algebra 1 common core curriculum -...
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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