The Power of Math: A Tool for Learning How to Think

Our approach to math values deep, conceptual understanding over rote memorization and analytical/critical thinking over algorithmic thinking. Our program also emphasizes learning through play, hands-on investigations, the use of manipulatives, and math club logic problems. We want our students to experience math as relevant, approachable, and engaging. 

Some highlights of our program:

  • Subject Expert Teachers: Students will be taught by talented teachers who specialize in teaching math at the elementary and middle school levels, not general education teachers. 
  • Leveled classes: Students will be taught in small groups split by level (not by age). Levels will cover similar topics but at varying degrees of difficulty. The pacing and depth will vary based on student ability. Stronger classes will supplement the topic with challenging Olympiad-style problems.
  • Logic: In addition to 5 periods of math, students in grades K-5 will have an additional period devoted to non-standard problems, logic puzzles and hands-on toys and games. Students will be exposed to (not an exhaustive list): counting principles, Fencepost problems, combinatorics, the pigeonhole principle, Venn diagrams, set theory, spatial reasoning, tiling problems, etc. To enhance learning, students will have access to manipulatives, including: Tangrams, Pentominoes, Geoblocks, Soma Cube (Кубики для всех) , and Сложи Узор; games including: SET, Mastermind, Chocolate Fix, Rush Hour, and Blokus; and materials from ReshiPeshi, Mousematics (Zhenya Katz), and other logic/developmental-math sources.
  • Middle School Math Offerings: Students in grades 6-8 will also have a total of 6 periods of math/week. This is split into 4 periods of Algebra and 2 periods of: 2D Geometry (first quarter), Combinatorics/Probability (second quarter), 3D Geometry (third quarter), and Statistics (fourth quarter).
  • Math Team: We are excited to make math team available as an after-school club for grades 3-8, and as a Period 0 club for grades 6-8. Math team will give interested students an opportunity to delve deeply into the rich mathematical topics found on the Math Kangaroo (for grades 1-8), Noetic (for grades 2-8), New England Math League (for grades 4-8), MOEMS (for grades 4-8), IMLEM (for grades 6-8), MathCounts (for grades 6-8) and AMC8 (for grades 6-8) competitions.
  • Deep Dives: To show our students that math is much more than what’s found in the textbook, we will regularly make time for deep dives into extra-curricular math topics, such as: fractals, infinity, Fibonacci numbers, cryptography, game theory, graph theory. Teachers can create deep dives based on their own interests and passions, as well as on the interests and requests of the students. Some of these deep-dives may lead to symposiums where middle school students will be allowed to work in small groups or individually to explore a topic of interest to them, and then to present their deep-dives to the class and to the school community.

Grades K-Grade 5

The backbone of our elementary math program will be Singapore Math’s Primary Mathematics curriculum and Art of Problem Solving’s Beast Academy Practice workbooks. 

For students who need more practice, we will supplement with materials from Singapore Math’s Extra Practice Workbooks.  For students who need an additional challenge, we will supplement with Singapore’s Intensive Practice Workbooks, and Challenging Word Problems, and math competition practice from Math Kangaroo, Noetic and (for upper elementary) NEML and MOEMS. This differentiated approach will allow us to cater to a wide range of abilities in each grade level. 

Singapore Math adheres to the CPA (Concrete->Pictorial->Abstract) approach which starts by allowing kids to manipulate concrete objects (counters, ten-blocks), then abstracts into the pictorial, and finally heads to the completely abstract world of mathematical symbols. Some other key features of Singapore Math are number bonds, bar modeling, and mental math.

Beast Academy focuses on developing conceptual understanding, so that students always understand the Why and How of what they’re learning. The workbooks present multiple strategies to inspire lateral thinking and are full of unusual and challenging problems for each topic.

Exceptional fifth and sixth graders who have completed the Primary Mathematics and Beast Academy curriculum will start on Art of Problem Solving’s Prealgebra textbook.

 

Kindergarten

Singapore Primary Mathematics 1A  

Numbers 0 to 10

Counting

Number Bonds

Making Number Stories

Addition within 10

Making Addition Stories

Addition With Number Bonds

 

Subtraction within 10

Making Subtraction Stories

Methods of Subtraction

Ordinal Numbers

Naming Positions

 

 

Numbers to 20

Counting and Comparing

Addition and Subtraction within 20

Shapes

Common Shapes

Length

Comparing Length

Measuring Length

Weight

Comparing Weight

Measuring Weight

Grade 1

Singapore Math 1B + Beast Academy 1 

 

Comparing Numbers

Comparing Numbers

Comparison by Subtraction

Numbers to 40

Counting

Tens and Ones

Addition and Subtraction

Adding Three Numbers

Multiplication

Adding Equal Groups

Making Multiplication Stories

Multiplication Within 40

Division

Sharing and Grouping

 

 

Graphs

Picture Graphs

Halves and Quarters

Making Halves and Quarters

Time

Telling Time

Numbers to 100

Tens and Ones

Order of Numbers

Addition Within 100

Subtraction Within 100

Money

Bills and Coins (U.S. currency)

Shopping

Grade 2

Singapore Math 2A   +   Beast Academy 1&2 Singapore Math 2B   +   Beast Academy 1&2

Numbers to 1000

Comparing Numbers

Hundreds, Tens and Ones

Addition and Subtraction

Meanings of Addition and Subtraction

Addition Without Renaming

Subtraction Without Renaming

Addition With Renaming

Subtraction With Renaming

Length

Measuring Length in Meters

Measuring Length in Centimeters

Measuring Length in Yards and Feet

Measuring Length in Inches

Weight

Measuring Weight in Kilograms

Measuring Weight in Grams

Measuring Weight in Pounds

Measuring Weight in Ounces

Multiplication and Division

Multiplication

Division

Multiplication Tables of 2 and 3

Multiplication Table of 2

Multiplication Table of 3

Dividing by 2

Dividing by 3

Addition and Subtraction

Finding the Missing Number

Methods for Mental Addition

Methods for Mental Subtraction

Multiplication and Division

Multiplying and Dividing by 4

Multiplying and Dividing by 5

Multiplying and Dividing by 10

Money (U.S. Currency)

Dollars and Cents

Adding Money

Subtracting Money

Fractions

Halves and Quarters

Writing Fractions

Time

Telling Time

Time Intervals

Capacity

Comparing Capacity

Liters

Gallons, Quarts, Pints and Cups

Graphs

Picture Graphs

Geometry

Flat and Curved Faces

Making Shapes

Area

Square Units

Grade 3 

Singapore Math 3A   +   Beast Academy 2&3 Singapore Math 3B   +   Beast Academy 2&3

Numbers to 10,000

Thousands, Hundreds, Tens and Ones

Numbers Patterns

Addition and Subtraction

Sum and Difference

Add Ones, Tens, Hundreds and Thousands

Two-step Word Problems

Multiplication and Division

by 2, 3, 4, 5, and 10

Looking Back

More Word Problems

Multiplying Ones, Tens and Hundreds

Quotient and Remainder

Dividing Hundreds, Tens and Ones

Multiplication Tables of 6, 7, 8 and 9

Looking Back

Multiplying and Dividing by 6

Multiplying and Dividing by 7

Multiplying and Dividing by 8

Multiplying and Dividing by 9

 

Money (U.S. currency)

Dollars and Cents

Addition

Subtraction

Mental Calculation

Addition

Subtraction

Multiplication

Division

Length

Meters and Centimeters

Kilometers

Yards, Feet and Inches

Miles

Weight

Kilograms and Grams

More Word Problems

Pounds and Ounces

Capacity

Liters and Milliliters

Gallons, Quarts, Pints and Cups

Graphs

Bar Graphs

Fractions

Fraction of a Whole

Equivalent Fractions

Times

Hours and Minutes

Other Units of Time

Geometry

Angles

Right Angles

Area and Perimeter

Area

Perimeter

Grade 4

Singapore Math 4A   +   Beast Academy 3&4 Singapore Math 4B   +   Beast Academy 3&4

Whole Numbers

Numbers 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

Tables and Graphs

Presenting Data

Angles

Measuring Angles

Perpendicular and Parallel Lines

Perpendicular Lines

Parallel Lines

Area and Perimeter

Rectangles and Squares

Composite Figures

Decimals

Tenths

Hundredths

Thousandths

Rounding off

The Four Operations of Decimals

Addition and Subtraction

Multiplication

Division

 

Measures

Multiplication

Division

Symmetry

Symmetric Figures

Solid Figures

Identifying Solid Figures

Volume

Cubic Units

Volume of a Cuboid

Grade 5

Singapore Math 5A    +   Beast Academy 4&5 Singapore math 5B    +   Beast Academy 4&5

Whole Numbers

Place Values

Millions

Approximation and Estimation

Multiplying by Tens, Hundreds or Thousands

Dividing by Tens, Hundreds or Thousands

Order of Operations

Word Problems

Multiplication and Division by a 2-digit Whole Number

Multiplication

Division

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 Number

Word Problems

Area of Triangle

Finding the Area of a Triangle

Ratio

Finding Ratio

Equivalent Ratios

Comparing Three Quantities

Angles

Measuring Angles

Finding Unknown Angles

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

Percent

Writing Fractions as Percentage

Percentage of a Quantity

Average

Average

Rate

Rate

Graphs

Line Graphs

Triangles

Sum of Angles of a Triangle

Isosceles and Equilateral Triangles

Drawing Triangles

4-sided Figures

Parallelogram, Rhombuses and Trapezoids

Drawing Parallelograms and Rhombuses

Tessellations

Tiling Patterns

Volume

Cubes and Cuboids

Finding the Volume of a Solid

 

Grades 6–Grade 8

Grade 6 will use All Things Algebra and Art of Problem Solving textbooks, depending on level. For students who need an additional challenge, we will supplement with math competition practice from the above listed math competitions, as well as IMLEM, MathCounts and AMC8.

Starting in grade 6, math class will be split into 4 periods of Algebra and 2 periods of either Geometry (first quarter), Combinatorics/Probability (second quarter), 3D Geometry (third quarter), or Statistics (fourth quarter).

 

Grade 6

Algebra Geometry Probability and Statistics

Negative Numbers

Positive and Negative Numbers

Comparing Positive and Negative Numbers

Operations with Integers

Algebraic Expressions

Writing and Evaluating Algebraic Expressions

Simplifying Algebraic Expressions

Equations and Inequalities

Equations

Inequalities

Whole Numbers

Order of Operations

Factors and Multiples

Multiplication

Division

Decimals

Addition and Subtraction of Decimals

Multiplication of Decimals

Division of Decimals

Metric Measurements and Decimals

Fractions

Multiplication

Division

Order of Operations

Word Problems

Ratio

Ratio and Fraction

Ratio and Proportion

Changing Ratios

Rate

Average and Rate

Unit Rate

Speed

Average Speed

Percentage

Part of a Whole as a Percentage

One Quantity as a Percentage of Another

Solving Percentage Problems by Unitary Method

More Challenging Word Problems

Whole Numbers and Decimals

Fractions

Ratio

Percentage

Speed

Coordinates and Graphs

The Coordinate Plane

Distance between Coordinate Pairs

Changes in Quantities

Solid Figures

Drawing Solid Figures

Nets

Circles

Radius and Diameter

Circumference

Area

Volume

Solving Problems

Triangles and 4-sided Figures

Finding Unknown Angles

What is a Statistical Question?

Statistical Questions About One Variable Regarding Small, Well-Defined Groups

Collecting Data

Surveys, Observations, and Simple Experiments

Types of Variables (Categorical or Quantitative)

Data Displays

Tables

Pictograms

Dot Plots

Bar Graphs

Pie Graphs

Grade 7

Algebra Geometry Probability and Statistics

Factors and Multiples

Factors and Multiples

Prime Factorization and Exponential Notation

Greatest Common Factor (GCF)

Least Common Multiple (LCM)

Square Roots and Cube Roots

Real Numbers

Idea of Negative Numbers and the Number Line

Addition and Additive Inverse

Subtraction and Absolute Value of the Difference

Multiplication, Division, and Combined Operations of Integers

Rational Numbers

Real Numbers and Use of Calculators

Rounding Numbers to Decimal Places

Introduction to Algebra

The Use of Letters in Algebra

Evaluation of Algebraic Expressions and Formulas

Writing Algebraic Expressions to Represent Real-world Situations

Algebraic Manipulation

Like Terms and Unlike Terms

Distributive Law, Addition and Subtraction of Linear Algebraic Expressions

Simplification of Linear Algebraic Expressions

Factorization by Extracting Common Factors

Factorization by Grouping Terms

Simple Equations in One Variable

Simple Linear Equations in One Variable

Equations Involving Parentheses

Simple Fractional Equations

Forming Linear Equations to Solve Problems

Ratio, Rate, and Speed

Ratios Involving Rational Numbers

Average Rate

Speed

Percentage

Meaning of Percentage

Reverse Percentages

Percentage Increase and Decrease

Discount and Sales Tax

Number Patterns

Number Patterns and Sequences

General Term of a Sequence

Coordinates and Linear Graphs

Cartesian Coordinate System

Linear Graphs

Slopes of Linear Graphs

Inequalities

Solving Simple Inequalities

More Properties of Inequalities

Simple Linear Inequalities

Application of Simple Inequalities

 

Angles, Triangles, and Quadrilaterals

Points, Lines, and Planes

Angles

Perpendicular Bisectors and Angle Bisectors

Triangles

Quadrilaterals

Perimeters and Areas of Plane Figures

Perimeters and Areas of a Square, a Rectangle, and a Triangle

Circumference and Area of a Circle

Area of a Parallelogram

Area of a Trapezoid

Perimeters and Areas of Composite

Volumes and Surface Areas of Solids

Volumes and Total Surface Areas of a Cube and a Cuboid

Volume and Total Surface Area of a Prism

Volumes and Surface Areas of Composite Solids

Proportions

Scale Drawing

Map Scale and Calculation of Area

Direct Proportion

Inverse Proportion

 

Distributions

Measures of Center: Mean, Median, and Mode

Measures of Variability: Minimum, Maximum, Quartiles, Interquartile Range, Mean Absolute Difference

Shape

Data Analysis

Comparing Two Groups Using Distributions

Association Between Two Variables

Probability of Simple Events

Set Notation

The Meaning of Probability

Sample Space

Probability of Combined Events

Probability of Simple Combined Events

The Meaning of Probability

Independent Events

Further Probabilities

Grade 8

Algebra Geometry Probability and Statistics
Exponents and Scientific Notation

Positive Exponents and the Laws of Exponents

Zero and Negative Integer Exponents

Fractional Exponents

Comparing Exponents

Scientific Notation

Rounding Numbers to a Specified Number of Significant Figures

Estimations and Accuracy of Calculators

Linear Equations in Two Variables

Linear Equations in Two Variables

Solving Simultaneous Linear Equations in Two Variables using the Graphical Method

Solving Simultaneous Linear Equations in Two Variables using the Substitution Method

Solving Simultaneous Linear Equations in Two Variables using the Elimination Method

Solving Problems using Simultaneous Equations

Expansion and Factorization of Algebraic Expressions

Expansion of the Products of Algebraic Expressions

Special Products More Properties of Inequalities

Factorization by using Special Products of Algebraic Expressions

Quadratic Factorization and Equations

Factorization of ax^2 + bx +c

Solving Quadratic Equations by Factorization

Problem Solving Involving Quadratic Equations

Simple Algebraic Fractions

Simplifying Simple Algebraic Fractions

Multiplication and Division of Algebraic Fractions

Addition and Subtraction of Algebraic Fractions

Fractional Equations

More about Formulas

Graphs of Linear and Quadratic Functions

Linear Function

Graphs of Quadratic Functions

Graphs in Practical Situations

Tables, Charts and Graphs

Distance-Time Graphs

More About Quadratic Equations

Solving Quadratic Equations by Factorization

Completing the Square Method

Quadratic Formula

Graphical Method

Applications of Quadratic Equations

Congruence and Reflections

Congruence and Reflections

Translations, Rotations and Combining Transformations

Similarity

Enlargements and Similarity

Parallel Lines and Angles in Triangles and Polygons

Angles formed by Parallel Lines and Transversals

Interior and Exterior Angles of a Triangle

Angles Properties of Special Quadrilaterals

Polygons

Pythagorean Theorem

Pythagorean Theorem

The Converse of Pythagorean Theorem

Applications of Pythagoras Theorem

Coordinate Geometry

Distance Between Two Points

Slope of a Straight Line

Equation of a Straight Line

Mensuration of Pyramids, Cylinders, Cones and Spheres

Pyramids

Cylinders

Cones

Spheres

Understanding Data

Collecting and organizing data

Samples and Populations

Understanding Sample to Sample Variability

Limitations of Sample Information

Data Displays

Box-and-Whisker Plots

Line Graphs

Plotting Two Variables Simultaneously

Data Analysis

Measures of Correlation

Comparison of Conditional Proportions Across Categorical Variables