New Jersey Mathematics — Grade 6
Comprehensive Course Syllabus
Course Overview
Our New Jersey Grade 6 Mathematics course is designed around the New Jersey Student Learning Standards for Mathematics (NJSLS-M). Grade 6 marks an important transition from elementary mathematics to middle-school mathematics, with major emphasis on ratios and proportional relationships, the rational number system, algebraic expressions, equations and inequalities, geometry, and statistics.
Students develop stronger mathematical reasoning and learn to connect numbers, ratios, equations, graphs, geometry, data, and real-world applications.
Ratios & Ratio Reasoning
Understanding Ratios
Students learn to describe relationships between two quantities using ratios and appropriate ratio language.
Equivalent Ratios
Students create equivalent ratios and use tables, diagrams, and other representations to compare quantities.
Unit Rates
Students understand unit rates and use them to compare prices, speeds, quantities, and other real-world relationships.
Ratio Tables
Students create and interpret ratio tables to find missing values and identify relationships between quantities.
Ratio Diagrams
Students use tape diagrams and double number lines to represent and solve ratio problems.
Fractions & Rational Numbers
Dividing Fractions
Students extend their understanding of fractions to divide fractions by fractions using visual models, equations, and reasoning.
Positive & Negative Numbers
Students understand positive and negative numbers and their relationship to zero on a number line.
Rational Numbers
Students identify integers, fractions, and decimals as rational numbers and represent them in different forms.
Comparing Rational Numbers
Students compare and order rational numbers using number lines, inequalities, and mathematical reasoning.
Absolute Value
Students understand absolute value as distance from zero and apply it to mathematical and real-world problems.
Operations With Rational Numbers
Adding Rational Numbers
Students add positive and negative rational numbers using number lines, models, and mathematical rules.
Subtracting Rational Numbers
Students subtract rational numbers and understand subtraction as adding the opposite.
Multiplying Rational Numbers
Students multiply rational numbers and determine the sign of the resulting product.
Dividing Rational Numbers
Students divide rational numbers and apply appropriate strategies to solve real-world problems.
Order of Operations
Students evaluate numerical expressions involving multiple operations and grouping symbols.
Factors, Multiples & Numerical Reasoning
Greatest Common Factor
Students find the greatest common factor of whole numbers and apply it to mathematical problems.
Least Common Multiple
Students find the least common multiple of whole numbers and use it to solve problems involving repeated patterns.
Prime Factorization
Students break numbers into prime factors and use factorization to understand numerical relationships.
Distributive Property
Students use the distributive property to rewrite and simplify numerical expressions.
Numerical Structure
Students identify patterns and relationships within numerical expressions to develop efficient problem-solving strategies.
Algebraic Expressions
Variables
Students use variables to represent unknown or changing quantities in mathematical expressions.
Writing Algebraic Expressions
Students translate verbal descriptions and real-world situations into algebraic expressions.
Evaluating Expressions
Students substitute values for variables and calculate the value of algebraic expressions.
Equivalent Expressions
Students use properties of operations to create and recognize equivalent algebraic expressions.
Combining Like Terms
Students simplify basic algebraic expressions by identifying and combining like terms.
Equations & Inequalities
Understanding Equations
Students understand an equation as a statement that two expressions have equal values.
One-Step Equations
Students solve one-step equations using addition, subtraction, multiplication, or division.
Two-Step Equations
Students solve equations requiring multiple operations and explain the steps used.
Inequalities
Students understand and solve simple one-variable inequalities and represent their solutions on number lines.
Checking Solutions
Students substitute solutions into equations or inequalities to verify whether they are correct.
Variables, Relationships & Graphs
Dependent & Independent Variables
Students identify variables that change independently and variables whose values depend on other quantities.
Input & Output
Students examine how one quantity changes in response to another quantity using tables and equations.
Tables of Values
Students organize related quantities in tables and identify mathematical relationships.
Graphing Relationships
Students represent relationships between variables using coordinate graphs.
Real-World Relationships
Students use equations, tables, and graphs to represent situations involving quantities that change together.
Geometry – Area, Surface Area & Volume
Area of Polygons
Students calculate the area of rectangles, triangles, and other polygons using appropriate formulas and decomposition.
Area of Composite Figures
Students divide complex figures into simpler shapes to determine total area.
Surface Area
Students calculate the surface area of three-dimensional figures using nets, formulas, and geometric reasoning.
Volume
Students calculate the volume of rectangular prisms and other appropriate three-dimensional figures.
Real-World Geometry
Students apply area, surface area, and volume concepts to practical problems involving construction, packaging, design, and measurement.
Coordinate Geometry
Coordinate Plane
Students use coordinate planes to locate points and understand relationships between horizontal and vertical positions.
Four Quadrants
Students explore all four quadrants of the coordinate plane and work with positive and negative coordinates.
Plotting Ordered Pairs
Students plot and identify points using ordered pairs.
Geometric Figures on Coordinate Planes
Students use coordinates to represent and analyze geometric figures.
Distance & Geometry Applications
Students use coordinate information to solve appropriate distance, area, and geometric reasoning problems.
Statistics & Data Analysis
Statistical Questions
Students distinguish between questions that produce variable data and questions with a single predictable answer.
Data Collection
Students learn how data can be collected through surveys, observations, measurements, and other methods.
Data Distributions
Students organize and analyze data distributions to identify patterns and important characteristics.
Center of a Data Set
Students understand and calculate measures such as mean and median and use them to describe data.
Spread & Variability
Students explore how data values vary and use measures such as range to describe the spread of data.
Data Visualization & Interpretation
Dot Plots
Students create and interpret dot plots to represent numerical data.
Histograms
Students organize numerical data into intervals and use histograms to examine distributions.
Box Plots
Students develop an introductory understanding of box plots and use them to describe data distributions.
Comparing Data Sets
Students compare distributions using center, spread, clusters, gaps, peaks, and other characteristics.
Data-Based Conclusions
Students use evidence from data representations to make reasonable conclusions and communicate findings.
Mathematical Reasoning & Applications
Multi-Step Problem Solving
Students solve complex problems involving ratios, rational numbers, algebra, geometry, and data.
Mathematical Modeling
Students represent real-world situations using diagrams, tables, equations, graphs, and mathematical relationships.
Estimation & Reasonableness
Students estimate results and evaluate whether mathematical answers make sense in the context of a problem.
Mathematical Arguments
Students explain their reasoning, justify solutions, and evaluate the reasoning of others.
Real-World Mathematics
Students apply mathematics to situations involving shopping, rates, measurements, budgeting, science, travel, and everyday decision-making.
Teaching Methodology
Our Grade 6 Mathematics classes focus on conceptual understanding, mathematical reasoning, algebraic thinking, proportional reasoning, rational numbers, geometry, statistics, and real-world problem solving. Students learn through:
Learning Outcomes
By the end of Grade 6, students will be able to:
Assessment & Progress Tracking
Student progress is evaluated through: