Pifagore table. Simple word problems involving multiplication
- Addition and subtraction for numbers more than 20 without regrouping
- Time
- Introduction to simple equations of the form x-a=b, x+a=b, a-x=b. Balance. Parts of a whole
- Challenge analogies and patterns
- Geometry. 3D geometry
- Logic problems
- Combinatory problems
- Games. Blocks. Tangram

## Level 2 Program

- Addition and subtraction with regrouping
- Place value: ones, tens, hundreds
- Multiplication and division. Word problems involving multiplication
- Different types of word problems involving several steps of addition and subtraction. Expressions with variables – putting the basic word problems into expression form
- Order of operations
- Simple equations of the form x-a=b, x+a=b, a-x=b, ax=b
- Algorithms
- Introduction to sets
- Combinatorial problems
- Logic problems
- Geometry. 3D geometry

### Mathematics is the language in which the gods talk to people.

Plato, c. 427 BC – c. 347 BC

Mathematician and Philosopher

## Level 3 Program

- Order of operations, including parentheses
- Equations of the form ax+b=c and equations with parentheses
- Division with remainder
- Sets – Union intersection and Venn diagrams
- Logic
- Unit rate problems
- Proper and improper fractions
- Math modeling – problem solving
- Triangles, sum of angles in triangle
- Lines, segments, rays, parallel and perpendicular lines
- Parallelogram, trapezoid and rhombus
- Perimeter and area of the planar shapes
- Angels
- Money (as a model for decimals)
- Negative numbers
- Long multiplication and division

## Pre-Algebra

- LCM, GCD, Prime factors
- Venn Diagrams
- Negative numbers
- Factoring by grouping
- Multiplying polynomials
- Taking the common factor out of expressions
- Solving multi-steps equations
- Graphing inequalities
- Word problems with speed, time, and distance
- Comparing fractions and equations with fractions
- Mixed operations with fractions
- Absolute value and equations with absolute value
- Proportions and equations with proportions
- Algebraic expressions
- Functions
- Linear function
- Exponents and Exponential Function
- Cartesian Coordinates
- Parallelogram properties
- Circle
- Congruence
- Line of Symmetry
- Triangle Congruence tests
- Trapezoid and triangle areas

## Algebra I

- Addition and Multiplication Properties.
- Algebraic Expressions.
- out expressions.
- Negative Numbers.
- Arithmetic operations with fractions.
- Absolute Value.
- Simplifying rational expressions.
- Operations with decimals fractions.
- Converting fraction to decimal.
- Rational and Irrational Numbers.
- Word Problems.
- Inequalities in one and two-steps.
- Exponents.
- Inequalities with absolute value.
- Probability.
- Square root. Perfect square.
- Pythagoras Theorem.
- Simplifying single radical expressions.
- Proportions.
- Percentage.
- Counting (Combinatorics).

## Algebra II

- Systems of Equations
- Quadratic Inequalities
- Simplifying Expressions
- Arithmetic and Geometric Sequences
- Graphs and Functions
- Coordinate Geometry. Line Equation. Distance between point. Middle point.
- Inequalities with Absolute Value
- Quadratics – Completing Square.
- Quadratics – Quadratic Equation Formula
- Graphs of Functions
- Polynomial Function and Graphs
- Exponent Functions and Graphs
- Radical and Absolute Value Functions and Graphs
- Function Composition, Inverse Function.
- Graphing Inequalities.

### “Surely it is not knowledge, but learning; not owning but earning; not being there, but getting there; that gives us the greatest pleasure.”

Carl Friedrich Gauss, 1777 – 1855

Mathematician and Physicist

## Precalculus

- Vectors – Addition-Subtraction
- Vectors – Relativity of Velocity
- Vectors – Dot Products
- Trigonometry Definitions
- Trigonometry of a Right Triangle
- Trigonometry. Laws of Sine and Cosine
- Trigonometry Sums-Diff of Angles
- Trigonometry Double Half Angles
- Trigonometry Negative Angles
- Graphs of Functions Shifts, Reflections.
- Graphs of Trigonometric Functions
- Pascal Triangle
- Binomial Coefficients
- Domain and Range of Functions
- Inverse Trigonometric Functions
- Polynomial Synthetic Division, Remainder Theorem.
- Complex Numbers
- Even and Odd Functions
- Conic Sections – Ellipse, Hyperbola, Parabola

### Geometry

- The sum of angles in a triangle Theorem
- Equilateral and isosceles triangles
- Triangle Congruency Tests
- Triangle Bisector, Median and Altitude
- Parallel Lines. Five Euclid Geometry Postulates (Axioms)
- Parallelogram, Rhombus. Theorems
- Parallelogram and Triangle Areas
- Constructions with Compass and Ruler
- Triangle exterior angle Theorem
- Pythagoras Theorem
- Regular n-gon. Properties, Theorems
- Trapezoid. Trapezoid Area
- Concurrency of Triangle Bisectors, Medians, Altitudes and Middle Lines. Theorems
- Circumcircle, Incircle. Euler’s formula
- Sum of angles in a convex polygon and in a five-star
- A circle inscribed into an angle. Chord Theorem
- An angle standing on the diameter. Thales’ Theorem
- Constriction of a rectangle, rhombus and n-gon with a ruler and a compass
- Circle, Chord, Secant, Tangent
- Inscribed Angle, Chord-Tangent, Tangent-Secant, Chord-Chord Theorems
- Similar Triangles. AAA, SAS Theorems
- Triangle middle line. Triangle middle line Theorem
- Triangle Simson Line Theorem
- Cyclic Quadrilateral. Properties. Theorems
- Ptolemy Theorems
- Power of a point Theorem
- Heron Formula of Triangle Area. Five other formulas of the Triangle Area
- Bisector Theorem