Table of Contents
Math PreK - K Math Level 0 Math Level 1 Math Level 2 Math Level 3 Math Level 4 Math Level 5 Math Level 6 Math Level 7 Math Level 8 Math Level 9 Math Level 10
Math For PreK - K
Prerequisite: NO
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.
Math Level 0
Grades K - 1; Prerequisite: NO
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.
Math Level 1
Grades 1 - 2; Prerequisite: Completion of Math Level 0 or passing a math placement test
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.
Math Level 2
Grades 2 - 3; Prerequisite: Completion of Math Level 1 or passing a math placement test
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.
Math Level 3
Grades 3 - 4; Prerequisite: Completion of Math Level 2 or passing a math placement test
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).
Math 4
Main topics studied in Math 4
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.
Math 5
Main topics studied in Math 5
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. Pythagorean theorem.
Probability.
Binary numbers and operations with them.
Parallel lines, transversal lines, corresponding angles etc.
Congruence tests for triangles.
Math 6
Main topics studied in Math 6
Basic logic (knights and knaves, logic operations).
Set theory basics (basic operations and Venn diagrams).
Linear equations continued. Simple inequalities (Review).
Powers: an am=an+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 of linear equations.
Math 7
Main topics studied in Math 7
Combinatorics: choosing with and without repetitions. Pascal triangle; formulae 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 (using 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
- Plane patterns and symmetries.
- Introduction to Calculus.
Math 8
Main topics studied in Math 8
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 special quadrilaterals, similar triangles, Thales theorem, inscribed angles.
Logic and Truth tables.
Chinese Remainder Theorem.
Fermat's Little Theorem.
Math 9
Main topics studied in Math 9
- 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.
Optional topics
Trigonometry. Trigonometric equations and formulas.
Advanced geometry with vectors: Ceva theorem, Ptolemy theorem, nine point circle.
Math 10
Main topics studied in Math 10
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.