Algebra

This math unit introduces and develops foundational algebra skills, advancing from simple to more complex concepts. Initially, students balance shapes using simple ratios, exploring basic equality principles and ratio application. They delve further into understanding algebra by interpreting the meaning of a dot as multiplication in algebraic functions and applying simple substitution in balancing more complex scenarios with three beams. Progressively, the unit tackles linear equations, first by solving two-term equations and advancing to three-term equations, enhancing student skills in basic arithmetic operations and variable isolation. Concurrently, students learn to interpret algebraic expressions, distinguishing between operations like multiplication, addition, and exponentiation, with focus on how numbers and variables interact in an equation. Towards the latter stages, the unit emphasizes on translating verbal descriptions into algebraic equations and practicing variable substitution in algebraic expressions, both unbracketed and bracketed. These exercises reinforce understanding of algebra's fundamental concepts, setting a robust basis for advanced topics.Skills you will learn include:

• Number placeholders
• Concept of a variable
• Variable substitution
• Solving for variables

In this math unit, students progress through a sequence of topics that build foundational to advanced skills in algebra. The unit starts with basic skills such as expanding and simplifying algebraic expressions when multiplying a variable by a bracketed term, followed by solving linear equations with increasing complexity—from three to four terms. It then advances to manipulating algebraic fractions, where students solve and simplify equations that involve fractions with variables. The complexity in fraction manipulation progresses across orientations until students deal with comprehensive problems that require reducing fractions that involve variables to their simplest forms. Towards the end of the unit, the focus shifts to applying algebra in practical contexts using balance shapes. Students learn to analyze image-based problems and to use substitutions and subtraction to solve for the equations and answer visually represented through balance beams. This culminates in understanding complex ratios, substitutions, and algebraic manipulations through symbolic and visual interpretations, rounding out their algebraic skills with both numerical and real-world problem-solving abilities.Skills you will learn include:

• Multiplying variables
• Algebra syntax for multiplication and dot notation
• Solving for variables

In this math unit, students begin by expanding and simplifying algebraic expressions focusing on multiplying bracketed terms with the same variable, setting a foundational understanding of polynomial operations. They then progress to evaluating algebraic expressions through variable substitution, dealing initially with simple and negative terms, and advancing to more complex situations involving squared terms and negative coefficients. The practice intensifies as students substitute values into multiple fractional squared and bracketed squared terms, reinforcing their capacity to manage and compute expressions under specified conditions. Further advancing their algebraic skills, students practice solving basic linear equations to isolate variables, first with two terms and progressing to three terms, enhancing their handling of various algebraic functions. The unit culminates with advanced algebra concepts where students translate balanced shapes into equations, focusing on establishing and solving ratios, and involves visual and analytical skills by substituting and subtracting to find solutions in complex algebraic contexts. This flow from foundational polynomial operations to complex variable substitution and application in real-world contexts challenges students to deepen their understanding and proficiency in algebra.Skills you will learn include:

• Variable substitution
• Solving for variables

This math unit progresses through various aspects of understanding and calculating the slope of a line, as well as deriving other line characteristics such as rise and run using the slope formula. Initially, the unit introduces the basic terms "rise" and "run" and the concept of slope by identifying these components on a graph. Students then learn to compute the slope using the rise over run formula expressed as an equation. Progressively, they apply this understanding to determine the rise and the run from known values of slope and one of the other variables. Through practice, the unit strengthens students' ability to manipulate and solve equations involving slope, rise, and run. Later, this evolves into more complex tasks where slope is calculated between specific points or derived from graphical representations, enhancing skills in interpreting and analyzing linear relationships by applying algebraic methods and critical thinking.Skills you will learn include:

• Rise and run
• Calculating slope
• Calculating rise or run from slope

This math unit begins by introducing students to the fundamental skills of substituting numbers and variables into linear equations. Initially, students practice simple substitutions where numbers are replaced in equations with one defined variable, advancing to solve for unknown variables using these substitutions. As the unit progresses, the complexity increases as students learn to apply the substitution method to systems of linear equations, where they must substitute entire equations to simplify and solve for variables. The unit deepens understanding by requiring students to manipulate and simplify algebraic expressions to isolate variables and solve equations. Multiple choice questions are included to help verify their solutions. Towards the end of the unit, the focus shifts to practical applications, employing algebraic manipulations in balance scales scenarios where substitution and subtraction are used to solve more visually presented equations, enhancing problem-solving skills in real-world contexts. Finally, the unit circles back to simpler algebraic operations such as addition within systems of equations, ensuring students consolidate their understanding of basic operations within the context of linear systems. This approach builds a robust foundation in algebra, preparing students for more complex mathematical concepts.Skills you will learn include:

• Variable substitution
• Solving for variables
• Systems of equations
• Equation substitution

This math unit primarily develops an understanding of slopes and their applications in determining parallelism between lines. It starts by teaching students how to graph linear equations from the slope-intercept form and progresses to converting these equations between different formats, reinforcing their understanding of slope as a critical element in linear equations. The central theme evolves around identifying parallel lines through various representations of slope, including fractional, decimal, and zero forms, along with graph interpretations. Students are guided through recognizing parallel slopes directly from graphs, as well as determining them through algebraic equation conversions involving both the slope-intercept form and graphical representations. Additionally, the unit enhances skills in manipulating and understanding equations, fostering an in-depth comprehension of how slopes establish relationships between parallel lines, crucial for graphing and algebraic problem solving in coordinate geometry. The progress from basic graph plotting and slope identification to detailed analysis of slopes in different forms and their corresponding graphical interpretations encapsulates the unit’s comprehensive approach to understanding linear relationships.Skills you will learn include:

• Parallels
• Y = mx + b
• Ax + Cy = C
• Parallels of line equations
• Graphs from parallels

This math unit begins by teaching students how to recognize and calculate the slope of linear equations presented in various forms. Starting with converting standard form equations to slope-intercept form and directly finding slopes, the unit progresses to applying these skills by interpreting graphed lines and determining their standard form equations. Increasing complexity is introduced as students learn to calculate negative reciprocal slopes to identify perpendicular lines, initially focusing on understanding the negative inverse property through converting integer and decimal slopes. The unit further delves into graphical interpretations, allowing students to visually analyze lines on graphs to identify perpendicular slopes and convert these observations into different numerical and algebraic representations. The advanced topics cover converting between different forms of slope equations and understanding the relationship between slopes of perpendicular lines within different forms of linear equations, emphasizing practical applications and manipulation of slope and perpendicularity in various contexts.Skills you will learn include:

• Perpendiculars
• Y = mx + b
• Ax + Cy = C
• Perpendiculars of line equations
• Graphs from perpendiculars

This math unit begins with foundational practices in understanding and calculating the slope of a line through various methods and progressively moves towards applying these concepts to broader topics in linear equations and graphing. Initially, students explore the concept of slope using fact families and simple rise/run calculations from graphs. Progression occurs when students calculate the slope from specific points on a graph and ultimately advance to deriving slopes directly from rise and run values presented in equations. As the unit progresses, students take on tasks such as extrapolation of points from graphed lines based on linear equations and mathematical analysis to find specific points on a graph from given linear equations. The unit culminates with students identifying and manipulating linear equations based on slopes and intercepts from graphical representations and equations in standard form, enhancing their overall understanding of the relationship between algebraic expressions and their graphical manifestations in coordinate geometry.Skills you will learn include:

• Slope
• Y = mx + b
• Line equations
• Graphs from line equations

This math unit begins by introducing students to basic algebraic functions, starting with the multiplication of a single value with bracketed terms and progressing to more complex polynomial expressions. Initially, students practice distributing a single number across terms within parentheses, helping them recognize and simplify equivalent expressions. As the unit advances, the focus shifts to more intricate operations involving the same or different variables within bracketed terms, enhancing their ability to expand and simplify such expressions further. Midway through the unit, the emphasis is placed on removing values from these terms, reinforcing students' understanding and manipulation of algebraic expressions across various contexts. The complexity increases as students learn to factor quadratic equations and recognize equivalent expressions involving operations with variables, addition, subtraction, multiplication, and powers. Towards the end, the unit dives into the relationships between the roots of quadratic equations, exploring how sums and products of integers relate to polynomial coefficients, including exercises with negative numbers. This structured progression sharpens students' problem-solving skills in polynomials and quadratics, preparing them for advanced topics in algebra.Skills you will learn include:

• Polynomials
• Factoring polynomials
• GCF of polynomials

This math unit opens with foundational algebraic concepts, beginning with solving basic linear equations with one variable. As the unit progresses, the focus shifts towards more complex operations involving algebraic fractions, where students first learn to solve and simplify equations with fractions and eventually handle advanced fraction manipulations, including those with multiple variables. The unit proceeds to expand into polynomial manipulation, targeting skills from expanding expressions with a single variable multiplied by bracketed terms to handling polynomials involving multiple variables. Students practice distributing variables across terms and simplifying the resulting expressions—a vital skill for more advanced studies in algebra. Towards the end of the unit, the emphasis is on multiplying bracketed terms—both with the same and different variables—to reinforce understanding of the distributive property and improve the ability to expand and manipulate polynomial expressions. The unit concludes with exercises that involve solving for integer pairs that meet specific conditions, synthesizing earlier concepts with integer properties and polynomial reasoning.Skills you will learn include:

• Multiplying bracketed variables
• Multiplying two brackets of variables

This math unit develops the understanding and skills related to slopes and equations of lines, with a specific focus on parallelism. Initially, students learn to recognize and convert line equations between different forms, starting from understanding simple forms such as slope-zero intercept and slope-intercept forms, to more complex transformations involving standard forms and decimal representations of slope. As the unit progresses, the emphasis shifts to applying these foundational skills to understand parallel lines. Students practice identifying parallel slopes by converting equations between various formats including zero-intercept, slope-y-intercept, fraction form, and graph representation to standard forms. Through these exercises, students enhance their ability to interpret and manipulate different algebraic expressions of linear equations, deepening their grasp of how slopes indicate parallelism and how lines can be graphically and algebraically analyzed and compared for this property.Skills you will learn include:

• Parallels
• Y = mx + b
• Ax + Cy = C
• Parallels of line equations
• Graphs from parallels

This math unit focuses on understanding and applying the concept of perpendicular slopes within different contexts of linear equations. It begins with basic calculations to find the negative reciprocal of given integer slopes and progresses to handling fractional and decimal slopes to identify perpendicular lines. The unit further develops by having learners convert and determine perpendicular slopes between different forms of linear equations, such as slope-intercept form, zero-intercept form, and standard form. Additionally, learners practice converting these equations for graphical representation, aiding in visual understanding and verification of perpendicular relationships. The depth of the unit increases as students move from initially identifying perpendicular slopes in simpler formats to manipulating complex algebraic forms and graphing them, thus building a comprehensive skill set in analyzing and constructing perpendicular lines within coordinate geometry. Throughout the unit, the primary emphasis remains on mastering the concept that the product of the slopes of perpendicular lines is -1, and applying this understanding in various mathematical scenarios.Skills you will learn include:

• Perpendiculars
• Y = mx + b
• Ax + Cy = C
• Perpendiculars of line equations
• Graphs from perpendiculars

This math unit begins with understanding algebraic functions in the context of finding integer pairs that satisfy conditions of sum and product in quadratic expressions, incorporating negatives for complexity. Students progress to manipulating quadratic equations directly by identifying relationships between their roots, sums, and products. Initially, they focus on the fundamentals such as solving and understanding polynomials and quadratic equations, moving towards intermediate skills like identifying the greatest common factor (GCF) and factoring quadratic expressions efficiently. As the unit advances, students delve deeper into polynomial algebra by systematically transforming quadratic equations through removal of common factors and simplification processes. They practice converting from standard form to simplified expressions, mastering the skill of distinguishing correct factorization and manipulation strategies. Furthermore, the unit integrates the application of these foundational and intermediate algebraic skills in various problem-solving scenarios involving polynomial expressions, thereby enhancing understanding of advanced polynomial properties and manipulations within the broader context of algebraic functions.Skills you will learn include:

• Polynomials
• Factoring polynomials
• GCF of polynomials

This math unit begins by building foundational skills in understanding slopes of line segments, both graphically and through coordinates, initially focusing on finding and verifying the slope values of line segments. Students practice calculating the slope using the formula and assess given slopes for accuracy in true/false formats. The unit progresses to finding the midpoints of segments, utilizing both graphical presentations and coordinate data, again using true/false questions to confirm understanding. Later, the unit introduces more complex concepts like perpendicular slopes and bisectors. Students learn to determine perpendicular slopes by applying the negative reciprocal rule and verify their correctness in true or false questions. The unit advances to constructing equations for perpendicular bisectors using both graphical and coordinate data, enriching students' skills in applying geometric concepts to solve problems involving midpoints, slopes, and perpendicular relations in line segments. The sequence moves from basic slope and midpoint identification to more intricate applications, such as creating and verifying perpendicular bisectors.Skills you will learn include:

• Midpoint of a segment
• Perpendiculars
• Perpendicular bisectors

This math unit begins with the foundational concept of identifying y-intercepts from linear equations in slope-intercept and standard forms using integer coefficients. As the unit progresses, it introduces the concept of x-intercepts, requiring students to manipulate equations set to zero in either variable while still using integer values. The complexity increases as the unit shifts to equations involving decimal coefficients. This additional challenge tests the students' ability to work with more precise values and enhances their algebraic manipulation skills. Towards the end of the unit, the focus shifts to finding intersection points between different types of lines including horizontal, vertical, and other linear equations demonstrating both integer and decimal solutions. This progression from basic intercept identification to solving for intersections between various lines helps students understand the graphical behavior of linear equations and their points of intersection.Skills you will learn include:

• Intersections
• Y = mx + b
• Horizontal line intersections
• Vertical line intersections
• Two linear equation intersections

This math unit begins with introducing the basics of quadratic formulas, transitioning from naming and identifying their purposes to delving deeper into characteristics such as the discriminant and its implications on quadratic graphs and roots. Students start by linking quadratic equations to their respective formulas and understanding the functions they describe. The unit progresses to interpreting the discriminant values to analyze how they influence the graph's appearance, the nature of the roots, and the count of roots in quadratic equations, further evaluating whether these roots are real or complex. The exercises escalate to involve calculating specific aspects like the radical roots and the x-coordinate of the vertex using quadratic formulas. Towards the end, the unit focuses on the comprehensive application of quadratic discriminants, including identifying discriminant values from graphs and examining the consistency of root types according to discriminant values, reinforcing a deeper understanding of the interplay between quadratic equations, their graphs, discriminants, and roots.Skills you will learn include:

• Quadratic equations
• Quadratic formula
• Discriminant
• Real roots
• Complex roots

This math unit begins by developing students' ability to identify and verify the midpoint of a line segment using graphical representations. As the unit progresses, it adds complexity by introducing the concept of perpendicular slopes and the calculation of slopes that are perpendicular to a given line segment. Students start with true/false questions to confirm their understanding of midpoints and perpendicular slopes and then move on to using formulas. The unit evolves to focus on finding the equation of the perpendicular bisector of line segments, both from graphical representations and by analyzing points directly. Towards the end, the unit consolidates these skills by requiring students to verify if equations presented to them correctly represent the perpendicular bisector of specified line segments, using both graphical and point-based information. Overall, this unit builds from basic midpoint validation to advanced application of formulas for constructing perpendicular bisectors, enhancing students' analytical geometry skills.Skills you will learn include:

• Midpoint of a segment
• Perpendiculars
• Perpendicular bisectors

This math unit progresses through various skills related to quadratic functions, focusing extensively on vertex form. It begins by identifying different forms of quadratic equations. It then delves into the use of vertex form to solve practical problems related to the vertex, understanding min/max y-values, and determining the range of quadratic functions. This leads to exercises around graph interpretation, where students match quadratic equations to graphs, and finally, complete the square to transform equations into vertex form. Early exercises focus on recognizing and manipulating the vertex form to understand graphical properties like the vertex and the range. Later exercises are more algebraically intensive, where students practice the technique of completing the square with varying coefficients, ultimately facilitating a deeper understanding of the algebraic structures and transformations of quadratic equations. The unit caps off with mastering completing the square for different coefficients, solidifying an essential algebraic skill with quadratic functions.Skills you will learn include:

• Quadratic equations
• Vertex form
• Min/Max of Y value
• Range of function

This math unit guides students through advanced aspects of polynomial and quadratic algebra, focusing on skills ranging from basic operations to complex problem-solving. Initially, students learn to expand and simplify products of binomials containing either distinct or identical variables, setting a foundation in polynomial manipulation. Progression is evident as they delve into the difference of squares, first using variables and later integrating integers, enhancing their ability to factorize and simplify expressions. As the unit progresses, the focus shifts to handling squared expressions under square roots and solving for variables in contexts involving quadratic-like structures. Students also solve expressions using the difference of squares formula and exponents, which further sharpens their skills in simplifying and determining algebraic identities and equivalencies. Ultimately, students apply these concepts to more intricate problems, such as solving polynomial algebra where squared variables with coefficients are involved, culminating in solving rational equations, thereby achieving a comprehensive understanding of polynomial and quadratic equations.Skills you will learn include:

• Polynomials
• Squares of polynomial terms
• Difference of square terms
• Quadratic equations

This math unit begins with students learning how to expand and simplify algebraic expressions involving squared terms. As the unit advances, learners systematically delve into quadratic functions, starting with identifying whether quadratic polynomials are perfect squares. They practice the technique of completing the square, initially with simpler forms where the leading coefficient is 1 or -1, and subsequently handling quadratic equations with variable coefficients (both positive and negative). These exercises prepare students to transform quadratic expressions into vertex form, gradually moving from partial completion to fully completing the square. By the end of the unit, students become proficient in manipulating and transforming quadratic functions, developing key skills in rewriting equations to reveal maximum and minimum values and other properties critical for understanding the geometry of parabolas. This progression deepens their comprehension of algebraic structures and polynomial behavior in quadratic equations.Skills you will learn include:

• Polynomials
• Squares of polynomial terms
• Completing the square
• Factoring square polynomials

This math unit delves into the fundamentals of graphing circles on a coordinate plane, beginning with basic identification and placement of circle centers. Students first learn to graph circles given the center coordinates and then advance to calculating circle graphs based on specified radii. Progressing further, the unit teaches conversion of a circle's equation into its graphical representation by interpreting the meaning of value coefficients in the standard circle equation \( (x-h)^2 + (y-k)^2 = r^2 \). Students continue to refine their skills by extracting center coordinates and radii directly from the circle equations, enhancing their ability to visualize and plot these geometric forms accurately. The subsequent lessons expand these concepts by guiding students to derive a circle's standard equation using both center coordinates and radius. Towards the end of the unit, learners are equipped to transform a complete circle graph back into its algebraic equation, solidifying their understanding of the relationship between a circle’s graphical and algebraic representations. This step-by-step progression effectively builds foundational knowledge crucial for solving geometry and coordinate graphing problems involving circles.Skills you will learn include:

• Graphing circles
• Circle equation format
• Finding radius
• Finding center coordinate

This math unit focuses on developing a comprehensive understanding of quadratic functions through a progression of skills. Initially, students learn to determine and analyze the range of quadratic functions from their graphs and equations based on vertex form. These skills involve understanding the effects of vertex position and the direction a parabole opens (upward or downward). As students advance, they shift focus towards manipulating and translating quadratic equations and their graphs. They learn to convert graphs to vertex form equations, match equations to their respective graphs, and understand how the algebraic structure of these equations affects their graphical characteristics and range. Further into the unit, students apply techniques to complete the square, essential for converting quadratic equations into vertex form. This begins with partial completion when the leading coefficient is -1 or a negative number and progresses to fully completing the square to understand vertex position and to discern the properties like maximum and minimum values of the quadratic functions. This sequence deepens students' ability to manipulate and understand quadratic transformations, heading towards mastery in handling quadratic equations in various forms and contexts.Skills you will learn include:

• Quadratic equations
• Vertex form
• Completing the Square
• Converting to Vertex Form

This math unit progresses from basic to advanced skills in algebraic functions, focusing particularly on polynomials and quadratics. Initially, students learn to find the greatest common factor (GCF) within algebraic expressions, a foundational skill for simplifying and manipulating expressions. The unit progresses to more complex maneuvers such as removing and manipulating different or same variables from bracketed terms. As students progress, the focus shifts to factoring quadratic equations, first without coefficients and then with coefficients, where they apply their skills to split quadratic terms and identify correct factorizations. Later worksheets introduce the relationships between quadratic roots, coefficients, and their arithmetic properties (sum and product), culminating in an ability to solve and factorize quadratic expressions based on specific numerical criteria. This learning path enhances understanding of polynomial behavior and quadratic relationships, preparing students for deeper studies in algebra and related mathematics fields. The structured approach develops from identifying simple common factors to complex factorizations and understanding polynomial roots, reflecting a comprehensive learning curve within the algebraic scope.Skills you will learn include:

• Polynomials
• Factoring polynomials
• GCF of polynomials

This math unit initiates with the basic fundamentals of factoring quadratic equations, specifically focusing on transforming them into their factored forms. Initially, students practice factoring quadratics where a common factor is removed, enhancing their ability to simplify these expressions into binomials. As they progress, the unit shifts towards more complex applications, requiring students to identify and factor out the greatest common factor from quadratics presented in standard form. Further advancing, the unit tackles the challenge of splitting quadratic expressions with a leading coefficient by identifying numbers that appropriately add up to and multiply into particular values derived from the coefficients. Students practice these skills through a combination of split-term techniques and identifying common factors across different terms of the quadratic expressions. Towards the end of the unit, the emphasis lies on consolidating and applying various factoring skills to not only solve but also to correctly identify the most simplified forms of quadratic equations. This progression ensures a deepened understanding of polynomial factoring in quadrics, particularly in manipulating and solving expressions with leading coefficients.Skills you will learn include:

• Polynomials with Coefficient
• Factoring polynomials
• Leading Coefficient as Common Factor

This math unit begins by teaching students how to visually interpret and define functions through relation maps and progresses to detailed explanations of domain and range using various mathematical notations and representations. Starting with basic function definitions, students learn how to find domain and range using number lines and inequalities, gradually moving to translating these into set builder and interval notations without unions. The complexity increases as students learn to navigate between different representations, including verbal descriptions and symbolic expressions. Towards the end of the unit, the scope expands to include unions in domains and ranges, enhancing their ability to handle more complex scenarios by interpreting inequalities, set builder notations, and intervals that involve combining separate mathematical intervals. This progression builds a foundational understanding of functions, crucial for further study in calculus and algebra.Skills you will learn include:

• Domain and range of functions
• Unions in domain and range
• Inequalities
• Set builder
• Number line

This math unit progresses through a series of skills, focusing on understanding and defining the domain and range of functions through various representations and conditions. Initially, the unit addresses basic visual and symbolic representations involving the translation of inequalities and verbal descriptions into number lines and set builder notation, utilizing unions to depict composite intervals. As students progress, they learn to convert these representations into interval notation, further solidifying their understanding of function behavior over specified domains and ranges. The unit advances into more complex scenarios where students must determine function domains involving higher polynomials, linear and quadratic expressions under square roots, and functions defined by fractional expressions over linear, quadratic, and radical denominators. The tasks require careful analysis to avoid undefined expressions and adhere to the conditions provided by each mathematical model, enhancing proficiency in translating between different mathematical representations of domains, such as number lines and algebraic conditions. The increasing complexity aids in mastering the algebraic and graphical understanding necessary to analyze functions critically within defined parameters.Skills you will learn include:

• Domain and range of functions
• Unions in domain and range
• Domain of Linear Functions
• Domain of Fractions
• Domain of Radicals

This math unit focuses on the end behavior of polynomial functions, progressing from basic understanding to more complex application and analysis. Initially, students learn to interpret the end behavior of polynomials through graphical analysis, identifying trends as \(x\) approaches positive or negative infinity. They then progress to matching these behaviors with appropriate graphical representations and deducing rules based on graph trends. As the unit advances, students deal with the correlation between the highest power and the leading coefficient of polynomials and how these influence the end behavior. They learn to determine these elements from graphs, rules, and directly from polynomial functions. Finally, the unit covers predicting polynomial graphs based on a given set of highest power and leading coefficient values, wrapping up with an ability to match polynomial functions to their respective end behaviors and rules, essentially preparing them for practical applications and deeper studies in polynomial functions.Skills you will learn include:

• End behaviour of functions
• Highest power and leading coefficient rules
• Identify functions from end behavour

This math unit focuses on the method of completing the square to convert quadratic equations from standard form to vertex form, across various coefficients. Students start by learning to partially complete the square for quadratic expressions with both positive and negative coefficients, which is crucial for setting the foundation in understanding the transformation processes. The unit progresses to fully completing the square, first with coefficients of 1 and -1, making it simpler for students to grasp the method. Next, they handle more complex coefficients (denoted by N and -N), where they manipulate and adjust the quadratic terms. The skills build towards converting quadratic equations directly from standard to vertex form, refining their ability to locate the vertex of the parabola. This ability is essential for graph analysis and understanding the properties of quadratic functions, such as identifying maxima or minima and graph symmetry. Throughout the unit, multiple-choice problems help solidify these transformation skills and improve the recognition of correct vertex forms from given options.Skills you will learn include:

• Quadratic equations
• Vertex form
• Converting to Vertex Form
• Graph features from Standard Form

This math unit starts with understanding the basics of function composition, focusing on identifying the input, output, inner, outer, first, and second functions in various composite configurations. Skills progress to calculating the outputs of these compositions, reinforcing comprehension through practical application. The unit then advances to evaluating the domains of these compositions, particularly when involving root, linear, rational, or quadratic functions, underscoring the importance of determining the set of input values that make the function compositions well-defined and meaningful. The culmination of the unit involves mastering the concept of function inverses, both for straightforward functions and more complex exponential and logarithmic forms. Students learn to discern whether pairs of functions are inverses and calculate the inverse of given functions to deepen their understanding of functional relationships, preparing them for more advanced studies in function operations and algebra.Skills you will learn include:

• Composition of Functions
• Domain of Composed Functions
• Inversion of Functions

This math unit concentrates on the factorization of quadratic equations with leading coefficients. Starting with the basics of splitting the middle term of quadratics in standard form, students learn to manipulate and simplify expressions with a focus on finding specific pairs of numbers meeting certain sum and product conditions. Progressing through the unit, the emphasis shifts to identifying and extracting common factors between grouped terms, further refining their ability to factorize quadratics into binomial forms. The unit advances to more complex skills where students consolidate common binomial factors from quadratic terms, aimed at simplifying these into factored forms. Towards the end, the tasks require students to apply their developed proficiency in factorization by deciding the proper factorization from presented options, encouraging a deep understanding and practical problem-solving abilities in polynomial factoring within quadratic contexts involving various arithmetic strategies and algebraic manipulations.Skills you will learn include:

• Polynomials with Coefficient
• Factoring polynomials
• Leading Coefficient not a Common Factor

This math unit guides students through the progression of factoring polynomials, starting with simpler quadratic equations and moving towards more complex cubic and quartic equations, including different coefficients and orders. Initially, students learn to factor quadratic equations by identifying and pulling out common binomial factors and using techniques to split terms. The unit then transitions to fourth-order polynomials treated as quadratic expressions, enhancing students' ability to factor without hints and to independently recognize patterns, even with different coefficients (labeled variably). The unit then shifts focus to cubic polynomials, where students apply specific algebraic formulas like the sum of cubes and practice factoring by grouping. Throughout the unit, problems escalate in complexity and also include verification of the correctness of factoring, pushing students to refine their understanding and mastery of polynomial factoring in algebra. This structured approach gradually builds and reinforces algebraic manipulation skills necessary for handling higher-order polynomial equations.Skills you will learn include:

• Factoring higher order polynomials
• Sum of cubes factoring
• Factoring by grouping

This math unit focuses on the factorization of higher-order polynomials, starting with fourth-order polynomials treated as quadratic expressions and advancing toward third-order polynomials. Initially, students practice factoring quartic polynomials using methods that assume a leading coefficient of 1 or a variable coefficient. As they progress, the unit introduces both multiple-choice and true/false formats to deepen understanding and verify the correctness of the factorization steps. The unit then transitions to third-order polynomials, emphasizing the sum of cubes formula before advancing to more complex factoring by grouping. Initially, students apply this formula directly to polynomials expressed as a sum or difference of cubes. Subsequently, the focus shifts to grouping techniques, where students factor cubic polynomials into quadratic and linear factors and verify their steps through true/false exercises. The practice moves from simple recognition and application of the formula to more nuanced algebraic manipulation and verification of factorization results, building a comprehensive skillset in polynomial factorization.Skills you will learn include:

• Factoring higher order polynomials
• Sum of cubes factoring
• Factoring by grouping