# Mathematics

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

### The many dimensions of math

Even for young children, math is more than just a numbers game. Math has many dimensions, including:
• Number sense (e.g., the numeral “4” represents four objects, which is greater than 3 and less than 5)
• Geometry (e.g., patterns and shapes, each with unique features)
• Measurement (e.g., size, distance, amount)
• The language of math (e.g., more than, less than, equal to)
Spatial relations (e.g., in front of or behind; near or far) Numbers
• During the fourth year, many children can accurately count up to five items, some can count up to 10, and a few can count to 20
• Many four-year-olds can tell what number comes after a given number in a sequence up to 10. For example, if asked  “What comes after 1-2-3-4-5-6?” many four-year-olds can answer “7,” and so forth
• Given two numbers between one and 10, many five-year-olds can tell which of the two is larger

## K – Level

### Counting and cardinality

• Count to 100 by ones; skip count to 100 by tens
• Connect counting to cardinality
• Count objects to answer “how many”
• Compare two numbers between 1 and 10 in regards to
• More than/less than/equal to

### Operation and algebraic thinking

• Fluently add and subtract within 5 units
• Solve addition and subtraction stories 0-10 using objects or drawings
• Split numbers up to 10 in pairs in more than one way
• Determine the number that makes 10 when added to a given number

### Number and operations in base ten

• Understand the place values of numbers from 11-19
• Compose and split from 11-19 as a bundle of 10 ones and additional ones

### Measurement and data.

• Describe measurable attributes of objects
• Compare the difference between two objects
• Classify, count, and sort up to 10 objects

### Geometry.

• Name and compare shapes; describe similarities, differences, parts and attributes
• Identify shapes as 2D or 3D, as well as the relative positions of objects
• Model and draw shapes; compose simple shapes to make larger shapes

## 1 – Level

• Word problems
• Addition and subtraction up to 20
• Introduction to multiplication
• Parts of a whole
• Time
• Logic problems
• Geometry – 3D shapes
• Logic games
• Patterns

## 2 – Level

• Addition and subtraction of two-digit and three-digit numbers
• Word problems – Math modeling
• Multiplication and division
• Order of operations
• Algorithms
• Geometry – Lines, Angles, 3D Shapes
• Logic problems
• Equations x-a = b / x+a = b / a –x = b / ax = b
• Combinatorial problems

### Mathematics is the language in which the God speak to people.

Plato, c. 427 BC – c. 347 BC

Mathematician and Philosopher

## 3 – Level

• Sets – Union intersection and Venn diagrams
• Order of operations
• Division with remainder
• Equations
• Logic
• Proper and improper fractions
• Unit rate problems
• Math modeling – problem solving
• Lines, segments, rays, parallel and perpendicular lines
• Triangles, sum of angles in triangle
• Perimeter and area of the planar shapes
• Parallelogram, trapezoid and rhombus

## 4 – Level

• Order of operations
• Prime numbers
• Negative numbers
• Fractions
• Divisibility tests
• Symmetries
• Angles
• Math modeling
• Equations

## 5 – Level

• Prime factorization
• LCM and GCD
• Algebraic laws
• Negative numbers
• Equations with negative numbers
• Decimal fractions
• Word problems – math modeling
• Math statements: Exists, For All, If and Only If
• Powers and Exponent
• Powers of 2 and binary numbers
• Dirichlet’s Box Principle (Pigeonhole Principle)
• Part of a number
• Divisibility tests
• Parallel lines
• Congruence test for triangles
• Pythagorean theorem
• Probability

## 6 – Level

• Logic
• Set theory
• Powers and exponent
• Square roots
• Rational and irrational numbers
• Arithmetic and geometric progression
• Construction with ruler and compass
• Coordinate plane and graphs of functions
• Equations
• Math, modeling – word problems

### “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.