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 Includes:

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 (a×10na \times 10^na×10n).
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.

This unit on polynomials introduces Algebra I students to foundational concepts and operations with polynomial expressions, focusing on the classification, simplification, and manipulation of polynomial expressions and equations. Students will begin by exploring the properties of polynomials and learn to classify them based on degree and number of terms. As the unit progresses, students will gain skills in evaluating, adding, subtracting, and multiplying polynomials. The unit culminates in multi-step problems where students apply polynomial operations and simplify complex expressions. This unit builds essential algebraic skills that are critical for understanding higher-level algebra concepts, including factoring, functions, and equations.

Lessons in This Unit Includes:

1. Properties of Polynomials: Students begin by exploring the fundamental properties of polynomials, understanding terms like coefficients, degree, and the role of variables in polynomial expressions.
2. Classifying Polynomials: This lesson covers the classification of polynomials by degree (linear, quadratic, cubic) and by the number of terms (monomial, binomial, trinomial), helping students recognize and categorize polynomial expressions.
3. Evaluating Expressions and Equations: Students practice evaluating polynomial expressions and equations by substituting values for variables, reinforcing their understanding of polynomial structure.
4. Simplifying Expressions and Equations: Students learn to simplify polynomial expressions by combining like terms and applying the properties of operations, building a foundation for more complex manipulations.

This unit on equations and inequalities provides Algebra I students with the skills to solve, manipulate, and interpret both equations and inequalities in various forms. Starting with a review of basic equation-solving techniques, students progress to multi-step problems and equations with variables on both sides. The unit extends to inequalities, where students learn to solve, graph, and apply inequalities in real-world contexts. Finally, students will explore literal equations, focusing on solving for specific variables within formulas. By the end of the unit, students will be well-prepared to handle complex equations and inequalities in mathematical and practical applications.

Lessons in This Unit Includes:

1. Review Solving Equations: Students begin with a review of solving basic equations, reinforcing their understanding of operations, inverse operations, and maintaining balance.
2. Multi-Step Equations: This lesson introduces multi-step equations, where students learn to combine like terms, distribute, and use multiple operations to isolate the variable.
3. Equations with the Variable on Both Sides: Students practice solving equations with variables on both sides, learning to simplify and manipulate both sides of the equation to find a solution.
4. Solving Inequalities Review: This lesson reviews basic techniques for solving inequalities, reinforcing concepts such as reversing inequality symbols when multiplying or dividing by a negative number.

This unit on functions introduces Algebra I students to fundamental concepts such as function notation, operations with functions, and understanding domain and range. Students will learn to interpret functions as relationships between inputs and outputs and explore how to identify and compare functions graphically and algebraically. The unit emphasizes real-world applications, helping students understand how functions model various scenarios. By the end of the unit, students will be able to analyze function behavior, interpret graphs, and apply their knowledge to practical situations, building a strong foundation for advanced algebra and calculus.

Lessons in This Unit Includes:

1. Function Notation: Students begin by learning function notation, understanding how to use f(x) to represent functions and interpret the notation in various contexts.
2. Input/Output: This lesson explores the relationship between inputs and outputs in functions, reinforcing how each input maps to a unique output and the concept of a function as a rule.
3. Equality of Functions: Students learn to determine if two functions are equal by comparing their rules or outputs for specific inputs, building skills in function analysis.
4. Operations with Functions: This lesson introduces operations with functions, such as addition, subtraction, multiplication, and division, teaching students how to combine functions to create new ones.

This comprehensive unit on linear relationships and systems provides Algebra I students with an in-depth understanding of linear functions, their representations, and applications. Students will explore how to identify, interpret, and graph linear functions from equations, tables, and real-world scenarios. Through hands-on practice, they’ll develop skills in finding slope and y-intercept, writing equations, analyzing rates of change, and using linear regression to model data. The unit also covers systems of equations and inequalities, introducing multiple methods to solve and interpret solutions in context. By the end of the unit, students will be proficient in analyzing, modeling, and solving linear relationships and systems, equipping them with critical algebraic tools for advanced topics.

Lessons in This Unit Includes:

1. Introduction to Graphing: Students begin by learning the fundamentals of graphing on the coordinate plane, setting the stage for analyzing linear functions.
2. Identifying Linear Functions – Equations: This lesson focuses on recognizing linear functions in equation form, emphasizing the structure y=mx+b as a characteristic of linearity.
3. Identifying Linear Functions – Tables and Word Problems: Students learn to identify linear relationships in tables and word problems, using constant rate of change as a key indicator of linearity.
4. Finding Slope and y-intercept – Graphs: This lesson teaches students to find slope and y-intercept directly from a graph, understanding how these values define a line’s steepness and starting point.

This unit on exponential relationships introduces Algebra I students to the characteristics and applications of exponential functions, focusing on graphing, writing, and interpreting exponential models. Starting with a review of exponent rules, students will learn how exponential functions differ from linear functions and how to represent exponential growth and decay graphically and algebraically. By comparing exponential and linear models, students will gain a deeper understanding of how each type of function applies to real-world situations, such as population growth, depreciation, and compound interest. This unit builds essential skills in modeling and analyzing exponential relationships, preparing students for advanced algebraic and scientific applications.

Lessons in This Unit Includes:

1. Review Exponent Rules: Students begin by reviewing basic exponent rules, including the product, quotient, and power rules, to build a foundation for working with exponential expressions.
2. Graphing Exponential Functions: This lesson introduces students to graphing exponential functions, helping them recognize the characteristic curve of exponential growth and decay on the coordinate plane.
3. Writing Exponential Functions: Students learn to write exponential functions in the form y=a×b^x, identifying parameters such as the initial value and the growth or decay factor.

This unit on factoring introduces Algebra I students to the essential techniques for breaking down polynomials into simpler factors. Starting with the greatest common factor (GCF) of monomials, students will progressively learn various methods for factoring different types of polynomials, including factoring by grouping, factoring trinomials, and using the difference of two squares (DOTS) rule. By the end of the unit, students will gain proficiency in selecting and applying appropriate factoring methods, preparing them to simplify complex expressions, solve polynomial equations, and tackle higher-level algebraic problems.

Lessons in This Unit Includes:

1. GCF of Monomials: Students begin by identifying the greatest common factor of monomials, a foundational skill for factoring more complex polynomials.
2. Factoring by Using a GCF: This lesson teaches students to factor out the GCF from polynomial expressions, simplifying expressions by removing the common factor.
3. Factoring by Grouping: Students learn the technique of factoring by grouping, which is especially useful for polynomials with four terms, breaking the expression into pairs to factor out common terms.

This unit on quadratics introduces Algebra I students to the fundamental properties and methods for solving quadratic equations and analyzing quadratic functions. Students will start by identifying quadratic functions and progress through various techniques for solving quadratic equations, including factoring, completing the square, and the quadratic formula. The unit also covers graphing quadratic functions, with a focus on identifying key features such as the vertex, axis of symmetry, and maximum or minimum values. By the end of this unit, students will be able to solve real-world problems involving quadratic equations and analyze the behavior of quadratic functions on a graph, preparing them for advanced applications in algebra and calculus.

Lessons in This Unit Includes:

1. Identifying Quadratic Functions: Students begin by recognizing quadratic functions in standard form ax²+bx+c and understanding what makes a function quadratic based on its highest degree.
2. Solving ax²-c=0 Using Square Roots: This lesson introduces solving simple quadratic equations by isolating x2x^2×2 and taking the square root of both sides, focusing on cases without linear terms.
3. Solving a(x+b)²=0 Using Square Roots: Students learn to solve equations of the form a(x+b)²=0 by isolating the squared term and taking square roots, emphasizing symmetry in solutions.
4. Solving Quadratics with a=1 by Factoring: This lesson covers factoring quadratics where the leading coefficient a is 1, focusing on finding two numbers that multiply to the constant term and add to the linear coefficient.

This unit on function families introduces Algebra I students to a variety of function types, including quadratics, absolute values, square roots, polynomials, and piecewise functions. Students will explore how to graph these functions, analyze their transformations, and compare their unique characteristics. By learning to transform each function type, students gain a deeper understanding of how changes in parameters affect the shape and position of graphs. The unit also covers systems of equations involving multiple function families, encouraging students to recognize connections and differences among functions. By the end of this unit, students will develop a comprehensive understanding of function families, preparing them for advanced algebra and pre-calculus.

Lessons in This Unit Includes:

1. Transforming Quadratic Functions: Students learn how to transform quadratic functions by shifting, stretching, compressing, and reflecting their graphs, analyzing how these changes affect the vertex and axis of symmetry.
2. Graphing & Transforming Absolute Value Functions: This lesson focuses on graphing absolute value functions and applying transformations to observe changes in the “V” shape, vertex, and orientation of the graph.
3. Graphing & Transforming Square Root Functions: Students graph square root functions and explore transformations that shift, stretch, compress, or reflect the graph, noting how these changes affect the starting point and curve direction.
4. Comparing All Function Families: This lesson encourages students to compare the unique characteristics of quadratic, absolute value, and square root functions, focusing on their graphs, shapes, and transformations.

This unit on statistics provides Algebra I students with the tools to analyze and interpret data through various visual representations and statistical measures. Students will explore scatter plots to understand correlation types and learn to differentiate between correlation and causation. Through the study of two-way frequency tables, students will gain skills in organizing and interpreting categorical data. The unit also covers measures of center and spread, along with data displays such as dot plots, box plots, and histograms, allowing students to analyze distributions and identify outliers. By the end of the unit, students will be able to apply statistical concepts to real-world data, developing critical thinking skills for data interpretation.

Lessons in This Unit Includes:

1. Intro to Scatter Plots, Types of Correlation: Students begin by creating and interpreting scatter plots, identifying types of correlation (positive, negative, or none) and understanding how they represent relationships in data.
2. Correlation vs. Causation: This lesson emphasizes the difference between correlation and causation, helping students recognize that correlation does not imply a cause-and-effect relationship.
3. Correlation Coefficient: Students learn about the correlation coefficient, a numerical measure that quantifies the strength and direction of a linear relationship between two variables.
4. Construction of a Two-Way Frequency Table: This lesson introduces two-way frequency tables, where students learn to organize and display categorical data to explore relationships between two variables.

This unit on sequences introduces Algebra I students to the concepts of arithmetic and geometric sequences, focusing on how to define, compare, and apply both explicit and recursive rules. Students will learn to distinguish between arithmetic and geometric sequences, identify patterns, and write rules to describe each sequence type. Through these lessons, students will gain the skills to analyze and relate sequences, understanding how they represent predictable patterns in both mathematical and real-world contexts. By the end of the unit, students will have a foundational understanding of sequences, setting the stage for advanced topics in algebra and series.

Lessons in This Unit Includes:

1. Explicit Rule: Students learn to define sequences using the explicit rule, which allows them to find any term in a sequence directly from its position, providing a straightforward formula for sequence terms.
2. Recursive Rule: This lesson covers the recursive rule, where students learn to define a sequence based on its previous term, understanding how each term builds from the one before it.
3. Compare Explicit and Recursive Rule: Students compare the explicit and recursive rules, analyzing the advantages and limitations of each method for defining sequences and applying them to different contexts.