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 Intensive Practice curriculum and Art of Problem Solving’s Beast Academy Practice workbooks.
For students who need more practice, we will supplement with materials from Primary Mathematics, and Extra Practice. For students who need an additional challenge, we will supplement with Singapore 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
| Intensive Practice 1A | |||
|---|---|---|---|
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Numbers 0 to 10 Counting Number Bonds Making Number Stories Addition within 10 Making Addition Stories Addition With Number Bonds
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Subtraction within 10 Making Subtraction Stories Methods of Subtraction Ordinal Numbers Naming Positions
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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
| Intensive Practice 1B + Beast Academy 1 | |||
|---|---|---|---|
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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
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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
| Intensive Practice 2A + Beast Academy 1&2 | Intensive Practice 2B + Beast Academy 1&2 | ||
|---|---|---|---|
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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
| Intensive Practice 3A + Beast Academy 2&3 | Intensive Practice 3B + Beast Academy 2&3 | ||
|---|---|---|---|
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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
| Intensive Practice 4A + Beast Academy 3&4 | Intensive Practice 4B + Beast Academy 3&4 | ||
|---|---|---|---|
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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
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Measures Multiplication Division Symmetry Symmetric Figures Solid Figures Identifying Solid Figures Volume Cubic Units Volume of a Cuboid |
Grade 5
| Intensive Practice 5A + Beast Academy 4&5 | Intensive Practice 5B + Beast Academy 4&5 | ||
|---|---|---|---|
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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, Singapore Math’s Dimensions Math, or 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 | |
|---|---|---|---|
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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 | |
|---|---|---|---|
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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
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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
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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 |