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Unit I: Graphing to Solve Problems 55 – 62 days

Module: Working with Expressions and Equations 17-20 days

Lesson: Properties of Expressions 3 - 4 days

Topic Standards, Learning Objectives and Assessments

Commutative Property

Standards: A-SSE. A.2 Learning Objectives:

Define the commutative property and determine the operations in which it holds true

Associative Property

Standards: A-SSE. A.2 Learning Objectives:

Define the associative property and determine the operations in which it holds true

The Distributive Law

Standards: A-SSE.A.1, A-SSE.A.2 Learning Objectives:

Define the distributive law

Apply the distributive law as an alternative to order of operations and to expand expressions

Exercises Assessing: A-SSE.A.1, A-SSE.A.2 See Properties of Expressions Worksheet Solutions

Lesson: Working with One Variable 6 - 7 days


Number Sentences and Algebraic Equations

Standards: A-REI.B.3, A-SSE.A.1b Learning Objectives:

Understanding the elements and differences of number sentences and algebraic equations

Review how to solve equations

Solving Equations

Standards: A-REI.A.1,A-REI.B.3 Learning Objectives:

Solve equations and represent the solution as a solution set, a number line and in standard form

Exercises 1

Assessing: A-REI.B.3 See Solving Equations in One Variable Worksheet Solutions

Solving Inequalities

Standards: A-REI.B.3 Learning Objectives:

Solve and graph inequalities

Determine values within the solution set

Exercises 2

Assessing: A-REI.B.3 See Solving Inequalities in One Variable Worksheet Solutions

Solution Sets for Multiple Equations

Standards: A-SSE.A.2, A-REI.B.3 Learning Objectives:

Identify the difference between two equations joined by "and" and "or"

Solve for a solution set for multiple equations under the given restrictions

Exercises 3

Assessing: A-SSE.A.2, A-REI.B.3 See Solving Equations and Inequalities in One Variable Worksheet Solutions

The Zero Property

Standards: A-CED.A.3 Learning Objectives:

Understand the Zero Property and how it can be applied as a restriction

Solving Equations with Variables in the Denominator

Standards: A-CED.A.3, A-CED.A.4 Learning Objectives:

State the restrictions for an equation Rewrite equations with variables in the denominator as a

compound statement Apply the Zero Property when solving equations and

determine if the solution is true based on the restrictions Rearrange formulas to isolate for a specific variable using

triangles or algebraic methods

Exercises 4

Assessing: A-REI.A.1, A-CED.A.3, A-CED.A.4 See Solving Equations with a Variable in the Denominator Worksheet Solutions

Big Ideas Alignment Opportunity 1.1, 1.5

Lesson: Working with Two Variables 6 - 7 days


Review Learning Objectives:

Review the concepts necessary for the unit

Solution Sets to Equations with Two Variables

Standards: A-REI.D.10 Learning Objectives:

Solve for solutions to linear equations with two variables

Show that every point on a line is a solution to a linear equation

State restrictions on application problems and solve for a given value

Solution Sets to Inequalities with Two Variables

Standards: A-REI.D.12 Learning Objectives:

Graph inequalities with two variables and determine the solution

Compare how a solution to an inequality is different than a solution to a linear equation

Justify the reasonableness of solutions to application problems

Exercises 1 Assessing: A-REI.D.10,A-REI.D.12 See Solving Equations and Inequalities in Two Variables Worksheet Solutions

Solution Sets to Simultaneous Equations

Standards: A-REI.C.5,A-REI.C.6 Learning Objectives:

Graph simultaneous linear equations and inequalities and highlight the solution

Determine the solution to simultaneous equations by substitution, elimination and graphing

Determine the intersection of simultaneous inequalities by graphing

Exercises 2 Assessing: A-REI.C.6 See Simultaneous Equations and Inequalities Worksheet Solutions

Big Ideas Alignment Opportunity 1.2, 1.3, 5.2, 5.3, 5.4, 5.6, 5.7

Lesson: Module End 2 days

Exit Card

Module Assignment Assessing: A-SSE.A.1a, A-SSE.A.1b, A-SSE.A.2, A-APR.A.1 See Assignment Solutions

Module : Defining Functions 8 – 9 days

Lesson: Relations and Functions 3 - 4 days


Understanding Relations Standards: F-IF.A.1 Learning Objectives:

Define the term relation, and understand their different representations.

Identifying Functions Standards: F-IF.A.1 Learning Objectives:

Define the term function and understand the relationship between relations and functions.

Identify whether a given relation is a function or not using the vertical line test and other methods.

Use function notation to evaluate functions and apply these to real-life contexts.

Exercises Assessing: F-IF.A.1 See Relations and Functions Worksheet Solutions

Big Ideas Alignment Opportunity 3.1

Lesson: Function Notation 1 - 2 days


Introduction Standards: F-IF.A.2 Learning Objectives:

Write equations using function notation.

Evaluate and interpret statements that use function notation.

Exercises Assessing: F-IF.A.2, F-BF.A.1a See Function Notation Worksheet Solutions


Lesson: Domain and Range 2 days


Domain and Range Standards: F-IF.A.1, F-IF.B.5 Learning Objectives:

Define the terms domain and range. Determine the domain and range of a function and

interpret their meaning in a real-life context.

Exercises Assessing: F-IF.A.1, F-IF.B.5 See Domain and Range Worksheet Solutions



Exit Card

Module Assignment Assessing: F-IF.A.1, F-IF.A.2, F-IF.B.5, F-BF.A.1a See Assignment Solution There is also an optional worksheet for students to fill in while collecting their data – See Assignment Worksheet

Module : Graphing Functions 12 days

Lesson: Graphing Stories 4 days


Linear Piecewise Graphs Standards:F-IF.C.7, F-IF.C.7a, F.LE.A.1.B, F.IF.B.4 Learning Objectives:

Using videos and scenarios sketch the graph using Linear Piecewise Functions

Exercises 1 Assessing: F-IF.C.7, F-IF.C.7a, F.IF.B.4 See Graphing Stories Worksheet Solutions


Graphs of Quadratic Functions Standards: F-IF.C.7, F-IF.C.7a, F.IF.B.4 Learning Objectives:

Using videos and scenarios sketch the graph using Quadratic Functions.

Exercises 2 Assessing: F-IF.C.7, F-IF.C.7a, F.IF.B.4 See Graphing Stories Worksheet 2 Solutions

Graphs of Exponential Functions Standards: F.LE.A.1, F.LE.A.3, F.IF.B.4 Learning Objectives:

Using videos and scenarios sketch the graph using Exponential Functions.

Exercises 3 Assessing: F-IF.B.5, F-IF.C.7, F-IF.C.7a, F.IF.B.4 See Graphing Stories Worksheet 3 Solutions


Graphs of Two Stories Standards: F.IF.B.4, F.IF.C.9 Learning Objectives:

Using videos and scenarios, sketch the graph and interpret the resulting graph

Exercises 4 Assessing: F.IF.B.4, F.IF.C.9 See Graphing Stories Worksheet 4 Solutions

Lesson: Linear Functions 4 days


Graphing Linear Functions Standards: F-IF.A.1, F-IF.C.7, F-IF.C.7a Learning Objectives:

Graph linear functions using a table of values Understand partial and direct variation.

Using the Slope Standards: F-IF.B.5, F-IF.C.7, F-IF.C.7a Learning Objectives:

Graph linear functions using their slope and y-intercept

Exercises 1 Assessing: F-IF.B.5, F-IF.C.7, F-IF.C.7a See Linear Functions Worksheet Solutions

Slope as a Rate of Change Standards: F-IF.B.6 Learning Objectives:

Apply the slope of a linear function to solve problems involving average rate of change.

Intercepts Standards: F-IF.B.4, F-IF.C.7, F-IF.C.7a Learning Objectives:

Identify the intercepts of a function, their relevance and use them to answer questions in a real-life context.

Important Intervals Standards: F-IF.B.4, F-IF.C.7, F-IF.C.7a Learning Objectives:

Identify and use interval notation to describe intervals of increase and decrease, as well as positive and negative intervals.

Exercises 2 Assessing: F-IF.B.4, F-IF.C.7, F-IF.C.7a See Linear Functions Worksheet 2 Solutions

Big Ideas Alignment Opportunity 3.4, 3.5, 4.1, 4.2, 4.3

Lesson: Exponential Functions 3 days


Graphing Exponential Functions Standards: F-IF.B.5, F-IF.C.7, F-IF.C.7e, F-LE.B.5 Learning Objectives:

Graph exponential functions and identify their domain and range

Using Technology Standards: F-IF.C.7, F-IF.C.7e Learning Objectives:

Use technology to graph exponential functions

Exercises 1 Assessing: F-IF.B.5, F-IF.C.7, F-IF.C.7e See Exponential Functions Worksheet Solutions

Important Features Standards: F-IF.B.4, F-IF.C.7, F-IF.C.7e Learning Objectives:

Identify the intercepts of a function, their relevance and use them to answer questions in a real-life context.

Identify and use interval notation to describe intervals of increase and decrease, as well as positive and negative intervals.

Identify and describe the end behaviours of an exponential function.

Average Rate of Change Standards: F-IF.B.6 Learning Objectives:

Estimate the average rate of change of an exponential function from its graph.

Exercises 2 Assessing: F-IF.B.4, F-IF.B.6, F-IF.C.7, F-IF.C.7e See Exponential Functions Worksheet 2 Solutions

Big Ideas Alignment Opportunity 6.1, 6.2, 6.3



Exit Card

Module Discussion Standards: F-IF.C.9 Learning Objectives:

Compare two functions and describe their similarities and differences.

See Discussion Prompts

There is also an Extend Your Learning Solution – See Extend Your Learning: Instantaneous Rate of Change Solution

Module : Using Graphs to Solve Problems 11 - 12 days

Lesson: Solving Problems with Linear Models 2 days


Using Technology Standards: A.REI.C.6 Learning Objectives:

Solve (approximately, in some cases) for a solution to a system using graphing technology

Creating Linear Models Standards: A.REI.C.6, A-CED.A.2, A-REI.D.11, F-BF.A.1 Learning Objectives:

Create linear models to solve application problems for equations and inequalities with two variables

Exercises Assessing: A.REI.C.6, A-CED.A.2, A-REI.D.11, F-BF.A.1 See Creating Linear Models Worksheet Solutions


Lesson: Solving Problems with Exponential Models 4 - 5 days


Exponential Growth Standards: F-IF.8b, F-LE.A.1c, F-LE.A.2, F-BF.A.1a, F-LE.B.5 Learning Objectives:

Create a model for exponential growth

Exponential Decay Standards: F-IF.8b, F-LE.A.1c, F-LE.A.2, F-BF.A.1a, F-LE.B.5 Learning Objectives:

Create a model for exponential decay

Exercises 1 Assessing: F-LE.A.1c, F-BF.A.1a, F-LE.B.5 See Exponential Growth and Decay Worksheet Solutions

Financial Applications Standards: F-LE.A.1, F-BF.A.1a Learning Objectives:

Begin an explanation of finances, including simple interest examples to improve financial literacy

Exercises 2 Assessing: F-LE.A.1, F-BF.A.1a See Financial Applications Worksheet Solutions

Compound Interest Standards: A-CED.A.4, A-REI.C.6 Learning Objectives:

Apply exponential models to personal finance contexts Manipulate interest formulas to answer different real-life

problems

Exercises 3 Assessing: F-LE.B.5 See Financial Application of Exponential Equations Worksheet Solutions

Lesson: Analyzing Rates of Change 3 days


Analyzing Change Standards: F-IF.B.6 Learning Objectives:

Analyze distance-time graphs to determine the speed of an object

Exercises 1 Assessing: F-IF.B.6 See Analyzing Change Worksheet Solutions

Connecting Graphs Standards: F-IF.B.6 Learning Objectives:

Calculate rates of change from different contexts

Instantaneous Rates Standards: F-IF.B.6 Learning Objectives:

Define the term relation, and understand their different representations.

Exercises 2 Assessing: F-IF.B.6 See Average and Instantaneous Rate of Change Worksheet Solutions




Exit Card

Module Assignment Assessing: F-IF.A.1, F-IF.A.2, F-IF.B.5 See Assignment Solutions There is also an Extend Your Learning Solution – See Extending Your Learning: Speed-Time Graphs

Module : Sequences 7 - 9 days

Lesson: Arithmetic Sequences 3 days


Exploring Sequences Standards: F-LE.A.3, F-LE.A.1b Learning Objectives:

Explore arithmetic sequences and identify the pattern of common differences.

Understand and use the two types of formulas for arithmetic sequences; recursive and non-recursive.

Exercises 1 Assessing: F-LE.A.3, F-LE.A.1b See Arithmetic Sequences Worksheet 1 Solutions

Expressing Sequences Standards: F-IF.A.3, F-LE.A.1b Learning Objectives:

Express sequences as either recursive or non-recursive Understand and use the two types of formulas for

arithmetic sequences; recursive and non-recursive.


Arithmetic Sequences as Functions Standards: F-IF.A.3, F-LE.A.1ab, F-LE.A.2 Learning Objectives:

Compare arithmetic sequences to general knowledge of linear functions.

Incorporate function notation into sequences.


Summary Standards: F-IF.A.3, F-LE.A.1b, F-LE.A.2

Lesson: Geometric Sequences 2 - 3 days


Introduction Standards: F-IF.A.3, F-LE.A.1c Learning Objectives:

Explore geometric sequences and identify the patter of common ratios.

Exercises 1 Assessing: F-IF.A.3, F-LE.A.1c, F-LE.A.2 See Geometric Sequences Worksheet Solutions

Expressing Geometric Sequences Standards: F-IF.A.3, F-LE.A.1ac, F-LE.A.2 Learning Objectives:

Express sequences as either recursive or non-recursive

Understand and use the two types of formulas for arithmetic sequences; recursive and non-recursive.

Exercises 2 Assessing: F-IF.A.3, F-LE.A.1c, F-LE.A.2 See Geometric Sequences Worksheet 2 Solutions

Geometric Sequences as Functions Standards: F-IF.A.3, F-LE.A.1ac, F-LE.A.2 Learning Objectives:

Understand and use the formula for geometric sequences Compare geometric sequences to general knowledge of

exponential functions.

Exercises 3 Assessing: F-IF.A.3, F-LE.A.1c, F-LE.A.2 See Geometric Sequences Worksheet 3 Solutions

Summary Standards: F-IF.A.3, F-LE.A.1c, F-LE.A.2

Lesson: Recursive Sequences 1 - 2 days


The Fibonacci Sequence Standards: F-IF.A.3 Learning Objectives:

Recognize that sequences sometimes cannot be defined as geometric or arithmetic

Use the Fibonacci sequence to understand the behaviour of a recursive sequence.

See Additional Lesson Material for Fibonacci’s Sequence

Exercises Assessing: F-IF.A.3 See Recursive Sequences Worksheet Solutions

Lesson: Module End 1 day


Exit Card

Module Assignment Assessing: F-IF.A.2, F-IF.A.3, F-BF.A.1a, F-LE.A.2

See Assignment Solutions

There is also two Extend Your Learning Solutions – Extend Your Learning: Arithmetic and Geometric Sequences

Extend Your Learning: Domain and Range Solution

Unit II: Reasoning with Polynomial Functions

Module: Working with Polynomial Functions 17-25 days

Lesson: Classifying and Simplifying Polynomials 1-2 days


Introduction to Polynomials

Standards: A-SSE.A.1a,b, A-SSE.A.2, A-APR.A.1 Learning Objectives:

Define the terms associated with polynomials Classify the different types of polynomials Combine like terms to simplify polynomials Understand that polynomials are closed under

addition and subtraction

Exercises

Assessing: A-SSE.A.1a,b, A-SSE.A.2 See Polynomial Operations Worksheet 1 Solutions


Lesson: Multiplying Polynomials 1-2 days


Multiplying Polynomials

Standards: A-SSE.A.2, A-APR.A.1, N-RN.A.1, N-RN.A.2

Learning Objectives:

Apply exponent laws to multiply polynomials and then simplify the expression

Understand the different ways to rewrite a fraction as an exponent

Understand that polynomials are closed under multiplication

Exercises

Assessing: A-APR.A.1, A-SSE.A.2 See Polynomial Operations Worksheet 2 Solutions


Lesson: Types of Polynomials and Key Features 4 days


Introducing Polynomials Standards: A-SSE.A.1a Learning Objectives:

Define a polynomial function Review classification of polynomial, simplifying

polynomials and multiplying polynomials

Overview of Polynomial Shapes Standards: F-IF.B.4, F-IF.C.7c


o Overview the general characteristics of polynomial functions.

o Identify patterns in even degree and odd degree polynomial functions, in regards to end behavior, number of turns, number of x-intercepts and general shape

Determining Shapes from Equations

Standards: F-IF.B.4


Summarize the general characteristics of polynomial functions

Sketch the general shape of a polynomial from its equation.

Exercises Assessing: F-IF.B.4, F-IF.C.7c See Types of Polynomials and Key Features Worksheet Solutions Worksheet 2 Solutions

Lesson: Factoring Techniques: Common Factoring 1-2days


Common Factoring Standards: A-SSE.A.2


Using the greatest common factor, common factor polynomial expressions.

Exercises Assessing: A-SSE.A.2 See Common Factor Worksheet Solutions


Lesson: Factoring Techniques: Simple Trinomials 1-2 days


Simple Trinomials Standards: A-SSE.A.2


Factor trinomials where a = 1.

Exercises Assessing: A-SSE.A.2 See Factoring Simple Trinomials Worksheet Solutions


Lesson: Factoring Techniques: Complex Trinomials 1-2 days


Factoring Complex Trinomials Standards: A-SSE.A.2


Factor trinomials where a ≠ 1.

Exercises Assessing: A-SSE.A.2 See Factoring Complex Trinomials Worksheet Solutions


Lesson: Factoring Techniques: Perfect and Differences of Squares 1-2 days


Perfect and Differences of Squares Standards: A-SSE.A.2


Identify polynomials in the form of difference of squares and perfect square trinomials, and use the appropriate method to factor these types of expressions.

Exercises Assessing: A-SSE.A.2 See Perfect and Difference of Squares Worksheet Solutions


Lesson: Factoring Techniques: Factoring by Grouping 1-2 days


Factoring by Grouping Standards: A-SSE.A.2


Factor expressions with four terms by using the grouping method.

Exercises Assessing: A-SSE.A.2 See Factor by Grouping Worksheet Solutions


Lesson: Using Polynomial Features to Sketch Functions 3 days


Using the Zeros of a Function Standards: A-SSE.A.2, F-IF.C.8


Learn the square root principles Learn the zero product property Identify the x-intercepts of a polynomial function by

applying factoring techniques and the zero product property.

Create more accurate sketches of polynomial functions by using the zeros of a function.

Exercises Assessing: A-SSE.B.3, A-APR.B.3, F-IF.C.7c, F-IF.C.8 See Using Polynomial Features to Sketch Functions Worksheet Solutions


Lesson: Module End 3-4 days


Exit Card

Module Assignment Assessing: A-CED.A.2, F-IF.B.4, F-IF.C.7c

Module : Examining Quadratic Functions in More Detail 14 - 17 days

Lesson: Quadratic Functions 1 - 2 days


Key Features of Quadratic Functions

Standards: F-IF.C.7a Learning Objectives:

Examine the key features of quadratic functions in greater depth.

Identify the vertex, axis of symmetry, minimums, and maximums of quadratic functions.

Use second differences to identify quadratic functions. Use the leading coefficient of quadratic functions to determine

the shape.

Exercises Assessing: F-IF.C.7a See Quadratic Functions Worksheet Solutions

Big Ideas Alignment Opportunity 8.1, 8.2, 8.3

Lesson: The Forms of Quadratic Functions 1 - 2 days


The Forms of Quadratic Functions Standards: A-SSE.B.3a, F-IF.C.8a Learning Objectives:

Understand that quadratic functions can be represented in different, interchangeable forms: the standard form, the factored form, and the vertex form.

Identify which properties can be read and/or easily calculated from each form.

Exercises Assessing: A-SSE.B.3a, F-IF.C.8a See Quadratic Functions Worksheet 2 Solutions


Lesson: Solving Quadratic Functions By Inspection 2 days


Solving Quadratic Functions Standards: A-REI.B.4b Learning Objectives:

Solve quadratic functions by inspection

Exercises Assessing: A-REI.B.4b See Quadratic Functions Worksheet 3 Solutions


Lesson: Solving Quadratic Functions By Applying Factoring Techniques 2 days


Applying Factoring Techniques Standards: A-SSE.B.3a, A-REI.B.4b, F-IF.C.8a Learning Objectives:

Solve quadratic functions by applying factoring techniques.

Exercises Assessing: A-SSE.B.3a, A-REI.B.4b, F-IF.C.8a See Solving Quadratic Functions Worksheet 1

Lesson: Solving Quadratic Functions By Using the Quadratic Formula 2 days


Applying the Quadratic Formula Standards: A-REI.B.4b Learning Objectives:

Solve quadratic functions by applying the quadratic formula.

Exercises Assessing: A-REI.B.4b

See Solving Quadratic Functions Worksheet 2


Lesson: Solving Quadratic Functions By Completing the Square 2 days


Completing the Square Standards: A-SSE.B.3b, A-REI.B.4a,b, F-IF.C.8a Learning Objectives:

Solve quadratic functions by completing the square

Exercises Assessing: A-SSE.B.3b, A-REI.B.4a,b, F-IF.C.8a See Solving Quadratic Functions Worksheet 3


Lesson: Applying Quadratic Function Applications 2 days


Quadratic Function Applications Standards: A-REI.B.4a,b Learning Objectives:

Apply quadratic functions to real-world problems, and utilize the key features, different forms, and solving techniques from the module to answer these types of problems.

Exercises Assessing: A-REI.B.4a,b, F-IF.C.9 See Solving Quadratic Functions Worksheet 4

Lesson: Module End 2 - 3 days


Exit Card

Module Assignment Assessing: F-IF.C.7a, F.IF.C.8a, A-SSE.B.3a,b, A-REI.B.4a.b See Assignment Solutions There is also an Extend Your Learning Solution – See Extend Your Learning: Deriving the Quadratic Formula

Module : Transforming Functions 9 - 15 days

Lesson: Vertical Shifts 1 - 2 days


The c Value and Vertical Shifts Standards: F-BF.B.3, IF.C.7a Learning Objectives:

Adapt equations of functions to shift a function vertically

Exercises Assessing: F-BF.B.3 See Vertical Shifts Worksheet Solutions


Lesson: Horizontal Shifts 1 - 2 days


The d Value and Horizontal Shift Standards: F-BF.B.3, IF.C.7a Learning Objectives:

Adapt equations of functions to shift a function horizontally

Exercises Assessing: F-BF.B.3 See Horizontal Shifts Worksheet Solutions

Lesson: Vertical Stretches 1 - 2 days


The a Value and Vertical Stretches Standards: F-BF.B.3, IF.C.7a Learning Objectives:

Adapt equations of functions to stretch or compress a function vertically.

Exercises Assessing: F-BF.B.3 See Vertical Stretches Worksheet Solutions

Lesson: Horizontal Stretches 1 - 2 days


The k Value Standards: F-BF.B.3, IF.C.7a Learning Objectives:

Adapt equations of functions to stretch or compress a function horizontally.

Exercises Assessing: F-BF.B.3 See Horizontal Stretches Worksheet Solutions

Lesson: Multiple Transformations 1 - 2 days


Summary of Transformations Standards: F-BF.B.3 Learning Objectives:

Combine transformations to modify a graph in a number of ways.

Sketching Transformations Standards: F-BF.B.3 Learning Objectives:

Define the term relation and understand their different representations.

Exercises Assessing: F-BF.B.3 See Multiple Transformations Worksheet Solutions

Lesson: Even and Odd Functions 2 - 3 days


Defining Even and Odd Functions Standards: F-BF.B.3 Learning Objectives:

Define the terms even and odd. Look at the difference between even and odd functions

algebraically and graphically.

Effects of Transformations Standards: F-BF.B.3 Learning Objectives:

Investigate if functions stay even or odd after transformations are applied.

Exercises Assessing: F-BF.B.3 See Even and Odd Functions Worksheet Solutions



Exit Card

Module Quiz Assessing: F-BF.B.3

Module : Manipulation Functions 6 - 10 days

Lesson: Sums and Differences of Functions 1 - 2 days


Sums and Differences of Functions Standards: A-APR.A.1 Learning Objectives:

Understand and calculate a sum function and a difference function given two functions.

Exercises Assessing: A-APR.A.1 See Sums and Differences of Functions Solutions

Lesson: Products and Quotients of Functions 1 - 2 days


Products and Quotients of Functions

Standards: A-APR.A.1 Learning Objectives:

Understand and calculate a product and a quotient function given two functions.

Exercises Assessing: A-APR.A.1, F-BF.A.1b See Products and Quotients of Functions Solutions

Lesson: Understanding an Inverse 1 - 2 days


Understanding an Inverse Standards: F-BF.B.4a Learning Objectives:

Understand how an inverse function reverses the operations of the original function.

Overview of the properties of inverse functions.

Determining an Inverse Standards: F-BF.B.4a Learning Objectives:

Determine the inverse of a function represented by a set of ordered pairs, a written description, and a graph.

Exercises Assessing: F-BF.B.4a See Finding an Inverse Worksheet Solutions

Lesson: Calculating an Inverse 1 - 2 days


Calculating an Inverse Standards: F-BF.B.4a Learning Objectives:

Calculate the inverse of a function, given its algebraic expression.

Exercises Assessing: F-BF.B.4a See Calculating an Inverse Worksheet Solutions



Exit Card

Module Quiz Assessing: A-APR.A.1, F-BF.A.1b, F-BF.B.4a

Unit III: Modeling and Problem Solving 20-29 days

Module: Modeling Linear Functions 4 - 5 days

Lesson: Exploring Linear Models 2 days


Splitting the Bill

Standards: A-CED.A.1, A-REI.A.1, A-REI.B.3 Learning Objectives:

Create an equation in one variable and use it to solve a problem.

Explain each step in solving a simple problem Construct a viable argument to justify a solution method.

Splitting the Bill… Again

Standards: A-CED.A.1, A-REI.A.1, A-REI.B.3 Learning Objectives:



Exercises Assessing: A-CED.A.1, A-REI.A.1, A-REI.B.3 Learning Objectives:



See Exploring Linear Models Worksheet Solutions


Exit Card

Module Assignment Assessing: A-CED.A.1, A-REI.A.1, A-REI.B.3 There are three solutions depending on the assignment chosen

See The Music Studio Solutions

See The Assembly Line Solutions

See The Sales Membership Solutions


Module : Modeling with Exponential Functions 4 - 6 days

Lesson: Exploring Exponential Models 2 - 3 days


The Explosive Growth of Bacteria! Standards: A-CED.A.1, F-IF.C.7e, F-LE.A.2 Learning Objectives:

Create exponential equations in one variable to and use them to solve problems.

Graph exponential functions by hand or using technology, showing intercepts and end behaviour.

Construct exponential functions, from a description of a relationship.

See The Explosive Growth of Bacteria! Solutions

Keeping Bacteria Under Control Standards: A-CED.A.1, F-IF.C.7e Learning Objectives:

Create exponential equations in one variable to and use them to solve problems.

Graph exponential functions by hand or using technology, showing intercepts and end behaviour.

See Keeping Bacteria Under Control Solutions

Exercises Assessing: A-CED.A.1, F-IF.C.7e, F-LE.A.2 Answers will vary so there is no solution.



Exit Card

Module Assignment Assessing: A-CED.A.1, F-IF.C.7e, F-LE.A.2 See Sample Student Modeling with Exponential Functions Activity

Module : Modeling with Systems of Inequalities 4 - 6 days

Lesson: Exploring Systems of Inequalities 2 - 3 days


Minimizing the Cost Standards: A-CED.A.2, A-CED.A.3, A-REI.D.12, N-Q.A.1, N-Q.A.2, N-Q.A.3 Learning Objectives:

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

Represent constraints by systems of inequalities and interpret solutions in a modeling context.

Graph the solutions of a linear inequality in two variables as a half-plane.

Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Maximizing Profits Standards: A-CED.A.2, A-CED.A.3, A-REI.D.12, N-Q.A.1, N-Q.A.2, N-Q.A.3 Learning Objectives:

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

Represent constraints by systems of inequalities and interpret solutions in a modeling context.

Graph the solutions of a linear inequality in two variables as a half-plane.

Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Exercises Assessing: A-CED.A.2, A-CED.A.3, A-REI.D.12, N-Q.A.1, N-Q.A.2, N-Q.A.3

See Exploring Systems of Inequalities Worksheet Solutions



Exit Card

Module Assignment Assessing: A-CED.A.2, A-CED.A.3, A-REI.D.12

See Maximizing Profits Solutions


Module : Modeling Other Functions 4 - 6 days

Lesson: Exploring Other Models 2 - 3 days


The Absolute Value Function Standards: F-IF.C.7b Learning Objectives:

Graph the absolute value functions.

The Absolute Value Function… Again Standards: F-IF.C.7b Learning Objectives:

Identify the effect of changing the parameters in the absolute value function.

Exercises Assessing: F-IF.C.7b See The Cube Root Function Solutions



Exit Card

Module Assignment Assessing: F-IF.C.7b See The Square Root Function Solutions


Module : Modeling with Polynomials and Piecewise Functions 4 - 6 days

Lesson: Exploring Polynomials and Piecewise Functions 3 - 4 days


Discrete or Continuous Standards: F-IF.C.7b Learning Objectives:

Recognize the difference between a continuous or discrete function.

Using Piecewise Models Standards: F-IF.C.7b Learning Objectives:

Graph piecewise defined functions, including step functions.

Piecewise Graphing Stories Standards: F-IF.C.7b Learning Objectives:

Determine linear piecewise-defined functions based on a graph of the motion or object.

Exercises Standards: F-IF.C.7b Learning Objectives:

Determine linear piecewise-defined functions based on a graph of the motion or object.

See Exploring Polynomial and Piecewise Functions Worksheet Solutions



Exit Card

Module Assignment Assessing: F-IF.C.7b See The Flexible Data Plan Solutions

Unit IV: Data Management 26 - 29 days

Module: One Variable Statistics 13 - 14 days

Lesson: Representing Data 4 days


Creating Bar Graphs

Standards: S-ID.1 Learning Objectives:

Examine discrete data and create bar graphs to represent data sets visually.

Creating Histograms


Examine continuous data and note how it behaves differently from discrete data.

Create histograms to represent these types of data sets visually.

Exercises 1 Assessing: S-ID.1 See Representing Data Worksheet 1 Solutions

Using Data Frequency


Use frequency tables to create frequency polygons.

Understand relative frequency, and create relative frequency histograms and polygons.

Use cumulative frequency to create graphs and interpret the shape of data.

More Representations


Identify other types of representations; a pie chart, for example.

Study different, creative representations and look for misleading data.

Exercises 2 Assessing: S-ID.1 See Representing Data Worksheet 2 Solutions

Lesson: Measures of Central Tendency 4 - 5 days


Measuring Data

Standards: S-ID.2, S-ID.3 Learning Objectives:

Calculate mean, median and mode for data sets. Understand how the three measures can give a different

idea of the center of the data set.

Calculation Examples


Calculate mean, median and mode for data sets.

Choosing a Measure


Think critically about the type of data, and determine which measure of central tendency will give the best description.

Exercises 1

Assessing: S-ID.2, S-ID.3 See Measures of Central Tendency Worksheet 1 Solutions

Weighted Data


Calculate the mean of weighted data.

Grouped Data


Calculate the mean, median and mode of grouped data.

Interpreting Shapes


Compare a data set's mean, median and mode to determine if the data is symmetrical, positively skewed or negatively skewed.

Exercises 2

Assessing: S-ID.2, S-ID.3 See Measures of Central Tendency Worksheet 2 Solutions


Lesson: Dispersion and Deviation 3 days


The Spread of Data Standards: S-ID.1, S-ID.2, S-ID.3 Learning Objectives:

Calculate the range, quartiles and inter-quartile range for a set of data.

Create box and whisker diagrams to display this information.

Understand the idea of dispersion.

Measures of Spread Standards: S-ID.2, S-ID.3 Learning Objectives:

Calculate the standard deviation of a set of data.

Using Technology Standards: S-ID.2, S-ID.3 Learning Objectives:

Use Excel to calculate the standard deviation See Creating a Histogram Using Excel

Exercises Assessing: S-ID.1, S-ID.2, S-ID.3 See Dispersion and Deviation Worksheet Solutions



Exit Card

Module Assignment Assessing: S-ID.1, S-ID.2, S-ID.3 See Assignment Solutions There is also an Extend Your Learning Solution – See Extend Your Learning: Estimating Mean, Median and Mode

Module : Two Variable Statistics 13 - 15 days

Lesson: Categorical Data 4 - 5 days


Representing Categorical Data Standards: S-ID.B.5 Learning Objectives:

Create two-way frequency tables for bivariate categorical data.

Define and understand joint frequencies and marginal frequencies.

Using Relative Frequencies Standards: S-ID.B.5 Learning Objectives:

Realize the limitations of a two-way frequency table and utilize relative frequencies.

Exercise 1 Assessing: S-ID.B.5 See Categorical Data Worksheet 1 Solutions

Conditional Relative Frequencies Standards: S-ID.B.5 Learning Objectives:

Begin using conditional relative frequencies to identify associations and trends in bivariate categorical data.

Exercises 2 Assessing: S-ID.B.5 See Categorical Data Worksheet 2 Solutions

Lesson: Numerical Data 7 days


Representing Numerical Data Standards: S-ID.B.6 Learning Objectives:

Identify two variable numerical data and the terms associated with it.

Seeing Relationships Standards: S-ID.B.6, S-ID.B.6c Learning Objectives:

Represent bivariate numerical data using a scatter plot. Identify different types of correlations (positive, negative,

scattered, strong, weak, etc).

Exercises 1 Assessing: S-ID.B.6, S-ID.B.6c See Numerical Data Worksheet 1 Solutions

Lines of Best Fit Standards: S-ID.B.6, S-ID.B.6a, S-ID.B.6c, S-ID.B.7 Learning Objectives:

Algebraically determine the line of best fit for a given data set.

Make predictions based on the line of best fit.

Residual Values Standards: S-ID.B.6, S-ID.B.6a, S-ID.B.6b, S-ID.B.6c, S-ID.B.7 Learning Objectives:

Understand residual values and use them to compare two linear models to determine which is most accurate.

Understand the terminology of a 'least-squares line'. Use technology to determine a line of best fit.

Correlation Strength Standards: S-ID.B.8 Learning Objectives:

Understand the idea of correlation strength. Use Excel to calculate the correlation coefficient. Interpret r values in the context of a data set.

Curves of Best Fit Standards: S-ID.B.6, S-ID.B.6a, S-ID.B.6b Learning Objectives:

Identify, visually, functions that should be represented with a curve of best fit.

Use Excel to determine a curve of best fit and calculate an R2 value.

Use Residual Plots to analyze the fit of a function, and determine if a chosen model is appropriate.

Exercises 2 Assessing: S-ID.B.6, S-ID.B.6a, S-ID.B.6b, S-ID.B.6c, S-ID.B.7, S-ID.B.8 See Numerical Data Worksheet 2 Solutions

Effects of Outliers Standards:S-ID.B.6a, S-ID.B.8 Learning Objectives:

Identify outliers in a data set, and the effects they have on the correlation strength.

Correlation and Causation Standards: S-ID.C.9 Learning Objectives:

Distinguish between Correlation and Causation

Exercises 3 Assessing: S-ID.B.6a, S-ID.B.6c, S-ID.C.8, S-ID.C.9 See Numerical Data Worksheet 3 Solutions



Exit Card

Module Discussion Standards: S-ID.C.9 Learning Objectives:

Using an argumentative piece and critical thinking, defend a position in a debate that utilizes the concepts of correlation and causation.

See Arguing A Claim There is also an Extend Your Learning Solution – See Extend Your Learning: Two-way Frequency Tables and Venn Diagrams

unit i: graphing to solve problems 55 62 days module: …€¦ · · 2016-04-14lesson: working...

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