Adapted for TCSD on 5/2016 CCSS IP MATH III TEACHER ...€¦ · Adapted for TCSD on 5/2016 CCSS IP...
Transcript of Adapted for TCSD on 5/2016 CCSS IP MATH III TEACHER ...€¦ · Adapted for TCSD on 5/2016 CCSS IP...
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.