middle school math solution: algebra i

Ohio Correlation: Algebra I | 104/18/18

Middle School Math Solution: Algebra IOhio Correlation

8.MP MATHEMATICAL PRACTICESStandard Correlation

MP.1 Make Sense of problems and persevere in solving them.

Students learn that patience is often required to fully understand what a problem is asking. They discern between useful and extraneous information. They expand their repertoire of expressions and functions that can be used to solve problems.

This practice is evident in every lesson. Icons indicate which practice is emphasized in the lesson.

MP.2 Reason abstractly and quantitatively.Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; of considering the units involved; of attending to the meaning of quantities, not just how to compute them; and of knowing and fl exibly using diff erent properties of operations and objects.

Activities that use this practice have an icon located throughout the book.

Example: Module 1: Topic 1: Lesson 2: Activity 2.1 (p. M1-3)

MP.3 Construct viable arguments and critique the reasoning of others.

Students reason through the solving of equations, recognizing that solving an equation involves more than simply following rote rules and steps. They use language such as “If ___, then ___” when explaining their solution methods and provide justifi cation for their reasoning.



MP.4 Model with mathematics.Students also discover mathematics through experimentation and by examining data patterns from real-world contexts. They apply their new mathematical understanding of exponential, linear, and quadratic functions to real-world problems.





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MP.5 Use appropriate tools strategically.Students develop a general understanding of the graph of an equation or function as a representation of that object, and they use tools such as graphing calculators or graphing software to create graphs in more complex examples, understanding how to interpret results. They construct diagrams to solve problems.



MP.6 Attend to precision.Students use clear defi nitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure and labeling axes to clarify the correspondence with quantities in a problem. They make use of the defi nition of function when deciding if an equation can describe a function by asking, “Does every input value have exactly one output value?”



MP.7 Look for and make use of structure.Students develop formulas such as (a ± b)2 = a2 ± 2ab ± b2 by applying the distributive property. Students see that the expression 5 + (n – 2)2 takes the form of 5 plus “something squared,” and because “something squared” must be positive or zero, the expression can be no smaller than 5.



MP.8 Look for and express regularity in repeated reasoning.

Students see that the key feature of a line in the plane is an equal diff erence in outputs over equal intervals of inputs, and that the result of evaluating the expression (y2 – y1 )/(x2 – x1) points on the line is always equal to a certain number m. Therefore, if (x,y) is a generic point on this line, the equation m = (y2 – y1 )/(x2 – x1) .





NUMBER AND QUANTITIESReason quantitatively and use units to solve problems (Standards NQ.1–3).Standard Correlation

N.Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

TEXTBOOK: Module 1; Module 2Topic/Lesson: M1T1L1: Quantities and Relationships (M1-8 thru M1-20)M2T1L2: Making Sense of Four Representations of a Linear Function (M2-23 thru M2-40)M2T1L4: Comparing Linear Functions in Different Forms (M2-59 thru M2-67)M2T2L2: Literal Equations (M2-91 thru M2-102)

N.Q.2Define appropriate quantities for the purpose of descriptive modeling.

Note: Simple exponent expressions includes integer exponents only.

TEXTBOOK: Module 1; Module 3 Topic/Lesson: M1T1L1: Quantities and Relationships (M1-8 thru M1-20)M3T2L3: Modeling Using Exponential Functions (M3-1 thru M3-12)M3T2L4: Choosing a Function to Model Data (M3-1 thru M3-10)

N.Q.3Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.


TEXTBOOK: Module 1; Module 2; Module 3 Topic/Lesson: M1T3L1: Least Squares Regression (M1-167 thru M1-180)M1T3L2: Correlation (M1-181 thru M1-195)M1T3L4: Using Residual Plots (M1-211 thru M1-222)M2T2L3: Modeling Linear Inequalities (M2-103 thru M2-116)M2T2L4: Solving and Graphing Compound Inequalities (M2-117 thru M2-130)M3T2L1: Exponential Equations for Growth and Decay (M3-81 thru M3-92)



SEEING STRUCTURE IN EXPRESSIONSInterpret the structure of expressions (S.EE.1-2). Write expressions in equivalent forms to solve problems (Standard S.EE.3).Standard Correlation

A.SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients.


TEXTBOOK: Module 2; Module 5Topic/Lesson: M2T1L2: Making Sense of Four Representations of a Linear FUnction (M2-23 thru M2-40)M5T1L2: Key Characteristics of Quadratic Functions (M5-23 thru M5-46)M5T1L4: Comparing Functions Using Key Characteristics and Average Rate of Change (M5-1 thru M5-13)M5T2L1: Adding, Subtracting, and Multiplying Polynomials (M5-101 thru M5-125)

A.SSE.1.bInterpret complicated expressions by viewing one or more of their parts as a single entity.

TEXTBOOK: Module 5Topic/Lesson: M5T2L5: The Quadratic Formula (M5-175 thru M5-202)

A.SSE.2Use the structure of an expression to identify ways to rewrite it.

TEXTBOOK: Module 5Topic/Lesson: M5T2L2: Representing Solutions to Quadratic Equations (M5-127 thru M5-140)M5T2L3: Solutions to Quadratic Equations in Vertex Form (M5-141 thru M5-151)

A.SSE.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A.SSE.3.aFactor a quadratic expression to reveal the zeros of the function it defines.

TEXTBOOK: Module 5Topic/Lesson: T1L2: Key Characteristics of Quadratic Functions (M5-23 thru M5-46)T1L3: Transformations of Quadratic Functions (M5-47 thru M5-72)T2L2: Representing Solutions to Quadratic Equations (M5-127 thru M5-140)T2L3: Solutions to Quadratic Equations in Vertex Form (M5-141 thru M5-151)

MATHia: Unit: Forms of QuadraticsWorkspace: Converting Quadratics to General Form; Converting Quadratics to Factored Form; Converting Quadratics to Vertex Form

A.SSE.3.bComplete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

TEXTBOOK: Module 5Topic/Lesson: T2L4: Factoring and Completing the Square (M5-153 thru M5-174)

MATHia: Unit: Forms of QuadraticsWorkspace: Converting Quadratics to General Form; Converting Quadratics to Factored Form; Converting Quadratics to Vertex Form

A.SSE.3.cUse the properties of exponents to transform expressions for exponential functions. For example, 8t can be written as 23t.


TEXTBOOK: Module 3Topic/Lesson: T2L2: Interpreting Parameters in Context (M3-93 thru M3-102)



ARITHMETIC WITH POLYNOMIALS AND RATIONAL EXPRESSIONSPerform arithmetic operations on polynomials (Standards A.APR.1).Standard Correlation

A.APR.1 Understand that polynomials form a system analogous to the integers, namely, that they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

A.APR.1.aFocus on polynomial expressions that simplify to forms that are linear or quadratic.

TEXTBOOK: Module 5Topic/Lesson: T2L1: Adding, Subtracting, and Multiplying Polynomials (M5-101 thru M5-125)

MATHia: Unit: Polynomial Operations;; Quadratic Expression FactoringWorkspace: Introduction to Polynomial Arithmetic; Adding Polynomials; Subtracting Polynomials; Using a Factor Table to Multiply Polynomials; Multiplying Polynomials; Using a Factor Table to Multiply Binomials; Multiplying Binomials



CREATING EQUATIONSCreate equations that describe numbers or relationships (Standards A.CED.1–4).Standard Correlation

A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations and inequalities arising from linear, quadratic, simple rational, and exponential functions.

A.CED.1.aFocus on applying linear and simple exponential expressions.


TEXTBOOK: Module 2; Module 3Topic/Lesson: M2T1L2: Making Sense of Four Representations of a Linear Function (M2-23 thru M2-40)M2T2L1: Solving Linear Equations (M2-1 thru M2-12)M2T2L3: Modeling Linear Inequalities (M2-103 thru M2-116)M2T2L4: Solving and Graphing Compound Inequalities M2-117 thru M2-130)M3T1L2: Rational Exponents and Graphs of Exponential Functions (M3-23 thru M3-44)M3T2L1: Exponential Equations for Growth and Decay (M3-81 thru M3-92)M3T2L2: Interpreting Parameters in Context (M3-93 thru M3-102)

MATHia: Unit: Linear EquationsWorkspace: Modeling Rates of Change; Modeling Linear Equations Given Two Points; Modeling Linear Equations Given an Initial Point; Modeling Linear Functions using Multiple Representations

A.CED.1.bFocus on applying simple quadratic expressions

TEXTBOOK: Module 5Topic/Lesson: T3L1: Solving Quadratic Inequalities (M5-1 thru M5-10)

MATHia: Unit: Quadratic Models in Factored FormWorkspace: Modeling Area as Product of Monomial and Binomial; Modeling Area as Product of Two Binomials; Interpreting Maximums of Quadratic Models

A.CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.CED.2.aFocus on applying linear and simple exponential expressions.


TEXTBOOK: Module 2; Module 3Topic/Lesson: M2T3L1: Introduction to Systems of Equations (M2-1 thru M2-16)M2T3L2: Using Linear Combinations to Solve a System of Linear Equations (M2-1 thru M2-14)M2T3L3: Graphing Inequalities in Two Variables (M2-169 thru M2-184)M3T2L1: Exponential Equations for Growth and Decay (M3-81 thru M3-92)M3T2L2: Interpreting Parameters in Context (M3-93 thru M3-102)

A.CED.2.bFocus on applying simple quadratic expressions.

TEXTBOOK: Module 5Topic/Lesson: T3L1: Solving Quadratic Inequalities (M5-1 thru M5-10)T3L2: Systems of Quadratic Equations (M5-225 thru M5-236)




A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.

NOTE: Algebra I students should focus on linear constraints.

TEXTBOOK: Module 2; Module 3Topic/Lesson: M2T2L3: Modeling Linear Inequalities (M2-103 thru M2-116)M2T3L3: Graphing Inequalities in Two Variables (M2-169 thru M2-184)M2T3L4: Systems of Linear Inequalities (M2-2 thru M2-14)M2T3L5: Solving Systems of Equations and Inequalities (M2-1 thru M2-10)M2T3L6: Linear Programming (M2-1 thru M2-10)M3T3L1: Solving Quadratic Inequalities (M5-1 thru M5-10)

MATHia: Unit: Absolute Value EquationsWorkspace: Graphing Simple Absolute Value Equations using Number Lines; Solving Absolute Value Equations; Reasoning About Absolute Value Inequalities

A.CED.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A.CED.4.aFocus on formulas in which the variable of interest is linear or square.

TEXTBOOK: Module 2; Module 5Topic/Lesson: M2T2L2: Literal Equations (M2-91 thru M2-102)M5T1L4: Comparing Functions Using Key Characteristics and Average Rate of Change (M5-1 thru M5-13)



REASONING WITH EQUATIONS AND INEQUALITIESUnderstand solving equations as a process of reasoning and explain the reasoning (Standards REI.1) Solve equations and inequalities in one variable (Standards A.REI.3-4) Solve systems of equations (Standards A.REI.5-7) Represent and solve equations and inequalities graphically (Standards A.REI.10-12).Standard Correlation

A.REI.1Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

TEXTBOOK: Module 2Topic/Lesson: T2L1: Solving Linear Equations (M2-1 thru M2-12)

A.REI.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

TEXTBOOK: Module 2Topic/Lesson: T2L1: Solving Linear Equations (M2-1 thru M2-12)T2L3: Modeling Linear Inequalities (M2-103 thru M2-116)T2L4: Solving and Graphing Compound Inequalities (M2-117 thru M2-130)

MATHia: Unit: Linear InequalitiesWorkspace: Graphing Inequalities; Solving Two-Step Linear Inequalities; Representing Compound Inequalities

A.REI.4Solve quadratic equations in one variable.

A.REI.4.aUse the method of completing the square to transform any quadratic equation in x into an equation of the form (x − p)² = q that has the same solutions.

TEXTBOOK: Module 5Topic/Lesson: T2L4: Factoring and Completing the Square (M5-153 thru M5-174)T2L5: The Quadratic Formula (M5-175 thru M5-202)T3L1: Solving Quadratic Inequalities (M5-1 thru M5-10)

A.REI.4.bSolve quadratic equations as appropriate to the initial form of the equation by inspection, e.g., for x² = 49; taking square roots; completing the square; applying the quadratic formula; or utilizing the Zero-Product Property after factoring.

Note: Quadratic equations are limited to those that have only real solutions.

TEXTBOOK: Module 5Topic/Lesson: T2L2: Representing Solutions to Quadratic Equations (M5-127 thru M5-140)T2L5: The Quadratic Formula (M5-175 thru M5-202)T3L1: Solving Quadratic Inequalities (M5-1 thru M5-10)

MATHia: Unit: Quadratic Expression Factoring; Quadratic Equation SolvingWorkspace: Completing the Square; Solving Quadratic Equations by Factoring; Solving Quadratic Equations




A.REI.4.c. (+)Derive the quadratic formula using the method of completing the square.

A.REI.5Verify that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Note: This standard only addresses linear equations in two variables only.

TEXTBOOK: Module 2Topic/Lesson: T3L2: Using Linear Combinations to Solve a System of Linear Equations (M2-1 thru M2-14)

MATHia: Unit: Systems of Linear EquationsWorkspace: Solving Linear Systems using Linear Combinations

A.REI.6Solve systems of linear equations algebraically and graphically.

A.REI.6.aLimit to pairs of linear equations in two variables.

TEXTBOOK: Module 2Topic/Lesson: T3L1: Introduction to Systems of Equations (M2-1 thru M2-16) T3L2: Using Linear Combinations to Solve a System of Linear Equations (M2-1 thru M2-14)T3L5: Solving Systems of Equations and Inequalities (M2-1 thru M2-10)

MATHia: Unit: Systems of Linear EquationsWorkspace: Representing Systems of Linear Function; Solving Linear Systems using Any Method

A.REI.7Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

For example, find the points of intersection between the line y = −3x and the circle x² + y² = 3.

TEXTBOOK: Module 5Topic/Lesson: T3L2: Systems of Quadratic Equations (M5-225 thru M5-236)

A.REI.10Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).


TEXTBOOK: Module 1; Module 2; Module 3; Module 5Topic/Lesson: M1T1L1: Quantities and Relationships (M1-8 thru M1-20)M2T1L2: Making Sense of Four Representations of a Linear Function (M2-23 thru M2-40)M2T3L1: Introduction to Systems of Equations (M2-1 thru M2-16)M3T1L1: Geometric Sequences and Exponential Functions (M3-7 thru M3-22)M3T2L2: Interpreting Parameters in Context (M3-93 thru M3-102)M5T1L1: Exploring Quadratic Functions (M5-7 thru M5-22)M5T2L2: Representing Solutions to Quadratic Equations (M5-127 thru M5-14)

MATHia: Unit: Function OverviewWorkspace: Exploring Graphs of Linear Functions




A.REI.11Explain why the x-coordinates of the points where the graphs of the equation y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, making tables of values, or finding successive approximations.


TEXTBOOK: Module 2; Module 3; Module 5Topic/Lesson: M2T3L1: Introduction to Systems of Equations (M2-1 thru M2-16)M2T3L6: Linear Programming (M2-1 thru M2-10)M3T2L2: Interpreting Parameters in Context (M3-93 thru M3-102)M5T1L1: Exploring Quadratic Functions (M5-7 thru M5-22)M5T3L2: Systems of Quadratic Equations (M5-225 thru M5-236)

MATHia: Unit: Systems of Linear Equations; Quadratic Equation SolvingWorkspace: Representing Systems of Linear Function; Making Sense of Roots and Zeros

A.REI.12Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

TEXTBOOK: Module 2Topic/Lesson: T3L3: Graphing Inequalities in Two Variables (M2-169 thru M2-184)T3L4: Systems of Linear Inequalities (M2-2 thru M2-14)T3L5: Solving Systems of Equations and Inequalities (M2-1 thru M2-10)T3L6: Linear Programming (M2-1 thru M2-10)

MATHia: Unit: Linear Inequalities in Two VariablesWorkspace: Graphing Linear Inequalities in Two Variables; Systems of Linear Inequalities



INTERPRETING FUNCTIONSUnderstand the concept of a function, and use function notation (Standards F.IF.1-3) Interpret functions that arise in applications in terms of the context (Standards F.IF.4-5) Analyze functions using different representations- (F.IF.7-9)Standard Correlation

F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

TEXTBOOK: Module 1; Module 2Topic/Lesson: M1T1L1: Quantities and Relationships (M1-8 thru M1-20)M1T1L3: Recognizing Functions and Function Families (M1-39 thru M1-6)M2T1L1: Making Connections Between Arithmetic Sequences and Linear Functions (M2-1 thru M2-16)

MATHia: Unit: Function OverviewWorkspace: Introduction to Function Families; Understanding Linear Functions; Exploring Graphs of Linear Functions; Identifying Key Characteristics of Graphs of Functions

F.IF.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

TEXTBOOK: Module 2Topic/Lesson: T1L2: Making Sense of Four Representations of a Linear Function (M2-23 thru M2-40)T3L6: Linear Programming (M2-1 thru M2-10)

MATHia: Unit: Function OverviewWorkspace: Evaluating Linear Functions

F.IF.3Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n + 1) = f(n) + f(n − 1) for n ≥ 1.

TEXTBOOK: Module 1; Module 2Topic/Lesson: M1T2L1: Recognizing Patterns and Sequences (M1-87 thru M1-102)M2T1L1: Making Connections Between Arithmetic Sequences and Linear Functions (M2-1 thru M2-16)

MATHia: Unit: SequencesWorkspace: Describing Patterns in Sequences; Writing Sequences as Functions

F.IF.4For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include the following: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.




F.IF.4.b Focus on linear, quadratic, and exponential functions.


TEXTBOOK: Module 1; Module 2; Module 3; Module 5Topic/Lesson: M1T1L1: Quantities and Relationships (M1-8 thru M1-20)M1T1L2: Sequences (M1-1 thru M1-18)M1T1L3: Recognizing Functions and Function Families (M1-39 thru M1-62)M1T1L4: Recognizing Functions by Characteristics (M1-1 thru M1-13)M2T1L2: Making Sense of Four Representations of a Linear Function (M2-23 thru M2040)M2T1L3: Transforming Linear Functions (M2-41 thru M2-57)M3T1L3: Transformations of Exponential Functions (M3-45 thru M3-69)M5T1L1: Exploring Quadratic Functions (M5-7 thru M5-22)M5T1L2: Key Characteristics of Quadratic Functions (M5-23 thru M5-46)

F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.


TEXTBOOK: Module 1; Module 5Topic/Lesson: M1T1L3: Recognizing Functions and Function Families (M1-39 thru M1-62)M1T2L1: Recognizing Patterns and Sequences (M1-87 thru M1-102)M5T1L1: Exploring Quadratic Functions (M5-7 thru M5-22)

MATHia: Unit: Exponential FunctionsWorkspace: Relating the Domain to Exponential Functions

F.IF.7 Graph functions expressed symbolically and indicate key features of the graph, by hand in simple cases and using technology for more complicated cases. Include applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.

F.IF.7.a Graph linear functions and indicate intercepts.

TEXTBOOK: Module 2Topic/Lesson: T1L3: Transforming Linear Functions (M2-41 thru M2-57)

F.IF.7.b Graph quadratic functions and indicate intercepts, maxima, and minima.

TEXTBOOK: Module 5Topic/Lesson: T1L1: Exploring Quadratic Functions (M5-7 thru M5-22)T1L2: Key Characteristics of Quadratic Functions (M5-23 thru M5-46)T3L3: Using Quadratic Functions to Model Data (M5-1 thru M5-16)

MATHia: Unit: Forms of QuadraticsWorkspace: Sketching Quadratic Functions




F.IF.7.e Graph simple exponential functions, indicating intercepts and end behavior.


TEXTBOOK: Module 3Topic/Lesson: T1L3: Transformations of Exponential Functions (M3-45 thru M3 69)

F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.IF.8.a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

i. Focus on completing the square to quadratic functions with the leading coefficient of 1.

TEXTBOOK: Module 5Topic/Lesson: T1L2: Key Characteristics of Quadratic Functions (M5-23 thru M5-46)T2L4: Factoring and Completing the Square (M5-153 thru M5-174)

MATHia: Unit: Quadratic Expression Factoring; Forms of QuadraticsWorkspace: Completing the Square; Identifying Properties of Quadratic Functions; Converting Quadratics to General Form; Converting Quadratics to Factored Form; Converting Quadratics to Vertex Form

F.IF.8.b Use the properties of exponents to interpret expressions for exponential functions.

For example, identify percent rate of changeG in functions such as y = (1.02)t, and y = (0.97)t and classify them as representing exponential growth or decay.i. Focus on exponential functions evaluated at integer inputs.


TEXTBOOK: Module 3Topic/Lesson: T1L2: Rational Exponents and Graphs of Exponential Functions (M3-23 thru M3-44)T1L3: Transformations of Exponential Functions (M3-45 thru M3-69)T2L2: Interpreting Parameters in Context (M3-93 thru M3-102)

MATHia: Unit: Exponential FunctionsWorkspace: Using Properties of Exponents

F.IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.


TEXTBOOK: Module 2; Module 5Topic/Lesson: M2T1L4: Comparing Linear Functions in Different Forms (M2-59 thru M2-67)M5T1L4: Comparing Functions using Key Characteristics and Average Rate of Change (M5-1 thru M5-13)

MATHia: Unit: Linear Equations; Exponential Functions; Forms of QuadraticsWorkspace: Comparing Linear Functions in Different Form; Comparing Exponential Functions in Different Forms; Comparing Quadratic Functions in Different Forms



BUILDING FUNCTIONSBuild a function that models a relationship between two quantities (Standards F.BF.1-2) Build new functions from existing functions (Standards F.BF.3-4)Standard Correlation

F.BF.1Write a function that describes a relationship between two quantities.

F.BF.1.a Determine an explicit expression, a recursive process, or steps for calculation from context.

i. Focus on linear and exponential functions. ii. Focus on situations that exhibit quadratic or exponential relationships.


TEXTBOOK: Module 1; Module 3Topic/Lesson: M1T2L1: Recognizing Patterns and Sequences (M1-87 thru M1-102)M1T2L3: Determining Recursive and Explicit Expressions from Context (M1-1 thru M1-12)M3T1L1: Geometric Sequences and Exponential Functions (M3-7 thru M3-22)M3T2L3: Modeling Using Exponential Functions (M3-1 thru M3-12)

MATHia: Unit: SequencesWorkspace: Writing Recursive Formulas; Writing Explicit Formulas

F.BF.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

TEXTBOOK: Module 1Topic/Lesson: T2L2: Arithmetic and Geometric Sequences (M1-102 thru M1-134)T2L4: Modeling using Sequences (M1-147 thru M1-158)

F.BF.3Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

F.BF.3.aFocus on transformations of graphs of quadratic functions, except for f(kx).

TEXTBOOK: Module 2; Module 3; Module 5Topic/Lesson: M2T1L2: Making Sense of Four Representations of a Linear Function (M2-23 thru M2-40)M3T1L3: Transformations of Exponential Functions (M3-45 thru M3-69)M5T1L3: Transformations of Quadratic Functions (M5-47 thru M5-72)

MATHia: Unit: Linear and Quadratic Transformations; Function OperationsWorkspace: Shifting Vertically; Reflecting and Dilating using Graphs; Shifting Horizontally; Transforming using Tables of Values; Using Multiple Transformations; Operating with Functions on the Coordinate Plane




F.BF.4Informally determine the input of a function when the output is known.

F.BF.4.a Informally determine the input of a function when the output is known.

TEXTBOOK: Module 5Topic/Lesson: T3L3: Using Quadratic Functions to Model Data (M5-1 thru M5-16)

MATHia: Unit: Exponential Functions; Quadratic Models in General Form; Inverses of FunctionsWorkspace: Introduction to Exponential Functions; Modeling Projectile Motion; Recognizing Key Features of Vertical Motion Graphs; Recognizing Graphs of Inverses; Calculating Inverses of Linear Functions



LINEAR, QUADRATIC, AND EXPONENTIAL MODELSConstruct and compare linear, quadratic, and exponential models, and solve problems (Standards F.LE.1-3) Interpret expressions for functions in terms of the situation they model (Standard F.LE.5)Standard Correlation

FLE.1Distinguish between situations that can be modeled with linear functions and with exponential functions.

F.LE.1.a Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.


TEXTBOOK: Module 2; Module 3Topic/Lesson: M2T1L1: Making Connections Between Arithmetic Sequences and Linear Functions (M2-1 thru M2-16)M3T1L1: Geometric Sequences and Exponential Functions (M3-7 thru M3-22)

F.LE.1.bRecognize situations in which one quantity changes at a constant rate per unit interval relative to another.

TEXTBOOK: Module 2Topic/Lesson: T1L1: Making Connections Between Arithmetic Sequences and Linear Functions (M2-1 thru M2-16)

F.LE.1.cRecognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.


TEXTBOOK: Module 3Topic/Lesson: T2L1: Exponential Equations for Growth and Decay (M3-81 thru M3-92)

MATHia: Unit: Compare Linear and Exponential ModelsWorkspace: Recognizing Growth and Decay

F.LE.2Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

TEXTBOOK: Module 2; Module 3Topic/Lesson: M2T1L1: Making Connections Between Arithmetic Sequences and Linear Functions (M2-1 thru M2-16)Note: Students are not required to use fractional exponents)M3T1L1: Geometric Sequences and Exponential Functions (M3-7 thru M3-22)M3T1L2: Rational Exponents and Graphs of Exponential Functions (M3-23 thru M3-44)

F.LE.3Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.


TEXTBOOK: Module 3; Module 5Topic/Lesson: M3T2L1: Exponential Equations for Growth and Decay (M3-81 thru M3-92)M5T1L4: Comparing Functions Using Key Characteristics and Average Rate of Change (M5-1 thru M5-13)

F.LE.5Interpret the parameters in a linear or exponential function in terms of a context.


TEXTBOOK: Module 3Topic/Lesson: T1L1: Geometric Sequences and Exponential Functions (M3-7 thru M3-22)T2L1: Exponential Equations for Growth and Decay (M3-81 thru M3-92)T2L2: Interpreting Parameters in Context (M3-93 thru M3-102)



INTERPRETING CATEGORICAL AND QUANTITATIVE DATASummarize, represent, and interpret data on a single count or measurement variable (Standards S.ID.1-3) Summarize, represent, and interpret data on two categorical and quantitative variables (Standards S.ID.5-6) Interpret linear models (Standards S.ID.7-8).Standard Correlation

S.ID.1 Represent data with plots on the real number line (dot plotsG, histograms, and box plots) in the context of real-world applications using the GAISE model.

TEXTBOOK: Module 4Topic/Lesson: T1L1: Graphically Representing Data (M4-7 thru M4-16)T1L2: Determining the Better Measure of Center for a Data Set (M4-17 thru M4-34)T1L3: Comparing Data Sets (M4-35 thru M4-44)

MATHia: Unit: Numerical Summary StatisticsWorkspace: Comparing and Interpreting Measures of Center

S.ID.2In the context of real-world applications by using the GAISE model, use statistics appropriate to the shape of the data distribution to compare center (median and mean) and spread (mean absolute deviationG, interquartile rangeG, and standard deviation) of two or more different data sets.

TEXTBOOK: Module 4Topic/Lesson: T1L1: Graphically Representing Data (M4-7 thru M4-16)T1L2: Determining the Better Measure of Center for a Data Set (M4-17 thru M4-34)T1L3: Comparing Data Sets (M4-35 thru M4-44)

MATHia: Unit: Numerical Summary StatisticsWorkspace: Determining Appropriate Measures; Comparing and Interpreting Measures of Center

S.ID.3In the context of real-world applications by using the GAISE model, interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

TEXTBOOK: Module 4Topic/Lesson: T1L2: Determining the Better Measure of Center for a Data Set (M4-17 thru M4-34)T1L3: Comparing Data Sets (M4-35 thru M4-44)

MATHia: Unit: Numerical Summary StatisticsWorkspace: Measuring the Effects of Changing Data Sets; Comparing and Interpreting Measures of Center

S.ID.5Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

TEXTBOOK: Module 4Topic/Lesson: T2L1: Creating and Interpreting Frequency Distributions (M4-55 thru M4-71)T2L2: Relative Frequency Distribution (M4-73 thru M4-83)T2L3: Conditional Relative Frequency Distribution (M4-85 thru M4-94)T2L4: Drawing Conclusions from Data (M4-1 thru M4-10)




S.ID.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S.ID.6.c Fit a linear function for a scatterplot that suggests a linear association.


TEXTBOOK: Module 1; Module 3Topic/Lesson: M1T3L1: Least Squares Regression (M1-167 thru M1-180)M1T3L2: Correlation (M1-181 thru M1-195)M1T3L3: Creating Residual Plots (M1-197 thru M1-210)M1T3L4: Using Residual Plots (M1-211 thru M1-222)M3T2L3: Modeling Using Exponential Functions (M3-1 thru M3-12)M3T2L4: Choosing a Function to Model Data (M3-1 thru M3-10)

MATHia: Unit: Lines of Best Fit; Quadratic Equation SolvingWorkspace: Exploring Linear Regression; Using Regression Models

S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a liner model in the context of the data.

TEXTBOOK: Module 1Topic/Lesson: T3L1: Least Squares Regression (M1-167 thru M1-180)

MATHia: Unit: Compare Linear and Exponential Models; Lines of Best FitWorkspace: Recognizing Linear and Exponential Models; Exploring Linear Regression; Interpreting Lines of Best Fit

S.ID.8 Computer (using technology) and interpret the correlation coefficient of a linear fit.

TEXTBOOK: Module 1Topic/Lesson: T3L2: Correlatinn (M1-181 thru M1-195)

MATHia: Unit: Compare Linear and Exponential Models; Lines of Best FitWorkspace: Recognizing Linear and Exponential Models; Interpreting Lines of Best Fit

middle school math solution: algebra i

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