This unit on linear equations and expressions introduces 8th-grade students to fundamental algebraic concepts and problem-solving strategies involving expressions, equations, and angles. Starting with a review of algebraic basics and moving toward multi-step equations and real-world applications, students will build a strong foundation for understanding linear relationships. The unit also explores geometric applications of equations, such as solving for unknown angles in triangles and angle relationships formed by transversals. By the end of this unit, students will confidently analyze, create, and solve equations, deepening their understanding of algebraic and geometric concepts and preparing them for more advanced math.

Lessons in This Unit Include:

1. Algebraic Expression Review: Students begin with a refresher on algebraic expressions, reviewing terms, coefficients, and basic operations to build a foundation for equation-solving.
2. Distributive Property Review: This lesson focuses on distributive property, reinforcing its role in simplifying expressions and preparing for multi-step equation solutions.
3. One-Step Equations: Students practice solving simple one-step equations, gaining familiarity with using inverse operations to isolate variables.
4. Solve Two-Step Equations with Integers and Rational Numbers: Expanding to two-step equations, students apply operations to solve equations involving both integers and rational numbers.

This unit focuses on the study of volume for three-dimensional shapes with circular bases, as well as the application of the Pythagorean Theorem to solve problems involving right triangles and distance. Students will build on foundational geometry skills to calculate the volume of cylinders, cones, and spheres, then analyze volume accuracy and errors in calculations. The unit also covers important concepts in number theory, including the identification of rational and irrational numbers and the evaluation of square roots, which are essential for solving equations involving the Pythagorean Theorem. Through real-world applications and problem-solving activities, students will develop spatial reasoning and analytical skills, preparing them for high school geometry and algebra.

Lessons in This Unit Include:

1. Review: Volume of Rectangular Prisms: Students begin with a review of volume calculations for rectangular prisms, reinforcing volume concepts and setting the stage for more complex shapes.
2. Terms and Definitions of Solids with a Circular Base: This lesson introduces terms and properties of solids with circular bases, such as cylinders, cones, and spheres, providing a vocabulary foundation for volume calculations.
3. Missing Side of a Right Triangle: This lesson introduces the Pythagorean Theorem as a tool to find missing side lengths in right triangles, reinforcing understanding of squares and roots.
4. Pythagorean Theorem – Determine the Unknown Length: Students practice applying the Pythagorean Theorem (a²+b²=c²) to solve for unknown side lengths, with a focus on solving for both legs and the hypotenuse.

This unit introduces 8th-grade students to the study of geometric transformations, including translations, reflections, rotations, and dilations. Through these lessons, students will learn to manipulate shapes on the coordinate plane, exploring the concepts of congruence, similarity, and scale. Each transformation is taught both as an individual operation and as part of a sequence, allowing students to understand how multiple transformations can combine to produce complex results. This unit emphasizes spatial reasoning and precision, preparing students for more advanced studies in geometry and algebraic transformations.

Lessons in This Unit Include:

1. Transformations + Congruence: Students begin by exploring the concept of congruence in geometry, understanding how rigid transformations (translations, reflections, rotations) produce congruent figures.
2. Similar Figures: This lesson introduces similarity, teaching students to recognize when figures are similar based on proportional relationships and transformations that produce similar, but not congruent, figures.
3. Dilations: Students learn about dilations as a transformation that changes the size of a figure while preserving shape and proportional relationships, understanding the effect of scale factors on similarity.
4. Reflections: This lesson covers reflections across axes and lines on the coordinate plane, helping students understand symmetry and orientation changes

This unit introduces 8th-grade students to the concept of functions, focusing on understanding, creating, and analyzing linear functions in various contexts. Through hands-on activities and real-world applications, students will explore functions as relationships between inputs and outputs, represent functions with equations and graphs, and examine slope and intercepts as key components of linear relationships. The unit builds students’ ability to interpret and write equations, recognize proportional relationships, and differentiate between linear and nonlinear functions. By the end, students will be well-prepared to analyze and apply functions, a foundational concept for high school algebra and beyond.

Lessons in This Unit Include:

1. Intro to Functions: Students are introduced to functions, learning the basic definition and understanding how inputs and outputs relate in a functional relationship.
2. Creating a Rule: This lesson covers creating rules for functions, teaching students to identify patterns and represent relationships mathematically.
3. Input/Output: Students explore input-output tables, practicing substituting values to observe consistent patterns in functions.
4. Equality of Functions: Students learn to compare two functions to determine if they are equal, focusing on equivalent outputs for corresponding inputs.

This unit on linear relationships provides 8th-grade students with a comprehensive understanding of how to identify, interpret, and represent linear functions. Through exploration of graphs, tables, equations, and word problems, students will learn to identify linear relationships and calculate key elements such as slope and y-intercept. By understanding rate of change and practicing writing linear equations, students gain the skills to analyze and describe relationships between variables in real-world and mathematical contexts. This unit lays a strong foundation in algebraic reasoning, preparing students for more advanced studies in functions and algebra.

Lessons in This Unit Include:

1. Introduction to Graphing: Students begin by learning the basics of graphing, focusing on the coordinate plane and plotting points to visualize relationships.
2. Identifying Linear Functions – Equations: This lesson focuses on recognizing linear functions in equation form, emphasizing the standard y=mx+b structure.
3. Identifying Linear Functions – Tables and Word Problems: Students learn to identify linear relationships by analyzing tables and word problems, looking for consistent rates of change.
4. Finding Slope and y-intercept – Graphs: Students practice finding the slope and y-intercept of linear functions directly from graphs, understanding how these components shape the line.

This unit on statistics and data introduces 8th-grade students to analyzing relationships within data through scatter plots, lines of best fit, and two-way frequency tables. Students will learn to interpret associations between variables, distinguish between correlation and causation, and make predictions based on linear trends in scatter plots. Through the construction and analysis of two-way tables, students will explore how to organize and interpret categorical data, enhancing their data literacy skills. This unit emphasizes analytical thinking and statistical reasoning, preparing students for real-world data interpretation and foundational concepts in statistics.

Lessons in This Unit Include:

1. Identifying Association in Scatter Plots: Students begin by learning to identify associations (positive, negative, or none) in scatter plots, setting the stage for understanding data relationships.
2. Correlation vs. Causation: This lesson distinguishes between correlation and causation, helping students understand that association does not imply one variable causes another to change.
3. Creating Scatter Plots: Students practice plotting data points on scatter plots, learning to visually represent relationships and patterns within data sets.
4. The Slope-Intercept Form of the Line of Best Fit: This lesson introduces the line of best fit and teaches students to use the slope-intercept form (y=mx+b) to approximate trends within scatter plot data.

This unit on exponent properties introduces 8th-grade students to the fundamental rules and applications of exponents, including operations with exponents, working with roots, and distinguishing between rational and irrational numbers. Students will learn how to simplify expressions involving exponents, apply exponent laws, and simplify radicals, gaining a deeper understanding of exponential relationships. By the end of this unit, students will be equipped to evaluate and simplify complex expressions using exponents, preparing them for advanced algebraic concepts.

Lessons in This Unit Include:

1. Intro to Exponents: Students begin with the basics of exponents, learning to express repeated multiplication as exponential notation and understanding the parts of an exponent expression.
2. Negative and Zero Exponents: This lesson introduces the rules for negative and zero exponents, helping students interpret and simplify expressions with these values.
3. Multiplying and Dividing with the Same Base: Students learn to multiply and divide expressions with the same base, reinforcing their understanding of how exponents combine under these operations.
4. Power of a Power vs. Power of a Product: This lesson covers the distinctions between power of a power and power of a product rules, helping students expand and simplify more complex exponential expressions.

This unit introduces 8th-grade students to the concept of systems of equations, focusing on how to represent, interpret, and solve multiple linear equations simultaneously. Students will explore various methods for solving systems, including graphing, substitution, and elimination, and apply these techniques to real-world contexts. Through modeling and problem-solving, students will gain a deep understanding of how systems of equations can be used to compare options and analyze relationships between variables. This unit lays the foundation for advanced algebraic skills and prepares students for high school math.

Lessons in This Unit Include:

1. Graphing Linear Equations: Students begin by reviewing how to graph linear equations on the coordinate plane, setting the stage for solving systems by graphing.
2. Graphing with x- and y-Intercepts: This lesson reinforces finding and using intercepts to graph linear equations quickly, which is helpful in identifying points of intersection in systems.
3. Rewriting an Equation: Students practice rewriting linear equations in different forms, such as slope-intercept and standard form, to make graphing and comparison easier.
4. Testing Solutions in a System of Equations: Students learn to substitute values into equations to test whether a given point is a solution to the system, understanding the meaning of “solution” within a system.

This unit introduces 8th-grade students to scientific notation, a powerful tool for representing very large and very small numbers. Students will learn to convert between standard and scientific notation, understand the role of negative exponents, and perform operations with numbers in scientific notation. Through hands-on practice with addition, subtraction, multiplication, and division, students will gain fluency in working with exponents and scientific notation, applying these skills to real-world and mathematical contexts. This unit builds essential skills for managing large data values and is a key step in preparing students for advanced math and science courses.

Lessons in This Unit Include:

1. Convert Standard Notation to Scientific Notation: Students begin by learning how to convert large and small numbers from standard notation to scientific notation, emphasizing the structure of scientific notation (a10n).
2. Scientific Notation with Negative Powers of 10: This lesson introduces scientific notation with negative exponents, allowing students to represent very small numbers and understand the concept of decimal movement to the left.
3. Add and Subtract Numbers Written in Scientific Notation: Students learn to add and subtract numbers in scientific notation, practicing alignment of exponents and conversions as needed to simplify expressions.