Art of Problem Solving

Our Math I course is designed for students who are comfortable counting to 100, recognize numbers up to 100, and have begun developing fluency with addition and subtraction within 20. In this course, students will build on that foundation by mastering addition and subtraction up to 100—beginning with facts within 10, progressing to 20, and eventually reaching 100—with an emphasis on mental math strategies.

In the second part of this school year long course, students will be introduced to the concepts of multiplication and division, gaining an understanding of equal groups and learning basic facts up to 12. They’ll also explore standard units of measurement, including length, weight, and time, as well as foundational concepts in money, basic fractions, graphs, and two- and three-dimensional shapes.

Rather than relying on rote memorization, this course emphasizes deep conceptual understanding and the development of strong logical thinking and problem-solving skills. Students are encouraged to make connections between topics, apply prior knowledge, and develop confidence in their mathematical reasoning.

Our curriculum follows the Singapore Math approach, a globally respected method known for fostering deep mathematical understanding through problem-solving and logical reasoning.

Math I Topics:

• Numbers to 20: Counting and Comparing; Addition and Subtraction
• Number Bonds & Making Number Stories
• Addition: Making Addition Stories
• Addition With Number Bonds
• Subtraction: Making Subtraction Stories
• Methods of Subtraction
• Ordinal Numbers: Naming Positions
• Shapes: Common Shapes
• Length: Comparing & Measuring
• Weight: Comparing & Measuring
• Graphs: Picture Graphs
• Numbers to 40: Addition and Subtraction
• Adding Three Numbers
• Multiplication: Adding Equal Groups
• Making Multiplication Stories
• Multiplication Within 40
• Division: Sharing and Grouping
• Making Halves and Quarters
• Telling Time
• Numbers to 100: Tens and Ones
• Addition & Subtraction Within 100
• Money: Bills and Coins

Enrollment Guidelines:

• Returning AlphaMinds students who have successfully completed our Logic K class
• New students entering Grade 1
• Kindergarten students who demonstrate proficiency with basic addition and subtraction within 20 and are fluent first-grade-level readers (assessment required; please email info@alphamindsacademy.com)

Our Math II course is designed for students who have a strong command of addition and subtraction up to 100, particularly with mental math, and a solid understanding of place value and repeating patterns. Building on that foundation, students will advance to addition and subtraction up to 1000, with continued emphasis on mental strategies and number sense.

Students will begin learning multiplication tables up to 12 and the corresponding division facts. The course also introduces standard units of length, weight, and capacity in both metric and customary systems, along with the relationships among them. Students will explore fractions—including equivalent fractions and operations with like denominators—as well as money, time, graphs, area, and perimeter.

Throughout the year, students will apply their knowledge to increasingly complex word problems involving multiplication, division, and fractions. They’ll also engage with math-based puzzles and logic challenges designed to build strong critical thinking and problem-solving skills.

This course follows the Singapore Math approach, a globally recognized curriculum known for its emphasis on problem-solving and deep conceptual understanding.

Math II Topics:

• Numbers to 1000: Comparing Numbers
• Hundreds, Tens and Ones
• Addition and Subtraction Addition & Subtraction Without Renaming
• Addition & Subtraction with Renaming
• Multiplication & Division (tables of 2 -10)
• Addition and Subtraction: Finding the Missing Number
• Methods for Mental Addition & Subtraction
• Money: Adding & Subtracting Money
• Fractions: Halves and Quarters; Writing Fractions
• Time: Telling Time & Time Intervals
• Length: Measuring Length in Meters, Centimeters, Yards and Feet, Inches
• Weight: Measuring Weight in Kilograms, Grams, Pounds, Ounces
• Capacity: Comparing Capacity; Liters, Gallons, Quarts, Pints and CupsGraphs: Picture Graphs
• Geometry: Flat and Curved Faces; Making Shapes
• Area: Square Units

Enrollment Guidelines :

• Returning AlphaMinds students who have successfully completed our Math I class  in the previous school year.
• New students are admitted by assessment. Please email info@alphamindsacademy.com to request an assessment.

Our Math III course is designed for students who have confidently mastered addition and subtraction up to 1,000 using both vertical algorithms and mental math strategies; have a solid understanding of place value; know the multiplication table up to 10 and related division facts (with mastery up to 5 as a minimum); possess a basic understanding of fractions; and are comfortable solving simple multi-step word problems involving multiplication and division.

In this course, students will build on these skills by continuing with addition, subtraction, multiplication, and long division by a one-digit number, with a strong emphasis on mental strategies. Students will work with standard units of length, weight, and capacity in both the metric and customary systems, including compound unit operations and conversions between units.

We will deepen students’ understanding of fractions—covering equivalent fractions and performing addition and subtraction with like and unlike denominators—and expand on their knowledge of money, time, and other units of measurement. In geometry, we will move beyond basic shapes to study points, lines, and angles, laying the groundwork for future geometric reasoning.

Throughout the year, students will solve increasingly complex word problems involving multiplication, division, fractions, area, and perimeter. A special emphasis will be placed on developing problem-solving skills through non-routine word problems and mathematical puzzles across various topics.

This course follows the Singapore Math approach, a globally recognized curriculum known for its emphasis on problem-solving and deep conceptual understanding.

Math III Topics:

• Numbers to 10,000
  • Thousands, Hundreds, Tens and Ones
  • Numbers Patterns
• Addition and Subtraction within 10,000
• Multiplying Ones, Tens and Hundreds
• Quotient and Remainder
• Dividing Hundreds, Tens and Ones
• Multiplication Tables of 6, 7, 8 and 9
• Money (U.S. currency) Dollars and Cents

• Mental Calculation
  • Addition
  • Subtraction
  • Multiplication
  • Division
• Length
  • Meters and Centimeters
  • Kilometers
  • Yards, Feet, and Inches
  • Miles
• Weight
  • Kilograms and Grams
  • Pounds and Ounces
• Capacity
  • Liters and Milliliters
  • Gallons, Quarts, Pints, and Cups
• Graphs
  • Bar Graphs
• Fractions
  • Fraction of a Whole
  • Equivalent Fractions
• Time
  • Hours and Minutes
  • Other Units of Time
• Geometry
  • Angles
  • Right Angles
• Area and Perimeter
  • Area
  • Perimeter
  • Area of a Rectangle

Enrollment Guidelines:

• Returning AlphaMinds students who have successfully completed our Math II class in the previous school year.
• New students are admitted by assessment. Please email info@alphamindsacademy.com to request an assessment.

Our Math IV course is designed for students with a solid foundation in fractions and decimals, including operations with unlike denominators and introductory work with decimal multiplication and division. This course builds on those skills through more advanced applications, including multi-step word problems involving percents, fractions, ratios, and rates. Students will deepen their understanding of geometry through work with triangles, quadrilaterals, area, and perimeter, while also being introduced to special topics such as Pascal’s Triangle and basic probability. The course emphasizes logical thinking, creative problem solving, and real-world applications across a broad range of mathematical concepts.

This course follows the Singapore Math approach—an internationally acclaimed method known for its emphasis on deep conceptual understanding, problem solving, and number sense.

• Whole NumbersNumbers to 100,000
  • Rounding off Numbers
  • Factors
  • Multiples
• Multiplication and Division of Whole Numbers
  • Multiplication by a 1-digit Number
  • Division by a 1-digit Number and by 10
  • Multiplication by a 2-digit Number
• Fractions
  • Adding Fractions
  • Subtracting Fractions
  • Mixed Numbers
  • Improper Fractions
  • Fraction of a Set

• Decimals (thens, hundreds, thousands, rounding off)

• The Four Operations of Decimals
  • Addition and Subtraction
  • Multiplication
  • Division
• Tables and Graphs: Presenting Data
• Angles: Measuring Angles
• Perpendicular and Parallel Lines
• Area and Perimeter
• Measures (using multiplication and division)
• Symmetry & Symmetric Figures
• Solid Figures
• Volume

Enrollment Guidelines:

• • Returning AlphaMinds students who have successfully completed our Math III class in the previous school year.
  • New students are admitted by assessment. Please email info@alphamindsacademy.com to request an assessment.

Our Math V course  is is designed for students who have a solid foundation in working with fractions and decimals, including addition and subtraction of fractions with different denominators and multiplication and division of decimals by a whole number. We will continue with multiplication and division of fractions and mixed numbers, multiplication and division of decimals, order of operations, percentage and the connection of percent-fraction-decimals. Students will be solving word problems of increasing level of challenge involving fractions and percents, ratio and rate, triangle and quadrilateral geometry, more complex area, perimeter and volume problems.

Students will also engage in solving non-routine word problems and logic puzzles, applying math concepts in creative and challenging ways across various domains.

This course follows the Singapore Math approach—an internationally acclaimed method known for its emphasis on deep conceptual understanding, problem solving, and number sense.

List of Topics Covered in Math V (September – June) :

• Whole Numbers
• Place Values
• Millions
• Approximation and Estimation
• Multiplying and Dividing by Tens, Hundreds or Thousands
• Order of Operations
• Multiplication and Division by a 2-digit Whole Number
• Fractions
  • Fraction and Division
  • Addition and Subtraction of Unlike Fractions
  • Addition and Subtraction of Mixed Numbers
  • Product of a Fraction and a Whole Number
  • Product of Fractions
  • Dividing a Fraction by a Whole NumberArea of Triangle
• Ratios
• Decimals
  • Approximation and Estimation
  • Multiplication by Tens, Hundreds or Thousands
  • Division by Tens, Hundreds or Thousands
  • Multiplying by a 2-digit Whole Number
  • Conversion of Measurements
• Percentage
• Average
• Rate
• Graphs: Line Graphs
• Triangles
• 4-sided Figures
  • Parallelogram, Rhombuses and Trapezoids
  • Drawing Parallelograms and Rhombuses

• Volume
  • Cubes and Cuboids
  • Finding the Volume of a Solid
• Tessellations: Tiling Patterns

Enrollment Guidelines:

• • Returning AlphaMinds students who have successfully completed our Math IV class in the previous school year.
  • New students are admitted by assessment. Please email info@alphamindsacademy.com to request an assessment.

Geometry – Year I Course: Introduction to Geometry

This is the first year of a comprehensive two-year Geometry course that covers the full scope of high school geometry. Meeting once per week over 32 weeks, this course emphasizes the study of properties and applications of two- and three-dimensional geometric figures.

Students will explore key geometric concepts through a combination of visual reasoning, logical deduction, and real-world problem solving. Inductive and deductive thinking are emphasized, along with foundational proof-writing techniques used to establish the properties of geometric figures. This course also introduces basic right triangle trigonometry and geometric transformations.

Topics Covered Include:

• • Points, lines, planes, and angles: definitions, postulates, and relationships
  • Angle relationships with parallel lines and transversals
  • Triangle congruence: SSS, SAS, ASA, AAS and corresponding parts
  • Perimeter and area of two-dimensional shapes
  • Similar figures: ratios, proportions, and similar triangles
  • Right triangles and the Pythagorean Theorem
  • Quadrilaterals and special parallelograms

Recommended For:

• Returning AlphaMinds students who have successfully completed our Math MS I course or higher
• New students in grades 7–9 who have completed a Pre-Algebra course or higher.  New students are encouraged to take our placement assessment to ensure proper placement. Please email us at info@alphamindsacademy.com to request the test.

Our Math MS I (Pre-Algebra) course is designed for students who have a deep understanding of foundational number concepts and are confident working with whole numbers, fractions, decimals, and percents—including the relationships among them.

This course focuses on applying these core concepts to real-world situations through increasingly complex word problems. Students will learn key problem-solving strategies and explore mathematical patterns in a fun, creative, and intellectually engaging environment. This class aims to develop flexible thinking and strengthen students’ ability to translate real-life scenarios into mathematical expressions and equations.

In addition to reinforcing school-based concepts, this course introduces new content that deepens number sense and prepares students for pre-algebra.

Topics Covered Include:

• Prime factorization, Least Common Multiple (LCM), and Greatest Common Divisor (GCD)
• Fractions, decimals, and approximation
• Percent, rate, and ratio applications
• Operations with negative numbers and absolute value
• Algebraic properties: commutative, associative, and distributive laws
• Algebraic expressions and one-variable equations
• Translating word problems into algebraic equations and solving them
• Speed, rate, and proportional reasoning
• Introduction to geometry: area and circumference of a circle, triangle and quadrilateral properties, complex area, perimeter, and volume problems

Enrollment Guidelines:

• Returning AlphaMinds students who have successfully completed our Math V course in the previous school year.
• New students in grades 6–8 who have not yet taken a Pre-Algebra course.  New students are admitted by assessment. Please email info@alphamindsacademy.com to request an assessment.

Our Math MS II (Introduction to Algebra I) course is designed for students who have a strong foundation in Algebra and are ready to expand their skills with more advanced topics in algebra, introductory geometry, and logical problem solving. This course reinforces core algebraic principles while introducing more complex equations, functions, and geometric reasoning. Students will also encounter enrichment topics that deepen mathematical thinking and support success in competitive academic settings.

Topics covered include:

• Indices (Exponents)
• Radicals and rational expressions
• Algebraic manipulations and transformations
• Literal and quadratic equations (including completing the square and the quadratic formula)
• Absolute value equations and inequalities
• Fractional equations and inequalities
• Simultaneous linear equations
• Compound and system-based inequalities
• Rate, ratio, and percentage, including financial transaction problems
• Functions, sequences, and series
• Coordinate geometry: equations of circles, forming equations, parallel lines and angles
• Triangle geometry, congruence, and similarity
• Enrichment topics: Mathematical induction, combinatorics, Fibonacci sequence, and logical games

Throughout the course, students will develop logical reasoning, improve their problem-solving strategies, and gain confidence in working with multi-step word problems and abstract mathematical concepts. This course also helps prepare students for entrance exams to selective high schools.

Enrollment Guidelines:

• Returning AlphaMinds students who have successfully completed Math MS I course in the previous school year.
• New students are admitted by assessment. Please email info@alphamindsacademy.com to request an assessment.

Our Math MS III (Algebra I) course is a comprehensive Algebra I course that builds and expans on students’ prior knowledge of algebraic concepts. The course focuses on developing fluency with algebraic expressions and equations while deepening understanding of linear, quadratic, and polynomial functions. Emphasis is placed on problem-solving strategies, multi-step word problems, and real-world applications to promote strong mathematical reasoning and confidence.

Topics covered in this course include:

• Solving equations and absolute value equations
• Solving linear inequalities and compound inequalities
• Graphing linear functions and writing equations in multiple forms
• Modeling real-world contexts with linear equations
• Solving systems of equations (2 and 3 variables) and related word problems
• Factoring: trinomials (a = 1 and a > 1), special cases, grouping
• Solving quadratic equations by factoring, completing the square, and using the quadratic formula
• Working with polynomials: operations, long division, and synthetic division
• Exploring polynomial functions and writing equations from given points
• Radical expressions: simplifying and multiplying

This course equips students with the skills and confidence needed for success in advanced math classes, standardized tests, and real-world problem solving.

Enrollment Guidelines:

• Returning AlphaMinds students who have successfully completed Math MS II course in the previous school year.
• New students are admitted by assessment. Please email info@alphamindsacademy.com to request an assessment.

Our Math MS IV (Advanced Algebra I / Intro To Algebra II) course is the culmination of our Algebra I program and bridges into key Algebra II topics, offering students a deeper and more comprehensive understanding of algebraic and geometric concepts. Designed for advanced middle schoolers, this class challenges students with higher-level material and prepares them for future success in advanced mathematics.

Students will review and extend their knowledge of linear and quadratic functions, systems of equations, and factoring, while also exploring more complex topics such as rational and radical expressions, conic sections, and polynomial functions. This course emphasizes both conceptual understanding and practical application through real-world problems and multi-step exercises.

Math MS IV Topics Include:

• Linear Functions Review
• Writing the Equation of Lines
• Systems of Two Equations
• Solving Systems of Three Variables (with Elimination and Word Problems)
• Characteristics of Quadratic Functions
• Graphing Quadratic Functions (All Forms)
• Real-World Applications of Quadratics
• Factoring Polynomials
• Solving Quadratic and Nonlinear Equations
• Operating with Rational Expressions
• Complex Numbers and Complex Fractions
• Radical Expressions and Equations
• Writing Polynomial Functions
• Graphing and Writing Equations for: Circles, Ellipses, Hyperbolas
• Transformations of Quadratic and Absolute Value Functions

Enrollment Guidelines:

• Returning AlphaMinds Students who have successfully completed our Math MS III course in the previous school year
• New students are admitted by assessment. Please email info@alphamindsacademy.com to request an assessment prior to enrollment.

Our Math HS I (Advanced Algebra II / Introduction to Pre-Calculus) course is a rigorous course designed for students who are ready to move beyond Algebra I and dive into the deeper and more complex world of advanced mathematics. Building on the foundation established in earlier courses, this class blends advanced Algebra II with a wide range of Pre-Calculus topics to prepare students for future coursework in Calculus, physics, engineering, and beyond.

Students will develop fluency with exponential and logarithmic functions, strengthen their trigonometry skills, and explore key concepts in analytical geometry, vectors, and matrices. The course also introduces students to the fundamental principles of calculus, such as limits, continuity, basic differentiation, and integration—providing a head start on AP or college-level courses.

Through a mix of problem-solving, graphing, and real-world applications, students will build both the conceptual understanding and technical skills necessary for success in advanced math.

Enrollment Guidelines:

Returning AlphaMinds students who have successfully completed our Math MS IV class during the previous school year.

• • New Students are admitted by assessment. To request an assessment, please email us at info@alphamindsacademy.com.

Our Math HS I (Advanced Algebra II / Introduction to Pre-Calculus) course is a rigorous course designed for students who are ready to move beyond Algebra I and dive into the deeper and more complex world of advanced mathematics. Building on the foundation established in earlier courses, this class blends advanced Algebra II with a wide range of Pre-Calculus topics to prepare students for future coursework in Calculus, physics, engineering, and beyond.

Students will develop fluency with exponential and logarithmic functions, strengthen their trigonometry skills, and explore key concepts in analytical geometry, vectors, and matrices. The course also introduces students to the fundamental principles of calculus, such as limits, continuity, basic differentiation, and integration—providing a head start on AP or college-level courses.

Through a mix of problem-solving, graphing, and real-world applications, students will build both the conceptual understanding and technical skills necessary for success in advanced math.

Enrollment Guidelines:

Returning AlphaMinds students who have successfully completed our Math MS IV class during the previous school year.

• • New Students are admitted by assessment. To request an assessment, please email us at info@alphamindsacademy.com.

Our Math HS II – Intro to Calculus course is designed to introduce students to the foundational concepts of Calculus, building a bridge between Pre-Calculus and college-level Calculus. Through a combination of theory, problem-solving, and real-world applications, students will explore the core ideas of limits, derivatives, and integrals—equipping them with the tools and confidence needed for advanced math studies.

Course Topics Include:

• Limits and Continuity: Understanding the behavior of functions at specific points and over intervals.
• Derivatives: Learning how to compute and interpret derivatives, including the rules of differentiation, applications in motion, optimization, and graph analysis.
• Integrals: Exploring the concept of area under a curve, antiderivatives, and basic techniques of integration.
• Applications of Calculus: Solving real-world problems involving rates of change, area, and accumulated quantities.
• Introduction to Differential Equations: Simple separable equations and their applications.
• Review of Essential Pre-Calculus Topics: Reinforcement of key algebraic and trigonometric skills as needed.

Course Highlights:

• Deepen mathematical thinking and analytical reasoning
• Prepare for AP Calculus or college-level Calculus
• Hands-on practice with conceptual and applied problems
• Supportive environment with individualized guidance

Enrollment Guidelines:

• Returning AlphaMinds students who have completed our Math HS I course
• New students with strong backgrounds in Algebra II and Pre-Calculus (assessment required—please email info@alphamindsacademy.com)