New Jersey Mathematics — Grade 8
Comprehensive Course Syllabus
Course Overview
Our New Jersey Grade 8 Mathematics course is designed around the 2023 New Jersey Student Learning Standards for Mathematics (NJSLS-M).
Grade 8 represents an important transition toward high-school mathematics, with a strong emphasis on linear algebra, linear equations, functions, irrational numbers, exponents, geometry, the Pythagorean Theorem, and statistics. Students develop mathematical reasoning and modeling skills while preparing for Algebra and other high-school mathematics courses.
Real Numbers & Irrational Numbers
Rational & Irrational Numbers
Students distinguish between rational and irrational numbers and understand how both belong to the real number system.
Decimal Expansions
Students identify terminating, repeating, and non-repeating decimal representations of numbers.
Converting Repeating Decimals
Students convert repeating decimal representations into equivalent rational numbers.
Approximating Irrational Numbers
Students use rational approximations to estimate irrational numbers such as √2 and locate them on a number line.
Comparing Real Numbers
Students compare rational and irrational numbers using numerical approximations, number lines, and mathematical reasoning.
Exponents & Powers
Integer Exponents
Students apply the properties of integer exponents to simplify and evaluate numerical expressions.
Product of Powers
Students use exponent rules to simplify products involving powers with the same base.
Quotient of Powers
Students apply exponent rules when dividing powers with the same base.
Power of a Power
Students simplify expressions involving powers raised to additional powers.
Zero & Negative Exponents
Students understand and apply zero and negative exponent rules.
Scientific Notation
Introduction to Scientific Notation
Students represent extremely large and extremely small numbers using scientific notation.
Converting Standard & Scientific Notation
Students convert numbers between standard decimal form and scientific notation.
Comparing Quantities
Students use scientific notation to compare very large or very small quantities.
Operations with Scientific Notation
Students perform multiplication, division, addition, and subtraction involving scientific notation.
Real-World Scientific Notation
Students apply scientific notation to measurements involving science, technology, distance, population, and other real-world quantities.
Radicals & Square Roots
Square Roots
Students understand square roots as values that produce a given number when squared.
Cube Roots
Students understand cube roots and use them to solve simple equations involving cubes.
Perfect Squares & Cubes
Students identify perfect squares and perfect cubes and use them to simplify calculations.
Estimating Square Roots
Students estimate the value of square roots that are not perfect squares.
Simplifying Radicals
Students simplify numerical square roots by identifying perfect-square factors.
Proportional Relationships, Slope & Linear Equations
Proportional Relationships
Students connect proportional relationships to tables, graphs, equations, and real-world situations.
Unit Rate & Slope
Students understand that the unit rate of a proportional relationship corresponds to the slope of its graph.
Slope Between Two Points
Students calculate slope using two points and interpret its meaning in a real-world context.
Slope-Intercept Form
Students understand and use the equation y = mx + b, where m represents slope and b represents the y-intercept.
Graphing Linear Equations
Students graph linear equations using slope, intercepts, tables, and coordinate points.
Linear Equations in One Variable
Solving Linear Equations
Students solve linear equations using inverse operations and properties of equality.
Equations with Rational Coefficients
Students solve equations involving fractions, decimals, and other rational coefficients.
Distributive Property
Students use the distributive property to expand expressions while solving equations.
Combining Like Terms
Students simplify algebraic expressions by combining like terms.
One Solution
Students identify and solve equations that have exactly one solution.
Systems of Linear Equations
Introduction to Systems
Students understand systems as sets of two linear equations involving the same variables.
Graphing Systems
Students solve systems by graphing and identify solutions as points where two lines intersect.
Substitution Method
Students solve systems by substituting one equation into another.
Solving by Inspection
Students identify simple system solutions by analyzing equations and relationships directly.
No Solution Systems
Students identify systems whose graphs are parallel and therefore have no common solution.
Functions
Understanding Functions
Students understand a function as a rule that assigns exactly one output to each input.
Inputs & Outputs
Students identify independent and dependent variables and analyze how one quantity changes in response to another.
Functions from Tables
Students determine whether relationships represented in tables are functions and identify patterns.
Functions from Graphs
Students analyze graphs to determine function behavior and relationships between variables.
Functions from Equations
Students use equations to represent functions and determine outputs for given inputs.
Modeling with Linear Functions
Rate of Change
Students determine and interpret the rate at which one quantity changes relative to another.
Initial Value
Students identify and interpret the initial value of a linear relationship from equations, graphs, tables, and situations.
Constructing Linear Models
Students create linear functions to represent real-world relationships.
Interpreting Graphs
Students describe how a quantity changes over time by analyzing the shape and characteristics of a graph.
Increasing & Decreasing Functions
Students identify intervals where a function increases or decreases and interpret those changes in context.
Transformations, Congruence & Similarity
Translations
Students move geometric figures across the coordinate plane without changing their size or shape.
Reflections
Students reflect figures across lines and analyze how coordinates and orientation change.
Rotations
Students rotate figures around a point and analyze the resulting coordinates and orientation.
Dilations
Students enlarge or reduce figures using scale factors while maintaining their shape.
Congruent Figures
Students understand when figures have the same size and shape and identify transformations that demonstrate congruence.
Geometry & Triangle Relationships
Triangle Angle Sum
Students explain and apply the relationship between the three interior angles of a triangle.
Exterior Angles
Students investigate relationships between exterior and interior angles of triangles.
Parallel Lines & Transversals
Students analyze angle relationships created when a transversal crosses parallel lines.
Similarity of Triangles
Students use angle relationships to determine when triangles are similar.
Angle-Angle Similarity
Students use the AA criterion to establish similarity between triangles.
Pythagorean Theorem
Understanding the Pythagorean Theorem
Students understand the relationship a² + b² = c² for right triangles.
Proof of the Pythagorean Theorem
Students explore and explain visual or algebraic reasoning supporting the theorem.
Finding Missing Side Lengths
Students use the theorem to calculate unknown side lengths in right triangles.
Real-World Applications
Students apply the Pythagorean Theorem to construction, navigation, distance, measurement, and other real-world situations.
Converse of the Pythagorean Theorem
Students use the converse to determine whether a triangle is a right triangle.
Also Covered in This Course
Teaching Methodology
Our Grade 8 Mathematics classes focus on linear algebra, functions, equations, real numbers, geometry, statistics, probability, mathematical modeling, and advanced problem solving. Students learn through:
Learning Outcomes
By the end of Grade 8, students will be able to:
Assessment & Progress Tracking
Student progress is evaluated through: