# Mathematics

## About Our Math Programs

Our math program offers classes from Preschool through 10th Level. The higher Level courses cover both algebra and geometry, introduce new topics and offer students challenging problems. Our curriculum integrates advanced subjects into the standard school program, and includes SAT1 and SAT2 preparation. We aspire to make your child fall in love with math, while helping them succeed in school and on standardized tests.

## Preschool program (Math 4-5 years of age)(prerequisite for Math 0)

• Numbers name and counting up to 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

## Math 0 (Kindergarten) (prerequisite for Math 1)

• 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

## Math 1

• 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

## Math 2

• 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 God speak to people.

Plato, c. 427 BC – c. 347 BC

Mathematician and Philosopher

## Math 3

• 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

## 4 – Level

• Cartesian Coordinates
• LCM, GCD, Prime factors
• Venn Diagrams
• Negative numbers
• Comparing fractions and equations with fractions
• Absolute value and equations with absolute value
• Algebraic expressions
• Parallelogram properties
• Circle
• Introducing functions
• Mixed operations with fractions
• Congruence
• Line of Symmetry
• Triangle Congruence tests
• Trapezoid and triangle areas

## 5 – Level

• Addition and Multiplication Properties. Simple Equations
• Algebraic expressions
• Negative numbers
• Arithmetic operations involving division and fractions
• Equations with absolute value
• Word problems
• Logic problems
• Decimal fractions
• Rational and Irrational numbers
• Exponents and exponent properties
• Probability, addition, product and complementary rules
• Square Root
• Pythagorean theorem
• Converting rational decimals to fractions
• Proportions
• Percentage problems
• Pigeonhole Principle (Principle Dirichlet)
• System equations

## 6 – Level

• Proportions, percentage
• Sets, Morgan Laws
• Logical Operations: NOT, OR, AND, FOLLOWS
• Solving inequalities. An example: (2x-3)/(x-4)>0
• Square of sum, difference of squares
• Coordinate geometry
• Line equation y=mx+b
• Coordinates of the segment middle point, a distance between two points
• Equations of the perpendicular and parallel lines
• Circle equation with any center location
• Graphs and functions
• Quadratic equation. Solving by using formula and by completing square
• Parabola and algebraic vs. geometrical approaches to the same math problems
• Absolute value equations and inequalities
• Arithmetic and geometric progressions
• Systems of equations
• Graphing absolute value function

### “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

## 7 – Level

• Combinatorics
• Vectors
• Basic trigonometry
• Transformations: Reflection, rotation and composition
• Quadratic Equations. Vieta Theorem. Parabola
• Inequalities
• Fibonacci numbers

## 8 – Level

• Combinatorics. Binomial formula
• Divisibility. Euclid’s algorithm
• Euclidean Geometry

## 9 – Level

• Elements of math logic and Set Theory. Bijection and injection. Infinite sets and cardinality
• Functions and graphs. Even, odd, periodic, monotonic functions
• Exponential function. Logarithms. Equations and inequalities with exponents and logarithms
• Polynomials; division of polynomials.Vieta formulas
• Complex numbers
• Mathematical induction

## 10 – Level

• Sets and functions. Bijections
• Infinite sets and cardinality
• Equivalence relations
• Solving equivalences
• Euler function
A free first trial lesson is offered for all subjects. If you wish to sign up for any of our programs, a non-refundable payment for the month is due on the first lesson of the month. We accept personal checks or cash only.

# \$35 – 60 / 90

60 or 90 minute math lessons are available. The duration of the class varies by level.