CCSS IP MATH III TEACHER RESOURCE

Suggested Pacing Guide

Overview

The sub-lessons in Walch Integrated Math are designed to be covered over one, two, or three days,

depending on the depth and complexity of the topic. This pacing has been adapted to fit the block

schedule. The pacing guide that follows provides suggested pacing, but this should be viewed as a

flexible guideline only. If students need an extra day to solidify understanding, a one-day lesson may

be spread over two days, or a two-day lesson may be spread over three days. Conversely, if students

grasp a concept more quickly than suggested by the pacing guide, it is fine to shorten the duration of

the lesson and move on to the next topic.

Each sub-lesson features several components. The estimated time for each component is given

in parentheses. Components include: a Warm-Up, Instruction (including an Introduction, Key

Concepts, and Guided Practice), a Problem-Based Task, and Practice.

Please note: PowerPoint versions of each sub-lesson’s Warm-Up and Instruction are provided.

Warm-Up PowerPoints include a video clip and the Warm-Up Debrief. Instructional PowerPoints

feature the Introduction, Key Concepts, and selected Guided Practice Examples with links to

corresponding GeoGebra applets. Estimated times reflect presentation of these PowerPoint versions

and applets.

Guided Practice, Scaffolded Practice, and Practice

For each Guided Practice in the Teacher Resource (TRB), corresponding Scaffolded Practice

worksheets are provided in the Student Workbook (SWB). Practice problems may be assigned from

the SWB and/or the parallel Student Resource (SRB) worksheet for in-class work or homework

assignments. The SRB worksheets are designed to closely resemble the format of the SWB

worksheets, but are composed of different problems for additional practice.

*Due to the nature of the block schedule, at times multiple lessons will need to be taught in one class setting.*

Suggested Progression of One-Day with One Sub-Lesson

• Warm-Up PowerPoint and Debrief (10 minutes)

• Introduction and Key Concepts (10 minutes)

• One or two Guided/Scaffolded Practice Examples, including PowerPoint applet presentation

as appropriate (20 minutes)

• Problem-Based Task and discussion (20 minutes)

• Guided and Independent Practice from the SWB or SRB including Small Group Work

Adapted for TCSD on 5/2016

Suggested Progression of One-Day with Two Sub-Lessons

• Warm-Up PowerPoint and Debrief (10 minutes)

• Introduction and Key Concepts (10 minutes)

• Sub-Lesson 1

• One or two Guided/Scaffolded Practice Examples, including PowerPoint applet

presentation as appropriate (15 minutes)

• Problem-Based Task and discussion (10 minutes)

• Sub-Lesson 2

• One or two Guided/Scaffolded Practice Examples, including PowerPoint applet

presentation as appropriate (15 minutes)

• Problem-Based Task and discussion (10 minutes)

• Guided and Independent Practice from the SWB or SRB including Small Group Work

Suggested Pacing Guide

Assessments and Station Activities

Each lesson includes a Pre-Assessment and a Progress Assessment, and each unit concludes with a

Unit Assessment. Units also feature sets of Station Activities to complement instruction.

Pre-Assessments are short, multiple-choice assessments with five problems, designed to evaluate

prior knowledge of the upcoming lesson. These are brief and should not factor into a student’s grade.

Pre-Assessments are often given on the same day as the preceding lesson’s Progress Assessment, to

prepare for the upcoming lesson.

Progress Assessments include 10 multiple-choice problems and one extended-response problem.

Progress Assessments may not take an entire class period. The additional time may be used to review

before the assessment, or to begin the next lesson after the assessment.

Unit Assessments include 12 multiple-choice problems and three extended-response problems,

and generally require a full class period.

Station Activities generally require a full class period for the students to rotate through each

station and then to engage in a class discussion at the end. PG-2

CCSS IP Math III Teacher Resource Pacing Guide

© Walch Education

CCSS IP MATH III TEACHER RESOURCE

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Block Schedule

Unit 1: Inferences and Conclusions from Data (15 Days)

Unit Overview: Students learn about using the normal curve, as well as about populations versus random samples and random

sampling. Then, they learn about strategies for collecting data, including surveys, experiments, and observational studies.

Students estimate sample proportions and sample means and develop tools for comparing treatments and reading reports.

Finally, they look at making and analyzing decisions with data.

Lesson 1: Using the Normal Curve

Students explore the concept of probability distribution, and especially the normal distribution and uniform distribution. They

are also introduced to standard deviation. Next, students look more closely at normal distributions and learn how to find the

z-score. Finally, students learn three methods for determining whether a given situation follows a normal distribution.

Day Area of study/content Pages Standard(s)

Day 1

Lesson 1 Pre-Assessment

1.1.1: Normal Distributions and the 68–95–99.7 Rule

Pre-Assessment

TRB: U1-1

Instruction/Practice

TRB: U1-6–32

SRB: U1-5–22

SWB: 11–18

S–ID.4

Day 2 1.1.2: Standard Normal Calculations

TRB: U1-33–61

SRB: U1-23–39

SWB: 21–28

S–ID.4

Day 3 1.1.3: Assessing Normality

Lesson 2 Pre-Assessment

Instruction/Practice

TRB: U1-62–93

SRB: U1-40–62

SWB: 31–41

Pre-Assessment

TRB: U1-97–98

S–ID.4

Day 4 Station Activities Set 1: z-scores

Lesson 1 Progress Assessment

Stations

TRB: U1-473–483

SWB: 203–207

Assessment

TRB: U1-94–96

S–ID.4

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Lesson 2: Populations Versus Random Samples

This lesson begins with an in-depth look at the differences between populations and samples, as well as how to determine the

reliability and validity of a sample.

Day Area of study/content Pages Standard(s)

Day 5 1.2.1: Differences Between Populations and Samples TRB: U1-102–127

SRB: U1-67–81

SWB: 45–55

S–IC.1

Day 6 Lesson 2 Progress Assessment

Lesson 3 Pre-Assessment

TRB: U1-189–192

TRB: U1-193–194

Lesson 3: Surveys, Experiments, and Observational Studies

This lesson focuses on various ways of collecting data. First, students look at the diverse ways that data can be collected. Then,

they investigate more closely the steps needed to design a study so that the outcomes are reliable and relevant to the topic

being studied.

Day Area of study/content Pages Standard(s)

Day 7 1.3.1: Identifying Surveys, Experiments, and Observational

Studies

TRB: U1-198–215

SRB: U1-125–135

SWB: 91–98

S–IC.3

Day 8 1.3.2: Designing Surveys, Experiments, and Observational Studies

Lesson 4 Pre-Assessment

Instruction/Practice

TRB: U1-216–234

SRB: U1-136–146

SWB: 101–107

Pre-Assessment

TRB: U1-238–239

S–IC.3

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Lesson 4: Estimating Sample Proportions and Sample Means

Students learn about sample proportions and the standard error for the proportion. They explore binomial experiments and

binomial distributions, as well as the addition rule for mutually exclusive events. Then, they study sample means and their

relationship to population means, and take a look at the margin of error and the confidence level. Finally, students investigate

how to calculate the probability that a given value falls within a specified interval.

Day Area of study/content Pages Standard(s)

Day 9 Lesson 3 Progress Assessment

1.4.1: Estimating Sample Proportions

Assessment

TRB: U1-235–237

Instruction/Practice

TRB: U1-245–265

SRB: U1-152–159

SWB: 111–118

S–IC.4

Day 10 1.4.2: The Binomial Distribution TRB: U1-266–292

SRB: U1-160–178

SWB: 121–128

S–IC.4

Day 11 1.4.3: Estimating Sample Means TRB: U1-293–307

SRB: U1-179–184

SWB: 131–138

S–IC.4

Day 12 1.4.4: Estimating with Confidence TRB: U1-308–328

SRB: U1-185–196

SWB: 141–148

S–IC.4

Day 13 Station Activities Set 2: Distributions and Estimating

with Confidence

Lesson 5 Pre-Assessment

Instruction/Practice

TRB: U1-484–496

SWB: 209–216

Pre-Assessment

TRB: U1-332–333

S–ID.4

S–IC.4

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Lesson 5: Comparing Treatments and Reading Reports

Students learn how to question the validity of the conclusions and assumptions made based on reported data.

Day Area of study/content Pages Standard(s)

Day 14 1.5.3: Reading Reports TRB: U1-383–399

SRB: U1-230–239

SWB: 171–178

S–IC.6

Day 15 Lesson 4 Progress Assessment

Lesson 5 Progress Assessment

TRB: U1-329–331

TRB: U1-400–402

Unit Assessment

Day 15 Unit Assessment TRB: U1-454–458

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Unit 2A: Polynomial Relationships (16 Days)

Unit Overview: Students begin by exploring polynomial structures and operating with polynomials. Then, they learn how to

prove identities, graph polynomial functions, and solve systems of equations with polynomials. Finally, students learn about

geometric series.

Lesson 1: Polynomial Structures and Operating with Polynomials

Students review the vocabulary used when discussing polynomials. They practice adding, subtracting, and multiplying

polynomials and simplifying the results.

Day Area of study/content Pages Standard(s)

Day 1 Lesson 1 Pre-Assessment

2A.1.1: Structures of Expressions

2A.1.2: Adding and Subtracting Polynomials

Pre-Assessment

TRB: U2A-1

Instruction/Practice

TRB: U2A-4–16

SRB: U2A-3–8

SWB: 7–14

TRB: U2A-17–27

SRB: U2A-9–13

SWB: 17–23

A–SSE.1a

A–APR.

Day 2 2A.1.3: Multiplying Polynomials

Lesson 2 Pre-Assessment

Instruction/Practice

TRB: U2A-28–39

SRB: U2A-14–19

SWB: 27–33

Pre-Assessment

TRB: U2A-42

A–APR.1

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Lesson 2: Proving Identities

Students begin this lesson by exploring common polynomial identities, such as the difference of two squares and the square of

sums. Then they expand their investigation to include complex numbers in the polynomial identities. They end the lesson with

an exploration of the Binomial Theorem and a look at its usefulness when finding binomial expansions.

Day Area of study/content Pages Standard(s)

Day 3 Lesson 1 Progress Assessment

2A.2.1: Polynomial Identities

Assessment

TRB: U2A-40–41

Instruction/Practice

TRB: U2A-46–62

SRB: U2A-23–31

SWB: 37–43

A–SSE.1b

A–SSE.2

A–APR.4

Day 4 2A.2.2: Complex Polynomial Identities TRB: U2A-63–75

SRB: U2A-32–36

SWB: 47–53

N–CN.8 (+)

A–SSE.1b

A–SSE.2

A–APR.4

Day 5 2A.2.3: The Binomial Theorem

Lesson 3 Pre-Assessment

Instruction/Practice

TRB: U2A-76–91

SRB: U2A-37–46

SWB: 57–63

Pre-Assessment

TRB: U2A-94–95

A–SSE.1a

A–SSE.1b

A–SSE.2

A–APR.4

A–APR.5 (+)

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Lesson 3: Graphing Polynomial Functions

Students begin this lesson by analyzing the end behavior and number of turns of the graphs of polynomial functions. Then they

learn synthetic division of polynomials, and apply this to the Remainder Theorem. Their study of polynomials continues with

an exploration of how to find the zeros of a polynomial function. Lastly, students learn the Rational Root Theorem as a means

of locating the zeros of polynomials that are difficult to factor.

Day Area of study/content Pages Standard(s)

Day 6 Lesson 2 Progress Assessment

2A.3.1: Describing End Behavior and Turns

Assessment

TRB: U2A-92–93

Instruction/Practice

TRB: U2A-100–118

SRB: U2A-51–64

SWB: 67–74

F–IF.7c

Day 7 2A.3.2: The Remainder Theorem TRB: U2A-119–138

SRB: U2A-65–77

SWB: 77–83

A–APR.2

Day 8 2A.3.3: Finding Zeros TRB: U2A-139–156

SRB: U2A-78–87

SWB: 87–93

A–APR.3

N–CN.9 (+)

F–IF.7c

Day 9 2A.3.4: The Rational Root Theorem TRB: U2A-157–172

SRB: U2A-88–94

SWB: 97–103

A–APR.3

Day 10 Interpret expressions for functions in terms of the situation it

models. Introduce f(x)=ex as a model for continuous growth.

Can use lesson 2.5.2

from Math II

Can use lesson 2.10.1

from Math I

F.LE.3

F.LE.5

Day11 Station Activities Set 1: Polynomial Functions

Lesson 3 Progress Assessment

Lesson 4 Pre-Assessment

Instruction/Practice

TRB: U2A-311–323

SWB: 149–154

Assessment

TRB: U2A-173–176

TRB: U2A-177–179

N–CN.9 (+)

A–SSE.2

A–APR.2

A–APR.3

F–IF.2

F–IF.7c

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Lesson 4: Solving Systems of Equations with Polynomials

This brief lesson focuses on how to find the solution(s) to a system of equations graphically when at least one of the equations is

a polynomial. The systems of equations in this lesson also include absolute value equations and exponential equations.

Day Area of study/content Pages Standard(s)

Day 12 2A.4.1: Solving Systems of Equations Graphically

Lesson 5 Pre-Assessment

Instruction/Practice

TRB: U2A-182–209

SRB: U2A-97–115

SWB: 107–115

Pre-Assessment

TRB: U2A-216

A–REI.11

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Lesson 5: Geometric Series

This lesson provides an in-depth look at geometric series, beginning with the associated vocabulary. Students learn the

difference between recursive and explicit formulas. Next, students explore how to find the sum of a finite geometric series,

followed by how to find the sum of an infinite geometric series.

Day Area of study/content Pages Standard(s)

Day 13 Lesson 4 Progress Assessment

2A.5.1: Geometric Sequences

Assessment

TRB: U2A-210–215

Instruction/Practice

TRB: U2A-221–242

SRB: U2A-120–134

SWB: 119–126

A–SSE.4

Day 14 2A.5.2: Sum of a Finite Geometric Series

*Add Arithmetic Series*

TRB: U2A-243–270

SRB: U2A-135–150

SWB: 129–136

A–SSE.4

Day 15 2A.5.3: Sum of an Infinite Geometric Series TRB: U2A-271–290

SRB: U2A-151–163

SWB: 139–146

A–SSE.4

Day 16 Station Activities Set 2: Sequences and Series

Lesson 5 Progress Assessment

Stations

TRB: U2A-324–331

SWB: 155–158

Assessment

TRB: U2A-291–293

A–SSE.4

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Unit 2B: Rational and Radical Relationships (11 Days)

Unit Overview: Students work with operations involving rational expressions. Then, they learn to solve rational and

radical equations.

Lesson 1: Operating with Rational Expressions

Students learn the definition of a rational expression and how to simplify rational expressions. Then, they focus on adding and

subtracting rational expressions, followed by multiplying and dividing them.

Day Area of study/content Pages Standard(s)

Day 1 Lesson 1 Pre-Assessment

2B.1.1: Structures of Rational Expressions

Pre-Assessment

TRB: U2B-1

Instruction/Practice

TRB: U2B-5–22

SRB: U2B-4–12

SWB: 7–13

A–SSE.1a

A–SSE.1b

A–SSE.2

Day 2

2B.1.2: Adding and Subtracting Rational Expressions TRB: U2B-23–44

SRB: U2B-13–26

SWB: 17–23

A–APR.7 (+)

A–SSE.2

Day 3 2B.1.3: Multiplying Rational Expressions TRB: U2B-45–60

SRB: U2B-27–34

SWB: 27–34

A–APR.7 (+)

A–SSE.2

Day 4 2B.1.4: Dividing Rational Expressions

Lesson 2 Pre-Assessment

Instruction/Practice

TRB: U2B-61–79

SRB: U2B-35–46

SWB: 37–44

Pre-Assessment

TRB: U2B-83

A–APR.6

A–APR.7 (+)

A–SSE.2

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Lesson 2: Solving Rational and Radical Equations

Students first learn how to solve rational equations, and then how to solve radical equations. The lesson ends with students

solving systems of equations algebraically, including polynomial, radical, and rational equations.

Day Area of study/content Pages Standard(s)

Day 5 Lesson 1 Progress Assessment

2B.2.1: Solving Rational Equations

Assessment

TRB: U2B-80–82

Instruction/Practice

TRB: U2B-87–106

SRB: U2B-50–62

SWB: 47–53

A–REI.2

Day 6 Station Activities Set 1: Rational Expressions and Equations TRB: U2B-169–185

SWB: 77–82

A–SSE.2

A–APR.6

A–APR.7 (+)

A–REI.2

Day 7 2B.2.2: Solving Radical Equations TRB: U2B-107–126

SRB: U2B-63–75

SWB: 57–64

A–REI.2

Day 8 2B.2.3: Solving Systems of Equations TRB: U2B-127–155

SRB: U2B-76–95

SWB: 67–74

A–REI.11

Day 9 Station Activities Set 2: Solving Systems of Equations

Lesson 2 Progress Assessment

Stations

TRB: U2B-186–197

SWB: 83–88

Assessment

TRB: U2B-156–158

A–REI.11

Day 10 Graphing Rational Functions and Identifying Key Features

Milk Cartons

Honors Topic 7.1 F–IF.7d★ (+)

Unit/Comprehensive Assessment

Day 11 Comprehensive Unit Assessment (covering Units 2A and 2B) Comprehensive Unit Assessment

TRB: U2-CA1–5

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Unit 3: Trigonometry of General Triangles and Trigonometric Functions (13 Days)

Unit Overview: Students begin the unit with a study of radians and the unit circle. Then, they explore the trigonometry of

general angles, including the Law of Sines and the Law of Cosines. Finally, students move on to modeling periodic phenomena

with the graphs of the sine and cosine functions.

Lesson 1: Radians and the Unit Circle

Students explore the meaning of radian measure, as well as the relationship between radians, radius, and arc length

measurements on a circle. They also learn to convert from radians to degrees and vice versa. Then, students learn about the

unit circle, how to calculate distances using the three basic trigonometric functions, and how to find reference angles. This

is followed by the exploration of the special angles on the unit circle. Finally, students learn how to evaluate trigonometric

functions with the help of the unit circle.

Day Area of study/content Pages Standard(s)

Day 1 Lesson 1 Pre-Assessment

3.1.1: Radians

Pre-Assessment

TRB: U3-1

Instruction/Practice

TRB: U3-5–21

SRB: U3-4–12

SWB: 7–14

F–TF.1

F–TF.2

Day 2

3.1.2: The Unit Circle TRB: U3-22–45

SRB: U3-13–28

SWB: 17–25

F–TF.2

Day 3 3.1.3: Special Angles in the Unit Circle TRB: U3-46–69

SRB: U3-29–42

SWB: 29–35

F–TF.2

Day 4 3.1.4: Evaluating Trigonometric Functions TRB: U3-70–92

SRB: U3-43–57

SWB: 39–45

F–TF.2

Day 5 Station Activities Set 1: Trigonometric Functions

Lesson 1 Progress Assessment

Lesson 2 Pre-Assessment

Stations

TRB: U3-221–237

SWB: 107–116

Assessment

TRB: U3-93–95

TRB: U3-96–97

F–TF.2

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Lesson 2: Trigonometry of General Angles

Students discover how to find the measures of missing side lengths and angle measurements if the given triangle is not a right

triangle, by using the Law of Sines and the Law of Cosines. After learning these two useful formulas, students use the Law of

Sines and the Law of Cosines to solve problems.

Day Area of study/content Pages Standard(s)

Day 6 3.2.1: Proving the Law of Sines TRB: U3-101–124

SRB: U3-61–75

SWB: 49–59

G–SRT.9 (+)

G–SRT.10 (+)

Day 7 3.2.2: Proving the Law of Cosines TRB: U3-125–143

SRB: U3-76–88

SWB: 63–72

G–SRT.10 (+)

Day 8 3.2.3: Applying the Laws of Sines and Cosines TRB: U3-144–161

SRB: U3-89–99

SWB: 75–82

G–SRT.11 (+)

Day 9 Station Activities Set 2: The Laws of Sines and Cosines

Lesson 2 Progress Assessment

Lesson 3 Pre-Assessment

Stations

TRB: U3-238–250

SWB: 117–124

Assessment

TRB: U3-162–164

TRB: U3-165–166

G–SRT.9 (+)

G–SRT.10 (+)

G–SRT.11 (+)

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Lesson 3: Graphs of Trigonometric Functions

Students begin studying the periodic nature of trigonometric functions by looking at the graphs of the sine, cosine, and tangent

functions. This includes analyzing the period, frequency, amplitude, and midline of these functions.

Day Area of study/content Pages Standard(s)

Day 10 3.3.1: Periodic Phenomena and Amplitude, Frequency,

and Midline

TRB: U3-169–186

SRB: U3-103–113

SWB: 85–91

F–TF.5

Day 11 3.3.2: Using Trigonometric Functions to Model

Periodic Phenomena

TRB: U3-187–205

SRB: U3-114–125

SWB: 95–104

F–TF.5

Day 12 Symmetry, Periodicity, and Infinite Domain of

Trigonometric Functions

Using Inverse Trigonometric Functions to

Solve Problems

Honors 9.3

Honors 9.5

F–TF.3 (+)

F–TF.4 (+)

F–TF.7★ (+)

Day 13 Lesson 3 Progress Assessment TRB: U3-206–209

Unit Assessment

Day 13 Unit Assessment TRB: U3-210–214

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Unit 4A: Mathematical Modeling of Inverse, Logarithmic, and Trigonometric Functions (12 Days)

Unit Overview: Students begin by learning about the inverses of quadratics and other functions. This leads to learning about

graphing and interpreting logarithmic functions and models. Students continue exploring and applying the graphs of the sine

and cosine functions learned previously.

Lesson 1: Inverses of Functions

Students learn how to find the inverse of a quadratic function, and then how to find the inverse of other functions, such as

rational and radical functions.

Day Area of study/content Pages Standard(s)

Day 1

Lesson 1 Pre-Assessment

Inverses

Pre-Assessment

TRB: U4A-1–2

Instruction/Practice Use lesson 2.7.1 from Math II

F–BF.4a

Day 2 4A.1.1: Determining Inverses of Quadratic Functions TRB: U4A-5–35

SRB: U4A-3–25

SWB: 7–13

F–BF.4a

Day 3

4A.1.2: Determining Inverses of Other Functions TRB: U4A-36–64

SRB: U4A-26–44

SWB: 17–24

F–BF.4a

Day 4 Station Activities Set 1: Inverse Functions

Lesson 1 Progress Assessment

Lesson 2 Pre-Assessment

Stations

TRB: U4A-293–307

SWB: 105–113

Assessment

TRB: U4A-65–68

TRB: U4A-69–70

F–BF.4a

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Lesson 2: Modeling Logarithmic Functions

Students are introduced to logarithmic functions, and they explore logarithmic functions as inverses of exponential functions.

Next, students investigate common logarithms and natural logarithms. This is followed by a look at the graphs of logarithmic

functions. Finally, students learn how analyze and interpret situations that can be modeled with logarithmic functions.

Day Area of study/content Pages Standard(s)

Day 5 4A.2.1: Logarithmic Functions as Inverses TRB: U4A-74–95

SRB: U4A-48–61

SWB: 27–34

F–BF.4a

F–LE.4

Day 6 4A.2.2: Common Logarithms TRB: U4A-96–113

SRB: U4A-62–70

SWB: 37–44

F–IF.8

F–LE.4

Day 7 4A.2.3: Natural Logarithms TRB: U4A-114–135

SRB: U4A-71–82

SWB: 47–54

F–IF.8

F–LE.4

Day 8 4A.2.4: Graphing Logarithmic Functions TRB: U4A-136–161

SRB: U4A-83–101

SWB: 57–66

F–IF.7e

Day 9 4A.2.5: Interpreting Logarithmic Models

Lesson 3 Pre-Assessment

Instruction/Practice

TRB: U4A-162–180

SRB: U4A-102–112

SWB: 69–77

Pre-Assessment

TRB: U4A-185

F–IF.4

F–IF.5

F–IF.6

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Lesson 3: Modeling Trigonometric Functions

Students return to the analysis of the sine and cosine functions they studied previously, this time with a closer investigation into

the translation of trigonometric functions.

Day Area of study/content Pages Standard(s)

Day 10 Lesson 2 Progress Assessment

4A.3.1: Graphing the Sine Function

Assessment

TRB: U4A-181–184

Instruction/Practice

TRB: U4A-189–231

SRB: U4A-116–145

SWB: 81–89

F–IF.7e

Day 11 4A.3.2: Graphing the Cosine Function TRB: U4A-232–270

SRB: U4A-146–173

SWB: 93–101

F–IF.7e

Day 12 Lesson 3 Progress Assessment TRB: U4A-271–273

Unit Assessment

Day 12 Unit Assessment TRB: U4A-274–280

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Unit 4B: Mathematical Modeling and Choosing a Model (18 Days)

Unit Overview: Students revisit the process of creating equations in one variable and explore creating constraints and

rearranging formulas. They then learn about transforming models and combining functions. Students review various kinds of

functions, including linear, exponential, quadratic, piecewise, step, absolute value, square root, and cube root functions, all with

an eye to choosing a model for a real-world situation. Finally, students consider geometric models, including two-dimensional

cross sections of three-dimensional objects.

Lesson 1: Creating Equations

Students begin by reviewing vocabulary associated with equations and inequalities, and they practice writing equations to

represent various scenarios. Next, they take a closer look at the constraints that exist for some situations and some equations,

and learn how to find restricted domains. Finally, students apply their equation-solving skills to formulas, when they solve

formulas for a given variable.

Day Area of study/content Pages Standard(s)

Day 1

Lesson 1 Pre-Assessment

4B.1.1: Creating Equations in One Variable

Pre-Assessment

TRB: U4B-1–2

Instruction/Practice

TRB: U4B-7–35

SRB: U4B-5–24

SWB: 7–14

A–CED.1

Day 2 4B.1.2: Representing and Interpreting Constraints TRB: U4B-36–53

SRB: U4B-25–34

SWB: 17–23

A–CED.3

Day 3 4B.1.3: Rearranging Formulas

Lesson 2 Pre-Assessment

Instruction/Practice

TRB: U4B-54–80

SRB: U4B-35–52

SWB: 27–34

Pre-Assessment

TRB: U4B-85–86

A–CED.4

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Lesson 2: Transforming a Model and Combining Functions

Students take an in-depth look at transformations of functions. Next, they analyze functions both graphically and algebraically

to determine whether the functions are even, odd, or neither. Finally, students learn how to combine two functions by adding,

subtracting, multiplying, and dividing them, as well as by substituting one function into the other (composition of functions).

Day Area of study/content Pages Standard(s)

Day 4 Lesson 1 Progress Assessment

4B.2.1: Transformations of Parent Graphs

Assessment

TRB: U4B-81–84

Instruction/Practice

TRB: U4B-89–114

SRB: U4B-55–71

SWB: 37–45

F–BF.3

Day 5 4B.2.2: Recognizing Odd and Even Functions TRB: U4B-115–129

SRB: U4B-72–78

SWB: 49–56

F–BF.3

Day 6 4B.2.3: Combining Functions

Lesson 3 Pre-Assessment

Instruction/Practice

TRB: U4B-130–143

SRB: U4B-79–85

SWB: 59–66

Pre-Assessment

TRB: U4B-147–150

F–BF.1b

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Lesson 3: Comparing Properties Within and Between Functions

Students compare the features and the limitations of a real-world mathematical situation and the “pure” mathematical model

that can represent it, with a goal of finding the most accurate mathematical model possible. Next, students learn to calculate the

average rate of change of nonlinear functions. The lesson ends with an analysis of how to compare two functions that represent

a real-world scenario.

Day Area of study/content Pages Standard(s)

Day 7 Lesson 2 Progress Assessment

4B.3.1: Reading and Identifying Key Features of Real-World

Situation Graphs

Assessment

TRB: U4B-144–146

Instruction/Practice

TRB: U4B-154–187

SRB: U4B-89–112

SWB: 69–79

F–IF.4

F–IF.5

F–IF.6

Day 8 4B.3.2: Calculating Average Rates of Change TRB: U4B-188–209

SRB: U4B-113–128

SWB: 83–90

F–IF.6

Day 9 4B.3.3: Comparing Functions

Lesson 4 Pre-Assessment

Instruction/Practice

TRB: U4B-210–232

SRB: U4B-129–142

SWB: 93–100

Pre-Assessment

TRB: U4B-241–242

F–IF.6

F–IF.9

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Lesson 4: Choosing a Model

Students learn how to choose the best model (linear, exponential, or quadratic) for a given situation by analyzing the given data.

Then, they analyze more models, including piecewise functions, step functions, and absolute value functions. Students discover

which of these functions apply to different types of situations. Finally, they look at situations that are best modeled with square

root and cube root functions.

Day Area of study/content Pages Standard(s)

Day 10 Lesson 3 Progress Assessment

4B.4.1: Linear, Exponential, and Quadratic Functions

Assessment

TRB: U4B-233–240

Instruction/Practice

TRB: U4B-246–270

SRB: U4B-146–160

SWB: 103–112

A–CED.2

F–IF.4

F–IF.5

F–BF.3

Day 11 4B.4.2: Piecewise, Step, and Absolute Value Functions TRB: U4B-271–294

SRB: U4B-161–175

SWB: 115–125

F–IF.4

F–IF.5

F–IF.7b

F–BF.3

Day 12 4B.4.3: Square Root and Cube Root Functions TRB: U4B-295–317

SRB: U4B-176–191

SWB: 129–138

F–IF.4

F–IF.5

F–IF.7b

F–BF.3

Day 13 Station Activities Set 1: Choosing a Model

Lesson 4 Progress Assessment

Lesson 5 Pre-Assessment

Stations

TRB: U4B-417–434

SWB: 179–186

Assessment

TRB: U4B-318–323

TRB: U4B-324–325

F–IF.4

F–IF.5

F–IF.7b

F–BF.3

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Lesson 5: Geometric Modeling

Students find ways to model geometric situations, first by looking at cross sections of three-dimensional objects, and how these

cross-sectional areas can be used to model a given problem. The modeling continues as students explore the concept of density,

and how the density of a quantity can be compared to a basic unit of area or volume to solve real-world problems. Finally,

students explore the role of mathematics in the design of products and services.

Day Area of study/content Pages Standard(s)

Day 14 4B.5.1: Two-Dimensional Cross Sections of Three-Dimensional

Objects

TRB: U4B-329–347

SRB: U4B-195–206

SWB: 141–150

G–GMD.4

G–MG.1

Day 15 4B.5.2: Density TRB: U4B-348–367

SRB: U4B-207–220

SWB: 153–162

G–MG.2

Day 16 4B.5.3: Design TRB: U4B-368–390

SRB: U4B-221–234

SWB: 165–175

G–MG.3

Day 17 Station Activities Set 2: Geometric Modeling

Lesson 5 Progress Assessment

Stations

TRB: U4B-435–442

SWB: 187–190

Assessment

TRB: U4B-391–395

G–GMD.4

G–MG.1

G–MG.2

G–MG.3

Unit/Comprehensive Assessment

Day 18 Unit Assessment (covering Unit 4B) and/or Comprehensive Unit

Assessment (covering Units 4A and 4B)

Unit Assessment

TRB: U4B-396–403

Comprehensive Unit Assessment

TRB: U4-CA1–5

End-of-Course Assessment

End-of-Course Assessment

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additions as they become available.