# Mathematics

## 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

2. Algebraic Expressions.
3. out expressions.
4. Negative Numbers.
5. Arithmetic operations with fractions.
6. Absolute Value.
7. Simplifying rational expressions.
8. Operations with decimals fractions.
9. Converting fraction to decimal.
10. Rational and Irrational Numbers.
11. Word Problems.
12. Inequalities in one and two-steps.
13. Exponents.
14. Inequalities with absolute value.
15. Probability.
16. Square root. Perfect square.
17. Pythagoras Theorem.
19. Proportions.
20. Percentage.
21. Counting (Combinatorics).

## Algebra II

1. Systems of Equations
3. Simplifying Expressions
4. Arithmetic and Geometric Sequences
5. Graphs and Functions
6. Coordinate Geometry. Line Equation. Distance between point. Middle point.
7. Inequalities with Absolute Value
10. Graphs of Functions
11. Polynomial Function and Graphs
12. Exponent Functions and Graphs
13. Radical and Absolute Value Functions and Graphs
14. Function Composition, Inverse Function.
15. 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

2. Vectors – Relativity of Velocity
3. Vectors – Dot Products
4. Trigonometry Definitions
5. Trigonometry of a Right Triangle
6. Trigonometry. Laws of Sine and Cosine
7. Trigonometry Sums-Diff of Angles
8. Trigonometry Double Half Angles
9. Trigonometry Negative Angles
10. Graphs of Functions Shifts, Reflections.
11. Graphs of Trigonometric Functions
12. Pascal Triangle
13. Binomial Coefficients
14. Domain and Range of Functions
15. Inverse Trigonometric Functions
16. Polynomial Synthetic Division, Remainder Theorem.
17. Complex Numbers
18. Even and Odd Functions
19. Conic Sections – Ellipse, Hyperbola, Parabola

### Geometry

1. The sum of angles in a triangle Theorem
2. Equilateral and isosceles triangles
3. Triangle Congruency Tests
4. Triangle Bisector, Median and Altitude
5. Parallel Lines. Five Euclid Geometry Postulates (Axioms)
6. Parallelogram, Rhombus. Theorems
7. Parallelogram and Triangle Areas
8. Constructions with Compass and Ruler
9. Triangle exterior angle Theorem
10. Pythagoras Theorem
11. Regular n-gon. Properties, Theorems
12. Trapezoid. Trapezoid Area
13. Concurrency of Triangle Bisectors, Medians, Altitudes and Middle Lines. Theorems
14. Circumcircle, Incircle. Euler’s formula
15. Sum of angles in a convex polygon and in a five-star
16. A circle inscribed into an angle. Chord Theorem
17. An angle standing on the diameter. Thales’ Theorem
18. Constriction of a rectangle, rhombus and n-gon with a ruler and a compass
19. Circle, Chord, Secant, Tangent
20. Inscribed Angle, Chord-Tangent, Tangent-Secant, Chord-Chord Theorems
21. Similar Triangles. AAA, SAS Theorems
22. Triangle middle line. Triangle middle line Theorem
23. Triangle Simson Line Theorem