ALGEBRA 1 COMMON CORE CURRICULUM

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TABLE OF CONTENTS

Unit Section Pacing

(Days) Page

1 1-1 Evaluating Expressions 1 5

1 1-2 Simplifying expressions 1 6

1 1-3 Writing Expressions 1 7

1 1-4 Writing Equations and Inequalities 1 8

1 1-5 Representing Functions 1 9

1 1-6 Modeling with Functions 1 10

1 Unit 1 Task 1

1 Unit 1 Test 1

2 2-1 Solving Linear Equations 1 11

2 2-2 Solving Linear Inequalities 1 12

2 2-3 Modeling with One-Variable Linear Equations and Inequalities 1 13

2 2-4 Literal Equations and Inequalities 1.5 14

2 2-5 Rewriting Formulas 1.5 15

2 2-6 Linear Equations in Two Variables 1 16

2 2-7 Linear Inequalities in Two Variables 1.5 17

2 2-8 Modeling with Two-Variable Linear Equations and Inequalities 1.5 18

2 Unit 2 Task 1

2 Unit 2 Test 1

3 3-1 Solving Linear Systems by Graphing 1 19

3 3-2 Solving Linear Systems by Substitution 1 20

3 3-3 Solving Linear Systems by Adding or Subtracting 1 21

3 3-4 Solving Linear Systems by Multiplying 1 22

3 3-5 Solving Systems of Linear Inequalities 1.5 23

3 3-6 Modeling with Linear Systems 1.5 24

3 Unit 3 Task 1

3 Unit 3 Test 1

ALGEBRA 1 COMMON CORE CURRICULUM

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Unit Section Pacing

(Days) Page

4 4-1 Discrete Linear Functions 1 25

4 4-2 Continuous Linear Functions 1 26

4 4-3 Using Slope 1 27

4 4-4 Changing the Values of m and b in f x mx b 1 28

4 4-5 Writing Linear Functions 1 29

4 4-6 Operations with Linear Functions 1 30

4 4-7 Linear Functions and Their Inverses 1 31

4 4-8 Correlations 1 32

4 4-9 Fitting Lines to Data 1 33

4 4-10 Linear Regression 1 34

4 Unit 4 Task 1

4 Unit 4 Test 1

5 5-1 Discrete Exponential Functions 1 35

5 5-2 Exponential Growth Functions 1 36

5 5-3 Exponential Decay Functions 1 37

5 5-4 Changing the values of a and b in xf x ab 1 38

5 5-5 Solving Equations Involving Exponents 1.5 39

5 5-6 Performing Exponential Regression 0.5 40

5 5-7 Comparing Linear and Exponential Functions 1 41

5 5-8 Modeling with Exponential Functions 1 42

5 Unit 5 Task 1

5 Unit 5 Test 1

6 6-1 Piecewise Functions 1 43

6 6-2 Translating the Graph of f x x 1 44

6 6-3 Stretching, Shrinking, and Reflecting the Graph of f x x 1 45

6 6-4 Combining Transformations of the Graph of f x x 1 46

6 6-5 Solving Absolute Value Equations 1 47

ALGEBRA 1 COMMON CORE CURRICULUM

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Unit Section Pacing

(Days) Page

6 6-6 Modeling with Absolute Value Functions 1 48

6 Unit 6 Task 1

6 Unit 6 Test 1

7 7-1 Translating the Graph of 2f x x 1 49

7 7-2 Stretching, Shrinking, and Reflecting the Graph of 2f x x 1 50

7 7-3 Combining Transformations of the Graph of 2f x x 1 51

7 7-4 Solving Quadratic Equations Graphically 1 52

7 7-5 Solving Quadratic Equations Using Square Roots 1.5 53

7 7-6 Modeling with Quadratic Functions 1.5 54

7 Unit 7 Task 1

7 Unit 7 Test 1

8 8-1 Multiplying Binomials 1 55

8 8-2 Solving 2 0x bx c by Factoring 1.5 56

8 8-3 Solving 2 0ax bx c by Factoring 1.5 57

8 8-4 Solving 2 0x bx c by Completing the Square 1.5 58

8 8-5 Solving 2 0ax bx c by Completing the Square 1.5 59

8 8-6 Deriving the Quadratic Formula 1 60

8 8-7 Using the Quadratic Formula 1.5 61

8 8-8 Graphing Functions of the form 2f x ax bx c 1.5 62

8 8-9 Solving Systems of Linear and Quadratic Equations 1 63

8 8-10 Modeling with Quadratic Functions 1 64

8 Unit 8 Task 1

8 Unit 8 Test 1

9 9-1 Measures of Center and Spread 1 65

9 9-2 Data Distributions and Outliers 1 66

9 9-3 Histograms 1 67

9 9-4 Box Plots 1 68

ALGEBRA 1 COMMON CORE CURRICULUM

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Unit Section Pacing

(Days) Page

9 9-5 Two-Way Frequency Tables 1 69

9 Unit 9 Task 1

9 Unit 9 Test 1

90

Pages 70-77 list Common Core tasks linked by standard. Click on the link to access the task.

NOTE: The suggested pacing has been designed for a single semester block course. For year-long

courses, apply proportional pacing.

Highlighted Standards Key

Pink TN Focus Clusters (CRAs assess these)

Green Major works of the grade

Blue Supporting clusters

Yellow Additional clusters

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 1: ALGEBRAIC MODELING AND UNIT ANALYSIS

1-1 Evaluating Expressions

CCSSI Standards

N-Q.1 Use units as a way to understand… and to guide the solutions of multi-step problems…

A-SSE.1 Interpret expressions that represent a quantity in terms of its context.

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

A-SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single

entity.

Mathematical Practices

Practice #7 Differentiate between factors and terms. (Look for and make use of structure)

Academic Vocabulary

algebraic expression numerical expression

constant order of operations

coefficient term

evaluate variable

expression

Essential Question

How do you interpret and evaluate algebraic expressions that model real-world situations?

Skills

1. Use the order of operations to simplify algebraic expressions

2. Identify coefficients

3. Identify constants

4. Identify the terms of an algebraic expression

5. Evaluate algebraic expressions

6. Use unit analysis to solve problems

Alignment to Current Textbook

Section 1-1 (pp.6-11), Section 1-6 (pp.40-45)

Notes

Common Core assumes students can operate with integers.

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 1: ALGEBRAIC MODELING AND UNIT ANALYSIS

1-2 Simplifying Expressions

CCSSI Standards

N-Q.1 Use units as a way to understand… and to guide the solutions of multi-step problems…

A-SSE.1 Interpret expressions that represent a quantity in terms of its context.

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

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

Mathematical Practices

Practice #7 Analyze the properties of real numbers used for simplifying expressions. (Look for and

make use of structure)

Academic Vocabulary

Commutative Property of Addition Associative Property of Multiplication

Associative Property of Addition multiplicative identity

additive identity multiplicative inverses

additive inverses Distributive Property

Commutative Property of Multiplication

Essential Question

How can you rewrite algebraic expressions?

Skills

1. Compare expressions

2. Use properties to simplify expressions

3. Identify properties

4. Simplify expressions

Alignment to Current Textbook

Section 1-7 (pp.46-51)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 1: ALGEBRAIC MODELING AND UNIT ANALYSIS

1-3 Writing Expressions

CCSSI Standards

N-Q.1 Use units as a way to understand… and to guide the solutions of multi-step problems…

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

A-SSE.1 Interpret expressions that represent a quantity in terms of its context.

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

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

Mathematical Practices

Practice #1 Translate verbal phrases into algebraic expressions so that they can be evaluated

mathematically. (Make sense of problems and persevere in solving them)

Academic Vocabulary

addition division

subtraction quotient

multiplication

Essential Question

How do you write algebraic expressions to model quantities?

Skills

1. Write an algebraic expression to model a phrase.

2. Write a phrase to model an algebraic expression.

3. Use unit analysis to guide modeling.

Alignment to Current Textbook

Section 1-1 (pp.6-9)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 1: ALGEBRAIC MODELING AND UNIT ANALYSIS

1-4 Writing Equations and Inequalities

CCSSI Standards

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

A-CED.1 Create equations and inequalities in one variable and use them to solve problems.

A-CED.3 Represent constraints by equations or inequalities… and interpret solutions as viable or

nonviable options in a modeling context.

Mathematical Practices

Practice #2 Represent a situation symbolically and expand the solution set based upon the units

being used. (Reason abstractly and quantitatively)

Academic Vocabulary

equation inequality

solution of an equation solution of an inequality

Essential Question

How do you represent relationships algebraically?

Skills

1. Write equations from verbal models.

2. Solve equations from verbal models.

3. Write inequalities from verbal models.

4. Solve inequalities from verbal models.

Alignment to Current Textbook

Section 2-1 (pp.77-82), Section 3-1 (pp.170-175)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 1: ALGEBRAIC MODELING AND UNIT ANALYSIS

1-5 Representing Functions

CCSSI Standards

N-Q.1 Choose and interpret the scale and the origin in graphs and data displays.

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 .

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes.

Mathematical Practices

Practice #2 Analyze inputs and outputs and their associated units. (Reason abstractly and

quantitatively)

Academic Vocabulary

function independent variable

domain dependent variable

range function rule

function notation

Essential Question

How do you represent functions?

Skills

1. Write the domain and range of a function.

2. Represent functions as equations, tables of values, and graphs.

Alignment to Current Textbook

Section 1-8 (pp.54-59)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 1: ALGEBRAIC MODELING AND UNIT ANALYSIS

1-6 Modeling with Functions

CCSSI Standards

N-Q.1 Choose and interpret the scale and the origin in graphs and data displays.

A-CED.1 Create equations… in one variable and use them to solve problems.

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 .

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.5 Relate the domain of a function to its graph.

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

F-BF.1.a Determine an explicit expression… from a context.

Mathematical Practices

Practice #3 Summarize findings and comment on the clarity and completeness of the findings for

paying off a loan using a function. (Construct viable arguments and critique the

reasoning of others)

Academic Vocabulary

function independent variable

domain dependent variable

range function rule

function notation

Essential Question

How can you model paying off a loan using a function?

Skills

1. Write a function rule from given information.

2. Make a table and a graph to represent a function.

3. Analyze a function model.

Alignment to Current Textbook

Section 1-8 (pp.54-59)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 2: LINEAR EQUATIONS AND INEQUALITIES

2-1 Solving Linear Equations

CCSSI Standards

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

A-REI.1 Explain 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.

A-REI.3 Solve linear equations.

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

Mathematical Practices

Practice #3 Recognize that finding the values such that two functions are equal uses the skills of

solving an equation Justifications should involve the properties of equality and other

properties. Show that the solution is correct by checking the values in the original

function. (Construct viable arguments and critique the reasoning of others)

Academic Vocabulary

equivalent equations Multiplication Property of Equality

Addition Property of Equality Division Property of Equality

Subtraction Property of Equality

Essential Question

How can you use the properties of equality to support your solution to a linear equation?

Skills

1. Solve a one-step linear equation.

2. Solve a multi-step linear equation.

3. Determine equality of functions where f x g x .

Alignment to Current Textbook

Section 2-1 (pp.77-82), Section 2-2 (pp.84-90), Section 2-3 (pp.92-98), Section 2-4 (pp.100-106)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 2: LINEAR EQUATIONS AND INEQUALITIES

2-2 Solving Linear Inequalities

CCSSI Standards

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

A-REI.1 Explain 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.

A-REI.3 Solve linear equations.

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

Mathematical Practices

Practice #7 Recognize that the properties of equality and the properties of inequalities are

structured in the same way. (Look for and make use of structure)

Academic Vocabulary

Addition Property of Inequality Multiplication Property of Inequality

Subtraction Property of Inequality Division Property of Inequality

Essential Question

How do you justify the solution to a linear inequality?

Skills

1. Justify the solution of an inequality.

2. Solve a multi-step linear inequality.

3. Represent the solution set of an inequality in set-builder form and on a number line.

4. Determine inequality of functions where f x g x .

Alignment to Current Textbook

Section 3-1 (pp.170-175), Section 3-2 (pp.176-181), Section 3-3 (pp.182-187), Section 3-4 (pp.190-195),

Section 3-5 (pp.196-202)

Notes

Include compound inequalities

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 2: LINEAR EQUATIONS AND INEQUALITIES

2-3 Modeling with One-Variable Linear Equations and Inequalities

CCSSI Standards

N-Q.1 Use units as a way to understand… and to guide the solutions of multi-step problems;

choose and interpret units consistently in formulas…

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

A-CED.1 Create equations and inequalities in one variable and use them to solve problems.

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

A-CED.3 Represent constraints by equations or inequalities… and interpret solutions as viable or

nonviable options in a modeling context.

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

A-SSE.1 Interpret expressions that represent a quantity in terms of its context.

F-IF.5 Relate the domain of a function to its graph.

Mathematical Practices

Practice #3 Exchange summaries and comment on the clarity and completeness of the argument

made by other students concerning a diet and exercise plan. (Construct viable arguments

and critique the reasoning of others)

Academic Vocabulary

No new vocabulary

Essential Question

How can you use linear equations and inequalities to analyze a weight-loss plan?

Skills

1. Model a real-world situation with a linear equation.

2. Model a real-world situation with a linear inequality.

Alignment to Current Textbook

Various problems from pp.77-106 and pp.170-202, Section 11-4 (pp.813-819)

Notes

See specific example problems on pages 76,79,86,94-95,102,172,177-178,184,192,197

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 2: LINEAR EQUATIONS AND INEQUALITIES

2-4 Literal Equations and Inequalities

CCSSI Standards

A-REI.1 Explain 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.

A-REI.3 Solve linear equations.

Mathematical Practices

Practice #6 Placing a restriction on the coefficient(s) of the variable in a literal equation or inequality

helps to generalize a class of equations or inequalities because it guarantees that the

literal equation or inequality will have a variable term and determines what happens to

the inequality sign when solving a literal inequality. (Attend to precision)

Academic Vocabulary

literal equation literal inequality

Essential Question

How do you solve literal equations and inequalities?

Skills

1. Solve literal equations for a specified variable.

2. Solve literal inequalities for a specified variable.

Alignment to Current Textbook

Section 2-5 (pp.107-111)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 2: LINEAR EQUATIONS AND INEQUALITIES

2-5 Rewriting Formulas

CCSSI Standards

A-CED.2 Create equations in two or more variables to represent relationships between

quantities…

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

solving equations…

G-MG.1 Use geometric shapes, their measures, and their properties to describe objects.

Mathematical Practices

Practice #4 Rewriting a formula for the area of a square in terms of its perimeter can be modeled by

a fenced-in piece of land. (Model with mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How do you rewrite formulas?

Skills

1. Solve a formula for a specified variable.

2. Write and rearrange formulas.

Alignment to Current Textbook

Section 2-5 (pp.107-111)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 2: LINEAR EQUATIONS AND INEQUALITIES

2-6 Linear Equations in Two Variables

CCSSI Standards

A-REI.10 Understand 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).

Mathematical Practices

Practice #7 Intercepts are easy to find and are sufficient to identify the line through the remaining

points. (Look for and make use of structure)

Academic Vocabulary

linear equation in two variables x-intercept

standard form of a linear equation y-intercept

solution of an equation in two variables

Essential Question

How do you graph the solutions to a linear equation in two variables?

Skills

1. Determine whether on ordered pair is a solution.

2. Graph a linear equation in standard form.

3. Graph vertical and horizontal lines.

4. Graph lines through the origin.

Alignment to Current Textbook

Section 4-4 (pp.256-262), Section 5-1 (pp.300-306), Section 5-2 (pp.307-312)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 2: LINEAR EQUATIONS AND INEQUALITIES

2-7 Linear Inequalities in Two Variables

CCSSI Standards

A-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the

boundary in the case of a strict inequality)…

Mathematical Practices

Practice #7 Graph the boundary line of a linear inequality in two variables and use a test point to

identify the half-plane of the solution set. (Look for and make use of structure)

Academic Vocabulary

linear inequality in two variables solution of an inequality in two variables

Essential Question

How do you graph a linear inequality in two variables?

Skills

1. Graph a linear inequality in two variables.

Alignment to Current Textbook

Section 6-5 (pp.428-434)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 2: LINEAR EQUATIONS AND INEQUALITIES

2-8 Modeling with Two-Variable Linear Equations and Inequalities

CCSSI Standards

N-Q.1 Use units as a way to understand… and to guide the solutions of multi-step problems;

choose and interpret units consistently in formulas…

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

A-SSE.1 Interpret expressions that represent a quantity in terms of its context.

A-CED.2 Create equations in two or more variables to represent relationships between

quantities…

A-CED.3 Represent constraints by equations or inequalities… and interpret solutions as viable or

nonviable options in a modeling context.

Mathematical Practices

Practice #5 Discuss how, for instance, the sales of t-shirts and blankets are ordered pairs that can be

graphed and that these ordered pairs meet a particular sales goal on the line, while the

ordered pairs that meet a minimum sales goal lie in a half-plane. (Model with

mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How can you use linear equations and inequalities to model the results of a fundraiser?

Skills

1. Model and graph a real-world situation with a linear equation in two variables.

2. Model and graph a real-world situation with a linear inequality in two variables.

Alignment to Current Textbook

Various problems from pp.256-262,300-312,428-434, Section 11-4 (pp.813-819)

Notes

See specific problems on pages 259,303,430

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 3: SYSTEMS OF EQUATIONS AND INEQUALITIES

3-1 Solving Linear Systems by Graphing

CCSSI Standards

A-REI.6 Solve systems of linear equations… approximately (e.g. with graphs), focusing on pairs of

linear equations in two variables.

Mathematical Practices

Practice #5 Look at the intersections of two lines to approximate the solution of the system using

visual tools. Adjust graph scales as necessary for more accurate estimations. Recognize

when the solution is exact. (Use appropriate tools strategically)

Academic Vocabulary

system of linear equations solution of a system of linear equations

Essential Question

How do you approximate the solution of a system of linear equations by graphing?

Skills

1. Solve systems of equations by graphing.

2. Estimate the solution of a system of equations by graphing.

3. Determine if a system of linear equations has one solution, no solution, or infinitely many

solutions.

Alignment to Current Textbook

Section 6-1 (pp.397-402)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 3: SYSTEMS OF EQUATIONS AND INEQUALITIES

3-2 Solving Linear Systems by Substitution

CCSSI Standards

A-REI.6 Solve systems of linear equations exactly… , focusing on pairs of linear equations in two

variables.

Mathematical Practices

Practice #7 When using substitution, look for structure when examining the system and identify the

variable that is easier to isolate. Rewrite one equation so that one variable is isolated on

one side of the equation and an equivalent expression containing the other variable is

on the other side. (Look for and make use of structure)

Academic Vocabulary

substitution method

Essential Question

How do you use substitution to solve a system of linear equations?

Skills

1. Solve systems of equations using the substitution method.

2. Determine if a system of linear equations has one solution, no solution, or infinitely many

solutions.

Alignment to Current Textbook

Section 6-2 (pp.404-410), Section 6-4 (pp.420-425)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 3: SYSTEMS OF EQUATIONS AND INEQUALITIES

3-3 Solving Linear Systems by Adding or Subtracting

CCSSI Standards

A-REI.6 Solve systems of linear equations exactly… , focusing on pairs of linear equations in two

variables.

Mathematical Practices

Practice #8 When solving a system of linear equations by adding or subtracting, notice that linear

systems with equations that have like terms with coefficients that are additive inverses

can be solved by adding and that those that have identical terms can be solved by

subtracting. (Look for and express regularity in repeated reasoning)

Academic Vocabulary

elimination method

Essential Question

How do you solve a system of linear equations by adding or subtracting?

Skills

1. Solve systems of equations by adding or subtracting.

2. Determine if a system of linear equations has one solution, no solution, or infinitely many

solutions.

Alignment to Current Textbook

Section 6-3 (pp.411-417), Section 6-4 (pp.420-425)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 3: SYSTEMS OF EQUATIONS AND INEQUALITIES

3-4 Solving Linear Systems by Multiplying

CCSSI Standards

A-REI.5 Prove 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.

A-REI.6 Solve systems of linear equations exactly… , focusing on pairs of linear equations in two

variables.

Mathematical Practices

Practice #3 Show by graphing 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. Move from concrete representations to the more abstract algebraic

proof. (Construct viable arguments and critique the reasoning of others)

Academic Vocabulary

elimination method

Essential Question

How do you solve a system of linear equations by multiplying?

Skills

1. Solve systems of equations by multiplying.

2. Determine if a system of linear equations has one solution, no solution, or infinitely many

solutions.

Alignment to Current Textbook

Section 6-3 (pp.411-417), Section 6-4 (pp.420-425)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 3: SYSTEMS OF EQUATIONS AND INEQUALITIES

3-5 Solving Systems of Linear Inequalities

CCSSI Standards

A-REI.12 Graph 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.

Mathematical Practices

Practice #7 When solving a system of linear inequalities in two variables, build upon the strategies of

solving compound inequalities in one variable and graphing a linear inequality in two

variables. Use boundary lines and test points to determine the solution of the system.

(Look for and make use of structure)

Academic Vocabulary

system of linear inequalities solutions of a system of linear inequalities

Essential Question

How do you solve a system of linear inequalities?

Skills

1. Solve systems of linear inequalities by graphing.

2. Describe the solutions of a system of linear inequalities.

Alignment to Current Textbook

Section 6-6 (pp.435-440)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 3: SYSTEMS OF EQUATIONS AND INEQUALITIES

3-6 Modeling with Linear Systems

CCSSI Standards

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…

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

A-CED.2 Create equations in two or more variables to represent relationships between

quantities…

A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or

inequalities, and interpret solutions as viable or nonviable options in a modeling context.

A-REI.6 Solve systems of linear equations exactly… , focusing on pairs of linear equations in two

variables.

A-REI.12 Graph 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.

Mathematical Practices

Practice #4 Construct algebraic and graphical models of real-world situations. Show how changing

the conditions of a situation affect the graphical model. Stress importance of checking

the model with different values, including values on the boundary line. (Model with

mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How can you use systems of linear equations or inequalities to model and solve contextual problems?

Skills

1. Model systems of linear equations.

2. Model systems of linear inequalities.

Alignment to Current Textbook

See specific example problems on pages 399,403,407,414,422,430,437

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

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UNIT 4: LINEAR FUNCTIONS

4-1 Discrete Linear Functions

CCSSI Standards

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is

a subset of the integers.

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes.

F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in

simple cases and using technology for more complicated cases.

F-IF.7a Graph linear… functions and show intercepts…

F-BF.2 Write arithmetic… sequences with an explicit formula, use them to model situations…

Mathematical Practices

Practice #7 Show how linear functions arise naturally from the structure of arithmetic sequences.

(Look for and make use of structure)

Academic Vocabulary

linear function

Essential Question

What are the characteristics of a discrete linear function?

Skills

1. Graph discrete real-world functions.

2. Identify the domain and range of discrete real-world functions.

Alignment to Current Textbook

Section 5-1 (pp.300-306)

Notes

Arithmetic sequences are on HMH pp.276-281

ALGEBRA 1 COMMON CORE CURRICULUM

26

UNIT 4: LINEAR FUNCTIONS

4-2 Continuous Linear Functions

CCSSI Standards

N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step

problems; …choose and interpret the scale and the origin in graphs and data displays.

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 .

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes.

F-IF.9 Compare properties of two functions each represented in a different way (algebraically,

graphically, numerically in tables, or by verbal descriptions).

Mathematical Practices

Practice #2 Compare the description of a heavy storm by a graph of a violent storm to help visualize

how to represent the heavy storm graphically (time in hours vs. rainfall in inches).

(Reason abstractly and quantitatively)

Academic Vocabulary

linear function

Essential Question

How are discrete and continuous linear functions alike, and how are they different?

Skills

1. Graph continuous real-world functions.

2. Identify the domain and range of continuous real-world functions.

Alignment to Current Textbook

Section 5-1 (pp.300-306)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

27

UNIT 4: LINEAR FUNCTIONS

4-3 Using Slope

CCSSI Standards

N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step

problems; …choose and interpret the scale and the origin in graphs and data displays.

A-CED.2 Create equations in two… variables to represent relationships between quantities; graph

equations on coordinate axes with labels and scales.

F-IF.4 For 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.

F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically

or as a table) over a specified interval. Estimate the rate of change from a graph.

F-IF.7 Graph functions expressed symbolically and show key features of the graph…

F-IF.7a Graph linear… functions and show intercepts…

Mathematical Practices

Practice #2 Use function notation to address the change in the output values of a function. Knows

why the change in input values is called the run, and why the change in the output

values is called the rise. (Reason abstractly and quantitatively)

Academic Vocabulary

constant function run

rate of change slope

rise

Essential Question

What is the slope of a linear function and how can you use it to graph the function?

Skills

1. Determine the slope of a linear function.

2. Classify the slope of a line.

3. Graph a line using the slope and y-intercept.

Alignment to Current Textbook

Section 5-3 (pp.314-321), Section 5-4 (pp.324-329)

Notes

See 8.F.3

ALGEBRA 1 COMMON CORE CURRICULUM

28

UNIT 4: LINEAR FUNCTIONS

4-4 Changing the Values of m and b in f x mx b .

CCSSI Standards

F-IF.4 For 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.

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes.

F-BF.3 Identify the effect of the graph of replacing f x by f x k , f kx ,… 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 graphs using technology.

F-LE.5 Interpret the parameters in a linear… function in terms of a context.

Mathematical Practices

Practice #5 Use a graphing calculator to display functions and to help make conclusions about how

different graphs are related geometrically. Graph pairs of linear functions that have

different y-intercepts and different slopes. (Use appropriate tools strategically)

Academic Vocabulary

No new vocabulary

Essential Question

How do the values of m and b affect the graph of the function f x mx b ?

Skills

1. Determine how changing the value of m affects the graph of f x mx b .

2. Determine how changing the value of b affects the graph of f x mx b .

Alignment to Current Textbook

Section 5-3 (pp.314-321), Section 5-4 (pp.324-329), Section 5-9 (pp.361-367)

Notes

See 8.F.3

ALGEBRA 1 COMMON CORE CURRICULUM

29

UNIT 4: LINEAR FUNCTIONS

4-5 Writing Linear Functions

CCSSI Standards

N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step

problems; …choose and interpret the scale and the origin in graphs and data displays.

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

A-CED.2 Create equations in two… variables to represent relationships between quantities; graph

equations on coordinate axes with labels and scales.

A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y f x

and y g x intersect are the solutions of the equation f x g x ;… Include cases

where f x and/or g x are linear… functions.

F-IF.4 For 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.

F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically

or as a table) over a specified interval. Estimate the rate of change from a graph.

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

F-LE.2 Construct linear… functions,… given a graph, a description of a relationship, or two input-

output pairs (include reading these from a table).

Mathematical Practices

Practice #4 Use the values of m and b to model real-world situations, such as divers and water

pressure. (Model with mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How can you represent a function symbolically from a graph, a verbal description, or a table of values?

Skills

1. Write a linear function from a verbal description.

2. Write a linear function from a table of values.

3. Write a linear function from a graph.

Alignment to Current Textbook

Section 4-3 (pp.249-255), Section 5-7 (pp.344-350), Section 5-8 (351-358)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

30

UNIT 4: LINEAR FUNCTIONS

4-6 Operations with Linear Functions

CCSSI Standards

N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step

problems; …choose and interpret the scale and the origin in graphs and data displays.

A-APR.1 …add, subtract, and multiply polynomials.

A-CED.2 Create equations in two… variables to represent relationships between quantities; graph

equations on coordinate axes with labels and scales.

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

F-BF.1a Determine an explicit expression… from a context.

F-BF.1b Combine standard function types using arithmetic operations.

F-LE.2 Construct linear… functions,… given a graph, a description of a relationship, or two input-

output pairs (include reading these from a table).

F-LE.5 Interpret the parameters in a linear… function in terms of a context.

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

Mathematical Practices

Practice #4 Create linear functions to model enrollment and revenue from a soccer camp, for

instance. (Model with mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How can you use operations to combine functions that model real-world situations?

Skills

1. Add linear functions.

2. Subtract linear functions.

3. Multiply linear functions.

Alignment to Current Textbook

Section 7-7 (pp.504-509)

Notes

HMH does not address adding and subtracting functions with function notation.

ALGEBRA 1 COMMON CORE CURRICULUM

31

UNIT 4: LINEAR FUNCTIONS

4-7 Linear Functions and their Inverses

CCSSI Standards

A-CED.2 Create equations in two… variables to represent relationships between quantities; graph

equations on coordinate axes with labels and scales.

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

F-BF.1a Determine an explicit expression… from a context.

F-BF.4 Find inverse functions.

F-BF.4a Solve an equation of the form f x c for a simple function f that has an inverse and

write an expression for the inverse.

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 .

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.7 Graph functions expressed symbolically and show key features of the graph…

F-IF.7a Graph linear… functions and show intercepts…

Mathematical Practices

Practice #4 Convert from Fahrenheit to Celsius by modeling with inverse functions. (Model with

mathematics)

Academic Vocabulary

inverse of a function

Essential Question

What is the inverse of a function, and how can you find the inverse of a linear function?

Skills

1. Find the inverse of a linear function.

Alignment to Current Textbook

None

Notes

Inverse functions are not addressed in our current HMH textbook.

ALGEBRA 1 COMMON CORE CURRICULUM

32

UNIT 4: LINEAR FUNCTIONS

4-8 Correlation

CCSSI Standards

S-ID.8 Compute… and interpret the correlation coefficient of a linear fit.

S-ID.9 Distinguish between correlation and causation.

S-IC.6 Evaluate reports based on data.

Mathematical Practices

Practice #2 Determine if correlation implies causation by reading an article and analyzing the data.

(Reason abstractly and quantitatively)

Academic Vocabulary

correlation correlation coefficient

Essential Question

How can you decide whether a correlation exists between paired numerical data?

Skills

1. Describe the correlation, if any, between paired data

Alignment to Current Textbook

Section 4-5 (pp.266-273)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

33

UNIT 4: LINEAR FUNCTIONS

4-9 Fitting Lines to Data

CCSSI Standards

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

F-BF.1a Determine an explicit expression… from a context.

F-LE.5 Interpret the parameters in a linear… function in terms of a context.

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

variables are related.

S-ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of

the data.

S-ID.6b Informally assess the fit of a function by plotting and analyzing residuals.

S-ID.6c Fit a linear function for a scatter plot that suggests a linear association.

S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in

the context of the data.

Mathematical Practices

Practice #2 Use multiple representations for the residuals, both as a table and as a scatter plot.

Explain why a scatter plot of residuals is helpful in determining whether a model for data

is suitable and good. (Reason abstractly and quantitatively)

Academic Vocabulary

extrapolation residual

interpolation residual plot

Essential Question

How do you find a linear model for a set of paired numerical data, and how do you evaluate the goodness

of fit?

Skills

1. Find a line of fit for data by drawing a line that passes as close as possible to the plotted points.

2. Create a residual plot and evaluate the fit.

3. Make predictions using a linear model for a set of paired data.

Alignment to Current Textbook

Section 4-5 (pp.266-273)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

34

UNIT 4: LINEAR FUNCTIONS

4-10 Linear Regression

CCSSI Standards

F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in

simple cases and using technology for more complicated cases.

F-IF.7a Graph linear… functions and show intercepts…

F-LE.5 Interpret the parameters in a linear… function in terms of a context.

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

variables are related.

S-ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of

the data.

S-ID.6b Informally assess the fit of a function by plotting and analyzing residuals.

S-ID.6c Fit a linear function for a scatter plot that suggests a linear association.

S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in

the context of the data.

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

Mathematical Practices

Practice #5 Describe the advantages of using a graphing calculator to find the line of best fit and do

a residuals plot from the data. (Use appropriate tools strategically)

Academic Vocabulary

linear regression

Essential Question

How do you use a graphing calculator to perform linear regression on a set of paired numerical data?

Skills

1. Perform linear regression using technology.

Alignment to Current Textbook

None

Notes

Regression is not addressed in our current HMH textbook.

ALGEBRA 1 COMMON CORE CURRICULUM

35

UNIT 5: EXPONENTIAL FUNCTIONS

5-1 Discrete Exponential Functions

CCSSI Standards

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is

a subset of the integers.

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes.

F-IF.7e Graph exponential… functions, showing intercepts and end behavior.

F-LE.2 Construct linear… functions,… given a graph, a description of a relationship, or two input-

output pairs (include reading these from a table).

Mathematical Practices

Practice #4 Understand how to identify the value of a, which is the initial value when 0x , and how

to identify the value of b, which is the ratio of successive output values for each unit

increase in the input values. (Model with mathematics)

Practice #7 Use the structure of geometric sequences and realize that discrete exponential functions

are structurally similar. (Look for and make use of structure)

Academic Vocabulary

exponential function

Essential Question

What are discrete exponential functions and how can you represent them?

Skills

1. Create a table of values and a graph from a given exponential function.

2. Write an exponential equation from a given table of values or graph.

Alignment to Current Textbook

Section 11-1 (pp.790-795), Section 11-2 (pp.796-802)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

36

UNIT 5: EXPONENTIAL FUNCTIONS

5-2 Exponential Growth Functions

CCSSI Standards

F-IF.1 Create equations in two or more variables to represent relationships between quantities.

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes.

F-IF.7e Graph exponential… functions, showing intercepts and end behavior.

F-LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per

unit interval relative to another.

F-LE.2 Construct linear… functions,… given a graph, a description of a relationship, or two input-

output pairs (include reading these from a table).

F-LE.5 Interpret the parameters in a… exponential function in terms of a context.

Mathematical Practices

Practice #2 Make predictions about the future value of an investment, which requires students to

take a problem situation and represent it symbolically, then understand the meaning of

the representation and use it to predict a result. (Reason abstractly and quantitatively)

Academic Vocabulary

exponential growth model

Essential Question

How do you write, graph, and interpret an exponential growth function?

Skills

1. Make a table of values for a given exponential growth function.

2. Write an exponential growth model for a given situation.

Alignment to Current Textbook

Section 11-3 (pp.805-812)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

37

UNIT 5: EXPONENTIAL FUNCTIONS

5-3 Exponential Decay Functions

CCSSI Standards

F-IF.4 For 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.

F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in

simple cases and using technology for more complicated cases.

F-IF.7e Graph exponential… functions, showing intercepts and end behavior.

F-LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per

unit interval relative to another.

F-LE.2 Construct linear… functions,… given a graph, a description of a relationship, or two input-

output pairs (include reading these from a table).

F-LE.5 Interpret the parameters in a… exponential function in terms of a context.

Mathematical Practices

Practice #4 Relate what you know about the price of a new car compared to the price of a used car

and display the changes in price over time with a model. (Model with mathematics)

Academic Vocabulary

exponential decay model

Essential Question

How do you write, graph, and interpret an exponential decay function?

Skills

1. Make a table of values for a given exponential growth function.

2. Write an exponential growth model for a given situation.

Alignment to Current Textbook

Section 11-3 (pp.805-812)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

38

UNIT 5: EXPONENTIAL FUNCTIONS

5-4 Changing the Values of a and b in xf x ab

CCSSI Standards

F-IF.4 For 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.

F-BF.3 Identify the effect of the graph of replacing f x by f x k , f kx ,… 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 graphs using technology.

Mathematical Practices

Practice #5 Use graphing calculators to compare functions. (Use appropriate tools strategically)

Academic Vocabulary

No new vocabulary

Essential Question

How does the graph of xf x ab change when a and b are changed?

Skills

1. Graph exponential functions.

Alignment to Current Textbook

Section 11-2 (pp.796-802)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

39

UNIT 5: EXPONENTIAL FUNCTIONS

5-5 Solving Equations Involving Exponents

CCSSI Standards

A-CED.1 Create equations and inequalities in one variable and use them to solve problems.

A.CED.2 Create equations in two or more variables to represent relationships between quantities.

A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y f x

and y g x intersect are the solutions of the equation f x g x ;… Include cases

where f x and/or g x are linear… functions.

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

F-BF.1a Determine an explicit expression… from a context.

F-LE.2 Construct… exponential functions, … given … a description of a relationship.

Mathematical Practices

Practice #7 When solving an equation involving a variable exponent, try to structure the solution so

that the equation in in the form x yb c . If b c , then x y . If b c , then solve by

graphing. (Look for an make use of structure)

Academic Vocabulary

No new vocabulary

Essential Question

How can you solve problems modeled by equations involving variable exponents?

Skills

1. Solve exponential equations by equating exponents.

2. Write and solve exponential equations by graphing.

Alignment to Current Textbook

None

Notes

Solving exponential equations is not addressed in our current HMH textbook.

ALGEBRA 1 COMMON CORE CURRICULUM

40

UNIT 5: EXPONENTIAL FUNCTIONS

5-6 Performing Exponential Regression

CCSSI Standards

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

F-BF.1a Determine an explicit expression… from a context.

F-LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per

unit interval relative to another.

F-LE.5 Interpret the parameters in a … exponential function in terms of a context.

S-ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of

the data.

S-ID.6b Informally assess the fit of a function by plotting and analyzing residuals.

Mathematical Practices

Practice #4 Analyzing residuals helps students evaluate how well a model fits the data. (Model with

mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How can you use exponential regression to model data?

Skills

1. Fit an exponential function to data.

2. Plot and analyze residuals of an exponential fit.

Alignment to Current Textbook

None

Notes

Regression is not addressed in our current HMH textbook.

ALGEBRA 1 COMMON CORE CURRICULUM

41

UNIT 5: EXPONENTIAL FUNCTIONS

5-7 Comparing Linear and Exponential Functions

CCSSI Standards

F-LE.1 Distinguish between situations that can be modeled with linear functions and with

exponential functions.

F-LE.1a Prove that linear functions grow by equal differences over equal intervals, and that

exponential functions grow by equal factors over equal intervals.

F-LE.1b Recognize situations in which one quantity changes at a constant rate per unit interval

relative to another.

F-LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per

unit interval relative to another.

F-LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually

exceeds a quantity increasing linearly,…

Mathematical Practices

Practice #6 Writing algebraic proofs requires presenting steps in a logical order, and using

mathematical notation to communicate reasoning effectively. (Attend to precision)

Academic Vocabulary

No new vocabulary

Essential Question

How can you recognize, describe, and compare linear and exponential functions?

Skills

1. Compare the growth rates of linear and exponential functions.

Alignment to Current Textbook

Section 11-4 (pp.813-819)

Notes

Comparing linear and exponential functions is loosely addressed in Section 11-4.

ALGEBRA 1 COMMON CORE CURRICULUM

42

UNIT 5: EXPONENTIAL FUNCTIONS

5-8 Modeling with Exponential Functions

CCSSI Standards

A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y f x

and y g x intersect are the solutions of the equation f x g x ;… Include cases

where f x and/or g x are linear… functions.

F-BF.1a Determine an explicit expression… from a context.

F-LE.1c Recognize situations in which a quantity grows or decays by a constant percent rate per

unit interval relative to another.

F-LE.2 Construct… exponential functions, … given … a description of a relationship.

F-LE.5 Interpret the parameters in a … exponential function in terms of a context.

S-ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of

the data.

Mathematical Practices

Practice #4 Stress the importance of checking a model with actual values and not assuming the

model is a good fit for the data. The model may be more accurate for years closer in to

the given data than for years farther out. (Model with mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How can you model changes in population using an exponential function?

Skills

1. Model exponential functions for real-world situations.

Alignment to Current Textbook

Section 11-4 (pp.813-819)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

43

UNIT 6: PIECEWISE AND ABSOLUTE VALUE FUNCTIONS

6-1 Piecewise Functions

CCSSI Standards

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.4 For 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.

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes.

F-IF.7b Graph… piecewise-defined functions, including step functions…

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

Mathematical Practices

Practice #4 Use multiple representations, such as tables and graphs, to help visualize the different

rules for specific piecewise functions. (Model with mathematics)

Academic Vocabulary

greatest integer function step function

piecewise function

Essential Question

How are piecewise functions and step functions different from other functions?

Skills

1. Write piecewise functions from graphs.

2. Graph piecewise functions.

Alignment to Current Textbook

Additional Topic A-2 (pp.AT5-AT8)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

44

UNIT 6: PIECEWISE AND ABSOLUTE VALUE FUNCTIONS

6-2 Translating the Graph of f x x

CCSSI Standards

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in

simple cases and using technology for more complicated cases.

F-IF.7b Graph… piecewise-defined functions, including step functions…

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

F-BF.3 Identify the effect of the graph of replacing f x by f x k , f kx ,… 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 graphs using technology.

Mathematical Practices

Practice #7 Look for patterns when constants are added or subtracted inside or outside the parent

function y x . Extend these patterns to construct the more general function

y x h k . (Look for and make use of structure)

Academic Vocabulary

absolute value function

Essential Question

What are the effects of the constants h and k on the graph of y x h k ?

Skills

1. Graph translations of the function f x x .

2. Write an absolute value function from its graph.

3. Determine the domain and range of absolute value functions.

Alignment to Current Textbook

pp.378-381

Notes

This topic is addressed as a Chapter 5 extension.

ALGEBRA 1 COMMON CORE CURRICULUM

45

UNIT 6: PIECEWISE AND ABSOLUTE VALUE FUNCTIONS

6-3 Stretching, Shrinking, and Reflecting the Graph of f x x

CCSSI Standards

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in

simple cases and using technology for more complicated cases.

F-IF.7b Graph… piecewise-defined functions, including step functions…

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

F-BF.3 Identify the effect of the graph of replacing f x by f x k , f kx ,… 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 graphs using technology.

Mathematical Practices

Practice #7 Look for patterns in the graph of f x a x for various values of a. Note that relating

transformations to a parent graph is also done with other types of functions. (Look for

and make use of structure)

Academic Vocabulary

No new vocabulary

Essential Question

What is the effect of the constant a on the graph of g x a x ?

Skills

1. Graph the function f x a x for various values of a.

2. Write a function for the graph of f x a x .

Alignment to Current Textbook

pp.378-381

Notes

This topic is addressed as a Chapter 5 extension.

ALGEBRA 1 COMMON CORE CURRICULUM

46

UNIT 6: PIECEWISE AND ABSOLUTE VALUE FUNCTIONS

6-4 Combining Transformation of the Graph of f x x

CCSSI Standards

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in

simple cases and using technology for more complicated cases.

F-IF.7b Graph… piecewise-defined functions, including step functions…

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

F-BF.1a Determine an explicit expression… from a context.

F-BF.3 Identify the effect of the graph of replacing f x by f x k , f kx ,… 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 graphs using technology.

Mathematical Practices

Practice #7 Look for and identify various combinations of the effects of the constants a, h, and k on

the graph of f x a x h k . (Look for and make use of structure)

Academic Vocabulary

No new vocabulary

Essential Question

What are the effects of the constants a, h, and k on the graph of g x a x h k ?

Skills

1. Graph the function f x a x for various values of a, h, and k.

2. Write a function for the graph of f x a x h k .

Alignment to Current Textbook

pp.378-381

Notes

This topic is addressed as a Chapter 5 extension.

ALGEBRA 1 COMMON CORE CURRICULUM

47

UNIT 6: PIECEWISE AND ABSOLUTE VALUE FUNCTIONS

6-5 Solving Absolute Value Equations

CCSSI Standards

A-CED.1 Create equations and inequalities in one variable and use them to solve problems.

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y f x

and y g x intersect are the solutions of the equation f x g x ;… Include cases

where f x and/or g x are linear… functions.

Mathematical Practices

Practice #4 Use modeling to symbolically represent real-world situations, such as distances, with

absolute value equations. (Model with mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How can you use graphing to solve equations involving absolute value?

Skills

1. Solve absolute value equations by graphing.

2. Solve absolute value equations using algebraic methods.

Alignment to Current Textbook

Section 2-6 (pp.112-117)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

48

UNIT 6: PIECEWISE AND ABSOLUTE VALUE FUNCTIONS

6-6 Modeling with Absolute Value Functions

CCSSI Standards

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.4 For 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.

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes.

F-IF.7b Graph… absolute value functions.

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

Mathematical Practices

Practice #4 Write and graph absolute value functions for real-world situations. Check the models for

correctness and accuracy. (Model with mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How can you use an absolute value function to plan a bank shot when playing pool?

Skills

1. Model real-world situations with absolute value functions.

Alignment to Current Textbook

See specific problems on pages 114,214

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

49

UNIT 7: QUADRATIC FUNCTIONS OF THE FORM 2

f x a x h k

7-1 Translating the Graph of 2f x x

CCSSI Standards

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.4 For 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.

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes.

F-IF.7a Graph… quadratic functions and show intercepts, maxima, and minima.

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

F-BF.3 Identify the effect of the graph of replacing f x by f x k , f kx ,… 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 graphs using technology.

Mathematical Practices

Practice #7 Realize that adding k to 2x moves the graph up for 0k or down for 0k and that

subtracting h from x moves the graph left for 0h or right for 0h . (Look for and

make use of structure)

Academic Vocabulary

parabola vertex

quadratic function

Essential Question

What are the effects of the constants h and k on the graph of 2

g x x h k ?

Skills

1. Graph functions of the form 2

f x x h k .

2. Given the graph of 2

f x x h k , write its function.

Alignment to Current Textbook

Section 9-2 (pp.619-625), Section 9-3 (626-631), Section 9-4 (pp.633-639)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

50

UNIT 7: QUADRATIC FUNCTIONS OF THE FORM 2

f x a x h k

7-2 Stretching, Shrinking, and Reflecting the Graph of 2f x x

CCSSI Standards

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.4 For 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.

F-IF.7a Graph… quadratic functions and show intercepts, maxima, and minima.

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

F-BF.3 Identify the effect of the graph of replacing f x by f x k , f kx ,… 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 graphs using technology.

Mathematical Practices

Practice #7 Note how the graphs of the form 2f x x k , 2

f x x h , and 2f x ax have the

same structure as the graph of 2f x x but are translated vertically or horizontally, or

are stretched or shrunk vertically. (Look for and make use of structure)

Academic Vocabulary

No new vocabulary

Essential Question

What is the effect of the constant a on the graph of 2g x ax ?

Skills

1. Graph functions of the form 2f x ax .

2. Given the graph of 2f x ax , write its function.

Alignment to Current Textbook

Section 9-4 (pp.633-639)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

51

UNIT 7: QUADRATIC FUNCTIONS OF THE FORM 2

f x a x h k

7-3 Combining Transformations the Graph of 2f x x

CCSSI Standards

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.4 For 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.

F-IF.7a Graph… quadratic functions and show intercepts, maxima, and minima.

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

F-BF.3 Identify the effect of the graph of replacing f x by f x k , f kx ,… 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 graphs using technology.

Mathematical Practices

Practice #4 Model transformations of quadratic functions as dropping an object from a given height.

The vertex ,h k is the maximum point of the graph and its values can be substituted

into the general equation 2

g x a x h k . (Model with mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How can you obtain the graph of 2

g x a x h k from the graph of 2f x x ?

Skills

1. Graph functions of the form 2

f x x h k .

2. Given the graph of 2

f x x h k , write its function.

Alignment to Current Textbook

Section 9-4 (pp.633-639)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

52

UNIT 7: QUADRATIC FUNCTIONS OF THE FORM 2

f x a x h k

7-4 Solving Quadratic Equations Graphically

CCSSI Standards

A-CED.1 Create equations and inequalities in one variable and use them to solve problems.

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

A-REI.11 Explain why the x-coordinates of the points where the graphs of the equations y f x

and y g x intersect are the solutions of the equation f x g x ;… Include cases

where f x and/or g x are linear… functions.

Mathematical Practices

Practice #4 The distance model d t represents the distance a falling object falls as a function of

time t, in seconds. Discuss how to distinguish distance fallen from height above the

ground. (Model with mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How can you solve a quadratic equation by graphing?

Skills

1. Solve quadratic equations by graphing.

Alignment to Current Textbook

Section 9-5 (pp.642-647)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

53

UNIT 7: QUADRATIC FUNCTIONS OF THE FORM 2

f x a x h k

7-5 Solving Quadratic Equations Using Square Roots

CCSSI Standards

A-CED.1 Create equations and inequalities in one variable and use them to solve problems.

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

A-REI.4b Solve quadratic equations by inspection (e.g. for 2 49x ), taking square roots,…

Mathematical Practices

Practice #2 Work abstractly to solve a quadratic equation and then analyze the result in context. For

real-world problems, make sure to discard solutions that do not fit the context of the

problem (i.e. negative solutions where the independent variable is time). (Reason

abstractly and quantitatively)

Academic Vocabulary

square root

Essential Question

How can you solve a quadratic equation using square roots?

Skills

1. Solve quadratic equations by taking square roots.

Alignment to Current Textbook

Section 9-7 (pp.656-661)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

54

UNIT 7: QUADRATIC FUNCTIONS OF THE FORM 2

f x a x h k

7-6 Modeling with Quadratic Functions

CCSSI Standards

N-Q.1 Use units as a way to understand… and to guide the solutions of multi-step problems…

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

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret

statements that use function notation in terms of a context.

F-IF.4 For 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.

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

Mathematical Practices

Practice #4 Find quadratic models and interpret the model. Check the model with actual values and

do not assume that the model is a good fit to the data. (Model with mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How can you model a car’s gas mileage using a quadratic function?

Skills

1. Model with quadratic functions.

Alignment to Current Textbook

Section 11-4 (pp.813-819)

Notes

See specific example problems on pages 622,627-628,636,644,652,658,666,673

ALGEBRA 1 COMMON CORE CURRICULUM

55

UNIT 8: QUADRATIC FUNCTIONS OF THE FORM 2f x ax bx c

8-1 Multiply Binomials

CCSSI Standards

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

A-APR.1 …multiply polynomials.

Mathematical Practices

Practice #2 Use the mnemonic FOIL to contextualize the repeated application of the distributive

property to the multiplication of two binomials. This reasoning should be applied in a

reverse process when factoring quadratic trinomials later. (Reason abstractly and

quantitatively)

Academic Vocabulary

binomial term

monomial trinomial

polynomial

Essential Question

How can you use the distributive property to multiply binomials?

Skills

1. Classify expressions as monomials, binomials, trinomials, or polynomials.

2. Multiply binomials using the Distributive Property.

Alignment to Current Textbook

Section 7-8 (pp.512-519), Section 7-9 (pp.521-527)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

56

UNIT 8: QUADRATIC FUNCTIONS OF THE FORM 2f x ax bx c

8-2 Solving 2 0x bx c by Factoring

CCSSI Standards

A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain

properties of the quantity represented by the expression.

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

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

A-REI.4b Solve quadratic equations by inspection (e.g. for 2 49x ), taking square roots,…

F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and

explain properties of the function.

F-IF.8a Use the process of factoring… in a quadratic function to show zeros…

F-BF.1a Determine an explicit expression… from a context.

Mathematical Practices

Practice #1 Analyze equations and make conjectures about the form of the binomial factors.

Recognize special cases to help solve problems quickly and efficiently. (Make sense of

problems and persevere in solving them)

Academic Vocabulary

zeros zero-product property

Essential Question

How can you use factoring to solve quadratic equations in standard form when 1a ?

Skills

1. Factor trinomials of the form 2x bx c .

2. Solve quadratic equations of the form 2 0x bx c by factoring.

Alignment to Current Textbook

Section 8-3 (pp.560-567), Section 8-5 (pp.578-584), Section 8-6 (pp.586-591), Section 9-6 (pp.650-655)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

57

UNIT 8: QUADRATIC FUNCTIONS OF THE FORM 2f x ax bx c

8-3 Solving 2 0ax bx c by Factoring

CCSSI Standards

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

A-CED.1 Create equations and inequalities in one variable and use them to solve problems.

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

A-REI.4b Solve quadratic equations by inspection (e.g. for 2 49x ), taking square roots,…

F-IF.8 Write a function defined by an expression in different but equivalent forms to reveal and

explain properties of the function.

F-IF.8a Use the process of factoring… in a quadratic function to show zeros…

F-BF.1a Determine an explicit expression… from a context.

Mathematical Practices

Practice #7 Recognize the factor pairs of a and c that give the correct value of b. Take a structured

approach to determining the factor pairs that result in the correct trinomial. Recognize

that the zero-product property can be applied only to quadratic equations in standard

form because the property cannot be applied to equations equal to a number other than

zero. (Look for and make use of structure)

Academic Vocabulary

No new vocabulary

Essential Question

How can you use factoring to solve 2 0ax bx c when 1a ?

Skills

1. Factor trinomials of the form 2ax bx c .

2. Solve quadratic equations of the form 2 0ax bx c by factoring.

Alignment to Current Textbook

Section 8-4 (pp.568-574), Section 8-5 (pp.578-584), Section 8-6 (pp.586-591), Section 9-6 (pp.650-655)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

58

UNIT 8: QUADRATIC FUNCTIONS OF THE FORM 2f x ax bx c

8-4 Solving 2 0x bx c by Completing the Square

CCSSI Standards

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

A-REI.4a Use the method of completing the square to transform any quadratic equation in x into

an equation of the form 2

x p q that has the same solutions…

A-REI.4b Solve quadratic equations by inspection (e.g. for 2 49x ), taking square roots,…

Mathematical Practices

Practice #6 Be precise with terminology regarding the coefficients and constants in the quadratic

equation and with the numbers added to both sides. (Attend to precision)

Academic Vocabulary

completing the square

Essential Question

How can you solve 2 0x bx c without factoring?

Skills

1. Find the value of c that makes 2x bx c a perfect square trinomial.

2. Solve quadratic equations of the form 2 0x bx c by completing the square and using the

square root property.

Alignment to Current Textbook

Section 9-8 (pp.663-669)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

59

UNIT 8: QUADRATIC FUNCTIONS OF THE FORM 2f x ax bx c

8-5 Solving 2 0ax bx c by Completing the Square

CCSSI Standards

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

A-REI.4a Use the method of completing the square to transform any quadratic equation in x into

an equation of the form 2

x p q that has the same solutions…

A-REI.4b Solve quadratic equations by inspection (e.g. for 2 49x ), taking square roots,…

Mathematical Practices

Practice #6 Be precise with terminology regarding the coefficients and constants in the quadratic

equation and with the numbers added to both sides. (Attend to precision)

Academic Vocabulary

No new vocabulary

Essential Question

How can you solve 2 0ax bx c by completing the square when 1a ?

Skills

1. Find the value of c that makes 2ax bx c a perfect square trinomial.

2. Solve quadratic equations of the form 2 0ax bx c by completing the square and using the

square root property.

Alignment to Current Textbook

Section 9-8 (pp.663-669)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

60

UNIT 8: QUADRATIC FUNCTIONS OF THE FORM 2f x ax bx c

8-6 Deriving the Quadratic Formula

CCSSI Standards

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

A-REI.4a Use the method of completing the square to transform any quadratic equation in x into

an equation of the form 2

x p q that has the same solutions…

A-REI.4b Solve quadratic equations by inspection (e.g. for 2 49x ), taking square roots,…

Mathematical Practices

Practice #2 Perform a derivation of the quadratic formula. Explain the steps in the derivation.

(Reason abstractly and quantitatively)

Academic Vocabulary

quadratic formula

Essential Question

What is the quadratic formula and how can you derive it from 2 0ax bx c ?

Skills

1. Derive the quadratic formula.

Alignment to Current Textbook

Section 9-9 (pp.670-677)

Notes

The derivation is on HMH p.670

ALGEBRA 1 COMMON CORE CURRICULUM

61

UNIT 8: QUADRATIC FUNCTIONS OF THE FORM 2f x ax bx c

8-7 Using the Quadratic Formula

CCSSI Standards

A-CED.1 Create equations and inequalities in one variable and use them to solve problems.

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

A-REI.4b Solve quadratic equations by inspection (e.g. for 2 49x ), taking square roots,…

Mathematical Practices

Practice #6 Given quadratic equations, correctly identify the values of a, b, and c and then correctly

substitute them into the quadratic formula, paying close attention to the signs of the

numbers, especially when c is negative. Check the discriminant to determine if the

equation has real or non-real solutions. (Attend to precision)

Academic Vocabulary

discriminant

Essential Question

How do you solve quadratic equations using the quadratic formula?

Skills

1. Use the discriminant to describe the number and type of solutions of quadratic equations.

2. Solve quadratic equations using the quadratic formula.

Alignment to Current Textbook

Section 9-9 (pp.670-677)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

62

UNIT 8: QUADRATIC FUNCTIONS OF THE FORM 2f x ax bx c

8-8 Graphing Functions of the Form 2f x ax bx c

CCSSI Standards

F-IF.4 For 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.

F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative

relationship it describes.

F-IF.7a Graph… quadratic functions and show intercepts, maxima, and minima.

F-IF.8a Use the process of factoring… in a quadratic function to show zeros…

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

Mathematical Practices

Practice #1 Decide whether to graph by factoring or by completing the square. Persevere in

checking factors to determine factorability. If the function is not factorable, use

completing the square to graph. (Make sense of problems and persevere in solving

them)

Academic Vocabulary

No new vocabulary

Essential Question

How can you describe key attributes of the graph of 2f x ax bx c by analyzing its equation?

Skills

1. Graph equations of the form 2f x ax bx c .

2. Given the graph of 2f x ax bx c , write its function.

Alignment to Current Textbook

Section 9-2 (pp.619-625), Section 9-3 (pp.626-631)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

63

UNIT 8: QUADRATIC FUNCTIONS OF THE FORM 2f x ax bx c

8-9 Solving Systems of Linear and Quadratic Equations

CCSSI Standards

A-CED.2 Create equations in two or more variables to represent relationships between quantities.

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

A-REI.4b Solve quadratic equations by inspection (e.g. for 2 49x ), taking square roots,…

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

variables algebraically and graphically.

F-IF.4 For 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.

Mathematical Practices

Practice #5 Use technology to graph systems of equations. Use the Intersect feature to find or

estimate solutions. Recognize when solutions are exact or approximate. Check solutions

algebraically. (Use tools appropriately)

Academic Vocabulary

No new vocabulary

Essential Question

How can you solve a system of equations when one equation is linear and the other is quadratic?

Skills

1. Graph systems of linear and quadratic equations.

2. Solve systems of linear and quadratic equations.

Alignment to Current Textbook

None

Notes

These types of systems of equations are not addressed in our current HMH textbook.

ALGEBRA 1 COMMON CORE CURRICULUM

64

UNIT 8: QUADRATIC FUNCTIONS OF THE FORM 2f x ax bx c

8-10 Modeling with Quadratic Functions

CCSSI Standards

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

A-REI.4a Use the method of completing the square to transform any quadratic equation in x into

an equation of the form 2

x p q that has the same solutions…

A-REI.4b Solve quadratic equations by inspection (e.g. for 2 49x ), taking square roots,…

F-IF.4 For 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.

F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically

or as a table) over a specified interval. Estimate the rate of change from a graph.

F-IF.8a Use the process of factoring… in a quadratic function to show zeros…

Mathematical Practices

Practice #4 Routinely interpret mathematical results in the context of the situation and reflect on

whether the results make sense. Relate the domain and range of a model with its real-

world context and implication. Explain what each one means. (Model with mathematics)

Academic Vocabulary

No new vocabulary

Essential Question

How can you use quadratic functions to compare the motions of two baseballs that are thrown into the

air?

Skills

1. Model real-world situations with quadratic functions.

2. Determine the domain and range of quadratic function models.

Alignment to Current Textbook

Section 11-4 (pp.813-819)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

65

UNIT 9: DATA ANALYSIS

9-1 Measures of Center and Spread

CCSSI Standards

S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center

(median, mean) and spread (interquartile range, standard deviation) of two or more

different data sets.

Mathematical Practices

Practice #1 Solve real-world statistical analysis problems by forming general impressions while

entering data into a calculator. Organize and analyze results to make and justify

conclusions. (Make sense of problems and persevere in solving them)

Academic Vocabulary

first quartile range

interquartile range standard deviation

mean statistics

median third quartile

Essential Question

What statistics can you use to characterize and compare the center and spread of data sets?

Skills

1. Find the mean of a data set.

2. Find the first and third quartiles of a data set, as well as the interquartile range.

3. Find the median of a data set.

4. Find the standard deviation of a data set.

5. Find the range of a data set.

6. Compare the statistics of related data sets.

Alignment to Current Textbook

10-3 (pp.716-723)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

66

UNIT 9: DATA ANALYSIS

9-2 Data Distributions and Outliers

CCSSI Standards

S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center

(median, mean) and spread (interquartile range, standard deviation) of two or more

different data sets.

S-ID.3 Interpret differences in shape, center, and spread in the context of the data sets,

accounting for possible effects of extreme data points (outliers).

Mathematical Practices

Practice #2 Solve real-world statistical analysis problems by creating line plots for data sets,

analyzing the shapes of the distributions, recognizing how the shapes affect the

measures of center and spread, and making comparisons of the data sets. (Reason

abstractly and quantitatively)

Academic Vocabulary

outlier skewed to the right

skewed to the left symmetric

Essential Question

Which statistics are most affected by outliers, and what shapes can data distributions have?

Skills

1. Use line plots to display data.

2. Determine the effects of outliers on data sets.

3. Compare data distributions.

Alignment to Current Textbook

Section 10-1 (pp.700-708), Section 10-3 (pp.716-723)

Notes

Skew is not addressed in our current textbook.

ALGEBRA 1 COMMON CORE CURRICULUM

67

UNIT 9: DATA ANALYSIS

9-3 Histograms

CCSSI Standards

S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center

(median, mean) and spread (interquartile range, standard deviation) of two or more

different data sets.

Mathematical Practices

Practice #1 Develop a process to estimate the mean, the median, and the IQR of a data set based

solely on a histogram. Classify distributions as symmetric, skewed to the left, and skewed

to the right. (Make sense of problems and persevere in solving them)

Academic Vocabulary

No new vocabulary

Essential Question

How can you estimate statistics from data displayed in a histogram?

Skills

1. Create histograms to display data.

2. Determine (or estimate) the mean, standard deviation, median, and IQR of a data set displayed as

a histogram.

Alignment to Current Textbook

Section 10-2 (pp.709-715)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

68

UNIT 9: DATA ANALYSIS

9-4 Box Plots

CCSSI Standards

S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center

(median, mean) and spread (interquartile range, standard deviation) of two or more

different data sets.

Mathematical Practices

Practice #7 By understanding how the basic structure of a box plot represents the center, spread,

and shape of a data distribution, students can compare two box plots representing two

related sets of real-world data. Recognize that since outliers in the data set affect the

structure of a box plot, removing the outliers before constructing the box plot makes the

plot more useful for purposes of comparison. (Look for and make use of structure)

Academic Vocabulary

No new vocabulary

Essential Question

How can you compare data sets using a box plot?

Skills

1. Create a box plot for a set of data.

2. Interpret data displayed in a box plot.

3. Compare data sets using box plots.

Alignment to Current Textbook

Section 10-3 (pp.716-723)

Notes

ALGEBRA 1 COMMON CORE CURRICULUM

69

UNIT 9: DATA ANALYSIS

9-5 Two-Way Frequency Tables

CCSSI Standards

S-ID.5 Summarize 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.

Mathematical Practices

Practice #8 By repeating calculations for each cell in a two-way relative frequency table, become

proficient in the process of calculating relative frequency. Generalize the process to be

able to apply the same calculations and reasoning to any categorical data set organized

in a two-way frequency table. (Look for and express regularity in repeated reasoning)

Academic Vocabulary

conditional relative frequency two-way frequency table

joint relative frequency two-way relative frequency table

marginal relative frequency

Essential Question

How can categorical data be organized and analyzed?

Skills

1. Create relative frequency tables.

2. Create two-way frequency tables.

3. Create two-way relative frequency tables.

4. Calculate conditional relative frequencies.

Alignment to Current Textbook

Section 10-2 (pp.709-715)

Notes

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Tasks by Standard

A.REI.C.5,6 Babysitting

A-APR.A.1 Missing Function

A-APR.B.2 The Missing Coefficient Zeros and Factorization of a General Polynomial Zeros and Factorization of a Non-Polynomial Function Zeros and Factorization of a Quadratic Polynomial I Zeros and Factorization of a Quadratic Polynomial II

A-APR.B.3 Triple Trouble

A-APR.C.4 Trina’s Triangles

A-APR.D.6 Combined Fuel Efficiency Egyptian Fractions II

A-CED.A Cash Box

A-CED.A.1 Cash Box Basketball Buying a Car Harvesting the Fields Paying the Rent Planes and Wheat Sum of the Angles in a Polygon Throwing a Ball

A-CED.A.2 Cash Box Bernardo and Sylvia Play a Game Clea on an Escalator Global Positioning System I How Much Folate? Regular Tessellations of the Plane

A-CED.A.3 Cash Box Bernardo and Sylvia Play a Game Dimes and Quarters Growing Coffee How Much Folate? Writing Constraints

A-CED.A.4 Cash Box Equations and Formulas

A-REI.A How Does the Solution Change? Same Solutions

A-REI.A.2 Basketball Radical Equations

A-REI.B Integer Solutions to Inequality

A-REI.B.4 Integer Solutions to Inequality Two Squares are Equal

A.REI.B.4.b Integer Solutions to Inequality Braking Distance Springboard Dive

A-REI.C.6 Accurately Weighing Pennies I Accurately Weighing Pennies II Cash Box Find a System Pairs of Whole Numbers Quinoa Pasta II Quinoa Pasta III

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A-REI.C.7 Linear and Quadratic System The Circle and the Line

A-REI.D.10 Taxi! What is the True Cost of Purchasing an Automobile?

A-REI.D.11 Population and Food Supply Two Squares are Equal

A-REI.D.12 Fishing Adventures III Solution Sets

A-SSE.A.1 Animal Populations Delivery Trucks Increasing or Decreasing? [Variation 1] Kitchen Floor Tiles Mixing Candles Mixing Fertilizer Quadrupling Leads to Halving Radius of a Cylinder Seeing Dots The Bank Account The Physics Professor Throwing Horseshoes

A-SSE.A.2 An Integer Identity Animal Populations Computations with Complex Numbers Equivalent Expressions Seeing Dots Sum of Even and Odd

A-SSE.B Building a General Quadratic Function Taxes and Sales

A-SSE.B.3 Graphs of Quadratic Functions Ice Cream Increasing or Decreasing? [Variation II] Profit of a Company

A-SSE.B.3.c Forms of Exponential Expressions

A-SSE.B.4 A Lifetime of Savings Cantor Set Course of Antibiotics Triangle Series

F-BF.A.1 A Sum of Functions Kimi and Jordan Lake Algae Skeleton Tower Summer Intern

F-BF.A.1.a Compounding with a 5 Percent Interest Rate Compounding with a 100 Percent Interest Rate Susita’s Account The Canoe Trip [Variation I] The Canoe Trip [Variation II]

F-BF.A.1.c Crude Oil and Gas Mileage Flu on Campus Graphs of Compositions Temperature Conversions

F-BF.A.2 Car Depreciation

F-BF.A.3 Graph Shapes

F-BF.B.3 Building a General Quadratic Function Building a Quadratic Function from a Parent Function

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Building an Explicit Quadratic Function by Composition Identifying Even and Odd Functions Medieval Archer Transforming the graph of a Function

F-BF.B.4 Invertible or Not? U.S. Households

F-BF.B.4.a Temperature Conversions Temperature in Degrees Fahrenheit and Celsius

F-BF.B.4.c Latitude Rainfall

F-BF.B.5 Exponentials and Logarithms I Exponentials and Logarithms II

F-IF.4 Medication Dosage

F-IF.A Interpreting the Graph

F-IF.A.1 Interpreting the Graph Domains Parabolas and Inverse Functions Points on a Graph The Customers The Parking Lot Two Points Always Determine a Linear Function Using Function Notation I Your Father

F-IF.A.2 Interpreting the Graph Cell Phones Random Walk II The Random Walk Using Function Notation II Yam in the Oven

F-IF.A.3 Interpreting the Graph Aussie Fir Tree

F-IF.B Pizza Place Promotion

F-IF.B.4 Pizza Place Promotion As the Wheel Turns Average Cost How is the Weather? Influenza Epidemic Logistic Growth Model [Abstract] Logistic Growth Model [Explicit] Model Airplane Acrobatics Telling a Story with Graphs The Canoe Trip [Variation I] The Canoe Trip [Variation II] Throwing Baseballs Warming and Cooling

F-IF.B.5 Pizza Place Promotion Average Cost Oakland Coliseum The Canoe Trip [Variation I] The Canoe Trip [Variation II]

F-IF.B.6 Pizza Place Promotion Mathemafish Population The High School Gym

F-IF.C.7 Graphs of Quadratic Functions Identifying Graphs of Functions

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F-IF.C.7.c Graphs of Power Functions

F-IF.C.8.a Springboard Dive Which Function?

F-IF.C.9 Throwing Baseballs

F-LE.A Comparing Exponentials Extending the Definitions of Exponents [Version II] Rising Gas Prices What Functions Do Two Graph Points Determine?

F-LE.A.1 Basketball Bounces [Variation I] Basketball Bounces [Variation II] Exponential Functions Interesting Interest Rates Linear or Exponential?

F-LE.A.1.a Equal Differences Over Equal Intervals I Equal Differences Over Equal Intervals II Equal Factors Over Equal Intervals

F-LE.A.1.b Identifying Functions Illegal Fish In the Billions and Linear Modeling Linear Functions U.S. Population 1982-1988

F-LE.A.1.c Algae Blooms Basketball Rebounds Carbon 14 Dating [Variation II] Identifying Functions In the Billions and Exponential Modeling U.S. Population 1790-1860

F-LE.A.2 A Valuable Quarter Algae Blooms Basketball Bounces [Variation I] Basketball Bounces [Variation II] Basketball Rebounds Carbon 14 Dating in Practice II Do Two Points Always Determine a Linear Function II Do Two Points Always Determine a Linear Function I Do Two Points Always Determine an Exponential Function Two Points Determine an Exponential Function I Two Points Determine an Exponential Function II Doubling Your Money Finding Parabolas Through Two Points Population and Food Supply Rumors Sandia Aerial Team Snail Invasion Temperature in Degrees Fahrenheit and Celsius

F-LE.A.3 Exponential Growth vs. Linear Growth I Exponential Growth vs. Linear Growth II Exponential Growth vs. Polynomial Growth

F-LE.A.4 Accuracy of Carbon 14 Dating II Algae Blooms Bacteria Populations Carbon 14 Dating in Practice II Carbon 14 Dating Doubling Your Money Newton’s Law of Cooling

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Snail Invasion

F-LE.B.5 A Saturating Exponential Carbon Dating in Practice I Illegal Fish Newton’s Law of Cooling Taxi! U.S. Population 1982-1988

F-TF.B.5 As the Wheel Turns Foxes and Rabbits II Foxes and Rabbits III Round and Round We Go

F-TF.C.8 Farmer Task

F-TF.C.9 Sum and Difference Angle Formulas

G-C.A Two Wheels and a Belt

G-C.A.1 Two Wheels and a Belt Similar Circles

G-C.A.2 Two Wheels and a Belt Neglecting the Curvature of the Earth Right Triangles Inscribed in Circles I Right Triangles Inscribed in Circles II Tangent Lines and the Radius of a Circle

G-C.A.3 Two Wheels and a Belt Circumcenter of a Triangle Inscribing a Circle in a Triangle II Inscribing a Circle in a Triangle Inscribing a Triangle in a Circle Locating Warehouse Placing a Fire Hydrant

G-C.A.4 Two Wheels and a Belt Tangent to a Circle from a Point

G-C.B Setting Up Sprinklers Two Wheels and a Belt

G-C.B.5 Mutually Tangent Circles

G-CO.A Symmetries of a Circle Tangent Lines and the Radius of a Circle Unit Squares and Triangles

G-CO.A.3 Seven Circles II Symmetries of a Quadrilateral I Symmetries of a Quadrilateral II Symmetries of Rectangles

G-CO.A.4 Defining Reflections Defining Rotations

G-CO.A.5 Reflected Triangles

G-CO.B Are the Triangles Congruent? Is This a Rectangle? Reflections and Equilateral Triangles II Reflections and Equilateral Triangles Reflections and Isosceles Triangles

G-CO.B.6 Building a Tile Pattern by Reflecting Hexagons Building a Tile Pattern by Reflecting Octagons

G-CO.B.8 When Does SSA Work to Determine Triangle Congruence? Why Does ASA Work? Why Does SAS Work?

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Why Does SSS Work?

G-CO.C.9 Points Equidistant from Two Points in the Plane Tangent Lines and the Radius of a Circle

G-CO.C.10 Finding the Area of an Equilateral Triangle Seven Circles I

G-CO.C.11 Congruence of Parallelograms Is This a Parallelogram? Midpoints of the Sides of a Parallelogram

G-CO.D Placing a Fire Hydrant

G-CO.D.12 Angle Bisection and Midpoints of Line Segments Bisecting an Angle Construction of a Perpendicular Bisector Locating Warehouse Reflected Triangles

G-CO.D.13 Inscribing a Hexagon in a Circle Inscribing a Square in a Circle

G-GMD.A.1,2 Use Cavalieri’s Principle to Compare Aquarium Volumes

G-GMD.A.3 Centerpiece Doctor’s Appointment

G-GMD.B.4 Global Positioning System I Global Positioning System II Tennis Balls in a Can

G-GPE.A.1 Explaining the Equation for a Circle Slopes and Circles

G-GPE.A.2 Parabolas Focus and Directrix Lesson

G-GPE.B Is This a Rectangle?

G-GPE.B.4 A Midpoint Miracle Unit Squares and Triangles

G-GPE.B.5 A Midpoint Miracle Equal Area Triangles on the Same Base II Triangles Inscribed in a Circle Unit Squares and Triangles

G-MG.A Coins in a Circular Pattern Eratosthenes and the Circumference of the Earth Regular Tessellations of the Plane Running Around a Track I Running Around a Track II Paper Clip

G-MG.A.1 Global Positioning System II Hexagonal Pattern of Beehives How Many Cells are in the Human Body? How Many Leaves on a Tree? [Version II] How Many Leaves on a Tree? How Thick is a Soda Can I How Thick is a Soda Can II Seven Circles III Solar Eclipse Tennis Balls in a Can The Lighthouse Problem Tilt of Earth’s Axis and the Four Seasons Toilet Paper Roll Use Cavalieri’s Principle to Compare Aquarium Volumes

G-MG.A.2 Archimedes and the King’s Crown How Many Cells are in the Human Body? How Many Leaves on a Tree? [Version II]

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How Many Leaves on a Tree? How Thick is a Soda Can I How Thick is a Soda Can II

G-MG.A.3 Ice Cream Cone Satellite

G-SRT.A.1 Dilating a Line

G-SRT.A.2 Are They Similar?

G-SRT.A.3 Similar Triangles

G-SRT.B.4 Joining Two Midpoints of Sides of a Triangle

G-SRT.B.5 Bank Shot Congruence of Parallelograms Extensions, Bisections and Dissections in a Rectangle Is This a Rectangle? Unit Squares and Triangles

G-SRT.C Finding the Area of an Equilateral Triangle Seven Circles I

G-SRT.C.6,7,8 Mount Whitney to Death Valley

G-SRT.C.8 Coins in a Circular Pattern Neglecting the Curvature of the Earth Setting Up Sprinklers Seven Circles III Shortest Line Segment from a Point to a Line

G-SRT.D Seven Circles III

N-CN.A Computations with Complex Numbers

N-CN.A.1 Complex Number Patterns

N-CN.B.6 Complex Distance

N-CN.C.7 Solving for Complex Zeros

N-Q.A Traffic Jam

N-Q.A.1 Felicia’s Drive Fuel Efficiency Harvesting the Fields How Much is a Penny Worth? Ice Cream Van Runner’s World Selling Fuel Oil at a Loss Weed Killer

N-Q.A.3 Accuracy of Carbon Dating I Accuracy of Carbon Dating II Bus and Car Calories in a Sports Drink Dinosaur Bones Felicia’s Drive Weed Killer

N-RN.A.1 Extending the Definitions of Exponentials [Version II]

N-RN.A.2 Checking a Calculation of a Decimal Exponent Rational or Irrational?

N-RN.B Calculating the Square Root of 2 Rational or Irrational?

N-RN.B.3 Operations with Rational and Irrational Numbers

S-CP.A.1 Return to Fred’s Fun Factory

S-CP.A.1,4 The Titanic I

S-CP.A.2 Cards and Independence Return to Fred’s Fun Factory

S-CP.A.2,3,4,5 The Titanic II

S-CP.A.2,3,5 Rain and Lightning

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S-CP.A.3 Cards and Independence Lucky Envelopes

S-CP.A.4 How Do You Get to School?

S-CP.A.4,5 The Titanic III

S-CP.A.5 Breakfast Before School

S-CP.B.6 How Do You Get to School? The Titanic I The Titanic II The Titanic III

S-CP.B.7 Coffee at Mom’s Diner Rain and Lightning

S-CP.B.8 Fun Spinner

S-CP.B.9 Alex, Mel, and Chelsea Play a Game Random Walk III Random Walk IV Return to Fred’s Fun Factory

S-IC.A.1 Musical Preferences School Advisory Panel Strict Parents Why Randomize?

S-IC.A.2 Block Scheduling Sarah the Chimpanzee

S-IC.B.3 High Blood Pressure Strict Parents Words and Music II

S-IC.B.4 The Marble Jar

S-IC.C.9 High Blood Pressure

S.ID.A Accuracy of Carbon 14 Dating I

S-ID.A.1 Random Walk III

S-ID.A.1,2,3 Haircut Costs Speed Trap

S-ID.A.4 Do You Fit in This Car? SAT Scores Should We Send Out a Certificate?

S-ID.B.5 Musical Preferences

S-ID.B.6 Coffee and Crime

S-ID.C.7 Texting and Grades II

S-ID.C.7,8,9 Coffee and Crime

S-ID.C.9 Golf and Divorce

S-MD.A.2 Bob’s Bagel Shop Fred’s Fun Factory Sounds Really Good

S-MD.B.5 Sounds Really Good

S-MD.B.5,7 Fred’s Fun Factory

S-MD.B.6 Seating Chart

S-MD.B.6,7 Golden Ticket