Program of Our Math Classes

• Counting and Cardinality: Learn to count forward by ones up to 10 and associate each number with a specific quantity (one-to-one correspondence).

• Number Sense: Understand the relationship between numerals and their corresponding quantities up to 10. Use comparative terms such as greater than, less than, and equal to when analyzing sets of objects.

• Operations and Algebraic Thinking: Develop a foundational understanding of addition as combining sets and subtraction as separating or removing objects from a set. 

• Measurement and Data: Identify measurable attributes, including length, area, weight, and capacity. Compare two objects using mathematical vocabulary such as longer/shorter, equal in length, heavier/lighter, equal in weight, holds more/less, and equal capacity.

• Geometry (Spatial Reasoning): Recognize and describe the relative positions of objects in space using terms like beside, inside, next to, above, below, and under.

• Color Identification: Recognize and name primary and secondary colors.

• Geometry (Shapes): Identify, name, and describe basic two-dimensional geometric shapes (e.g., squares, circles, triangles, rectangles) and compare these with three-dimensional shapes found in real-world objects.

• Temporal Sequencing: Understand and describe the order of events using visual cues and sequencing terms such as before, after, first, next, and last. 

• Patterns and Logical Reasoning: Recognize, extend, and create repeating patterns. Solve basic analogies and introductory logic problems to develop reasoning skills.

• Cognitive Development: Enhance attention span, working memory, and fine motor skills through structured activities and guided practice.

• Exploratory Play: Engage in hands-on learning through games, block-building, and interactive activities that encourage mathematical exploration in a playful, meaningful context.

   

• Counting and Numbers: Count up to 20 and recognize zero on a number line. Count to 100 by ones and tens. Compare written numerals from 1 to 10.

• Operations: Decompose numbers up to 10 into pairs (e.g., 5 = 2 + 3). Represent and solve addition and subtraction problems within 10 using objects, number lines, or drawings. Break down numbers 11–19 into ten ones and additional ones (e.g., 18 = 10 + 8).

• Sorting and Sets: Sort, classify, and group objects by attributes. Introduce basic set concepts.

• Geometry: Identify, describe, and compare 2D and 3D shapes. Compose simple shapes into larger ones. Use spatial terms (e.g., above, below, next to).

• Measurement: Compare objects by length, weight, and capacity using terms like longer, shorter, heavier, or lighter.

• Patterns and Logic: Recognize, create, and extend patterns. Solve simple analogies and logic problems.

• Skill Development: Build attention, memory, and fine motor skills through games, blocks, and hands-on activities.

• Word Problems: Solve various addition and subtraction word problems with sums and differences up to 20.

• Place Value: Understand place value concepts for ones and tens. Represent numbers greater than 10 using visual models (e.g., base-ten blocks or number charts).

• Addition and Subtraction: Perform addition and subtraction with numbers greater than 20 without regrouping.

• Introduction to Multiplication and Division: Learn the basics of multiplication and division, including solving simple word problems and using the multiplication table (Pythagorean table).

• Basic Equations: Solve simple equations of the form x - a = b, x + a = b, and a - x = b. Explore balance concepts and understanding parts of a whole.

• Time: Read and interpret clocks to understand whole hours, half-hours, and minutes.

• Geometry: Identify, describe, and analyze two- and three-dimensional shapes and their properties.

• Patterns and Analogies: Solve more challenging pattern recognition tasks and analogies.

• Combinatorics: Explore basic combinatorial problems, including counting arrangements and possibilities.

• Logical Reasoning: Tackle simple logic puzzles to develop critical thinking skills

• Hands-On Activities: Reinforce learning through games, block-building, and tangram puzzles.

• Place Value: Understand the value of digits in the ones, tens, and hundreds places.

• Addition and Subtraction: Perform addition and subtraction with regrouping (carrying and borrowing).

• Multi-Step Word Problems: Solve complex word problems involving multiple addition and subtraction steps. Translate basic word problems into algebraic expressions with variables.

• Multiplication and Division: Master basic multiplication and division facts. Solve word problems using these operations

• Basic Equations: Solve simple equations of the form x - a = b, x + a = b, a - x = b, and a × x = b.

• Order of Operations: Apply the correct sequence of operations.

• Introduction to Sets: Understand sets, elements, and basic set notation.

• Algorithms: In mathematics, computer sciences, and everyday life.

• Geometry: Explore properties of two- and three-dimensional shapes, including faces, edges, and vertices.

• Combinatorics: Solve basic counting problems, including arrangements and combinations.

• Logical Reasoning: Develop problem-solving skills through logic puzzles and reasoning challenges.

• Interactive Learning: Engage with activities and lessons via Zoom for interactive, real-time learning.

• Sets and Venn Diagrams: Understand sets, including union and intersection. Solve word problems using Venn diagrams.

• Order of Operations: Apply the correct sequence of operations, including parentheses.

• Division and Multiplication:

  
   

  • - Perform division with remainders.
  • - Execute long multiplication.
  • - Solve long division problems with single-digit or simple two-digit divisors.

  
   

• Equations: Solve linear equations of the form ax + b = c, including those with parentheses.

• Negative Numbers: Understand negative numbers, including placement on the number line, and perform addition and subtraction with negative values.

• Fractions.

• Decimals and Money: Use money as a model for decimals. Perform addition and subtraction and solve word problems involving currency.

• Geometry: 

   

  • - Identify lines, segments, rays, parallel and perpendicular lines.
  • - Measure lengths and angles, including complementary and supplementary angles.
  • - Understand circles and calculate the circumference.
  • - Classify triangles (e.g., acute, right, obtuse) and apply the angle sum property (sum of angles equals 180°).
  • - Explore special quadrilaterals (parallelogram, rhombus, trapezoid) and calculate their perimeter and area.
  • - Break down complex shapes into quadrilaterals with right angles for area calculations.
  • - 3D Geometry: Recognize and analyze three-dimensional shapes and their properties.
• Advanced Logic: Develop problem-solving skills through complex logic puzzles (e.g., The Lady or the Tiger challenges).
   

• 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: aⁿ 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.

Optional topics

• 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