Middle School Math; Main Areas of Study

The math program will follow New York State’s Common Core recommendations.

The list/order of topics below is not absolute; it is liable to change depending on student understanding and mastery. In addition some topics may be supplemented or shortened/omitted.

5th Grade:

Topics for Module 1: Place Value and Decimal Fractions

  1. Multiplicative Patterns on the Place Value Chart
  2. Decimal Fractions and Place Value Patterns
  3. Place Value and Rounding Decimal Fractions
  4. Adding and Subtracting Decimals
  5. Multiplying Decimals
  6. Dividing Decimals

Topics for Module 2: Multi-Digit Whole Number and Decimal Fraction Operations

  1. Mental Strategies for Multi-Digit Whole Number Multiplication
  2. The Standard Algorithm for Multi-Digit Whole Number Multiplication
  3. Decimal Multi-Digit Multiplication
  4. Measurement Word Problems with Whole Number and Decimal Multiplication
  5. Mental Strategies for Multi-Digit Whole Number Division
  6. Partial Quotients and Multi-Digit Whole Number Division
  7. Partial Quotients and Multi-Digit Decimal Division
  8. Measurement Word Problems with Multi-Digit Division

Topics for Module 3: Addition and Subtraction of Fractions

  1. Equivalent Fractions
  2. Making Like Units Pictorially
  3. Making Like Units Numerically
  4. Further Applications

Topics for Module 4: Multiplication and Division of Fractions and Decimal Fractions

  1. Equivalent Fractions
  2. Making Like Units Pictorially
  3. Making Like Units Numerically
  4. Further Applications

Topics for Module 5: Addition and Multiplication with Volume and Area

  1. Concepts of Volume
  2. Volume and the Operations of Multiplication and Addition
  3. Area of Rectangular Figures with Fractional Side Lengths
  4. Drawing, Analysis, and Classification of Two-Dimensional Shapes

Topics for Module 6: Problem Solving with the Coordinate Plane

  1. Coordinate Systems
  2. Patterns in the Coordinate Plane and Graphing Number Patterns from Rules
  3. Drawing Figures in the Coordinate Plane
  4. Problem Solving in the Coordinate Plane
  5. Multi-Step Word Problems

6th Grade:

Topics for Module 1: Ratios and Unit Rates

  1. Representing and Reasoning About Ratios
  2. Collections of Equivalent Ratios
  3. Unit Rates
  4. Percent

Topics for Module 2: Arithmetic Operations Including Division of Fractions

  1. Dividing Fractions by Fractions
  2. Multi-Digit Decimal Operations—Adding, Subtracting, and Multiplying
  3. Dividing Whole Numbers and Decimals
  4. Number Theory—Thinking Logically About Multiplicative Arithmetic

Topics for Module 3: Rational Numbers

  1. Understanding Positive and Negative Numbers on the Number Line
  2. Order and Absolute Value
  3. Rational Numbers and the Coordinate Plane

Topics for Module 4: Expressions and Equations

  1. Relationships of the Operations
  2. Special Notations of Operations
  3. Replacing Letters and Numbers
  4. Expanding, Factoring, and Distributing Expressions
  5. Expressing Operations in Algebraic Form
  6. Writing and Evaluating Expressions and Formulas
  7. Solving Equations
  8. Applications of Equations

Topics for Module 5: Area, Surface Area, and Volume Problems

  1. Area of Triangles, Quadrilaterals, and Polygons
  2. Polygons on the Coordinate Plane
  3. Volume of Right Rectangular Prisms
  4. Nets and Surface Area

Topics for Module 6: Statistics

  1. Understanding Distributions
  2. Summarizing a Distribution that is Approximately Symmetric Using the Mean and Mean Absolute
    Deviation
  3. Summarizing a Distribution that is Skewed Using the Median and the Interquartile Range
  4. Summarizing and Describing Distributions

7th Grade:

Topics for Module 1: Ratios and Unit Rates

  1. Proportional Relationships
  2. Unit Rate and the Constant of Proportionality
  3. Ratios and Rates Involving Fractions
  4. Ratios of Scale Drawings

Topics for Module 2: Rational Numbers

  1. Addition and Subtraction of Integers and Rational Numbers
  2. Multiplication and Division of Integers and Rational Numbers
  3. Applying Operations with Rational Numbers to Expressions and Equations

Topics for Module 3: Expressions and Equations

  1. Use Properties of Operations to Generate Equivalent Expressions
  2. Solve Problems Using Expressions, Equations, and Inequalities
  3. Use Equations and Inequalities to Solve Geometry Problems

Topics for Module 4: Percent and Proportional Relationships

  1. Finding the Whole
  2. Percent Problems Including More than One Whole
  3. Scale Drawings
  4. Population, Mixture, and Counting Problems Involving Percents

Topics for Module 5: Statistics and Probability

  1. Calculating and Interpreting Probabilities
  2. Estimating Probabilities
  3. Random Sampling and Estimated Population Characteristics
  4. Comparing Populations

Topics for Module 6: Geometry

  1. Unknown Angles
  2. Constructing Triangles
  3. Slicing Solids
  4. Problems Involving Area and Surface Area
  5. Problems Involving Volume

8th Grade, Algebra 1:

Topics for Module 1: Relationships between quantities, and reasoning with equations and their graphs

  1. Introduction to functions studied this year – graphing stories
  2. The structure of expressions
  3. Solving inequalities & equations

Topics for Module 2: Descriptive statistics

  1. Shapes and Centers of Distributions
  2. Describing Variability and Comparing Distributions
  3. Categorical Data on Two Variables
  4. Numerical Data on Two Variables

Topics for Module 3: Linear & exponential functions

  1. Linear & exponential sequences
  2. Functions & their graphs
  3. Transformations of functions
  4. Using functions & graphs to solve problems

Topics for Module 4: Polynomials & quadratic expressions, equations, and functions

  1. Quadratic expressions, equations, functions, and their connection to rectangles
  2. Using different forms for quadratic functions
  3. Function transformations and modeling

Topics for Module 5: A synthesis of modeling with equations and functions

  1. Elements of modeling
  2. Completing the modeling cycle