©2009 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- August 24th – October 2nd (29 days; 2 days for 6 weeks review/test, 2 days for BoY)
5-6 DAYS (allowing opening day
Major Concept #1: Transformations of Functions
Overarching
Idea
Teacher
Guiding
Questions
262
Matrix
Strand
Attributes of Functions
Matrix
#
Pre-Calculus
flexibility)
Recognizing the attributes connected to different functions to relate throughout the course.




How do different parent functions differ? Linear to Constant? Quadratic to Cubic? Etc?
When does a function translate vertically? Horizontally? Reflect? Stretch? Shrink?
What are some patterns that are observed when different transformations are placed on certain parent functions?
How are the attributes of each function changed when a transformation is applied to it?
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
The student defines
functions, describes
characteristics of
functions, and translates
among verbal, numerical,
graphical, and symbolic
representations of
functions, including
polynomial, rational, power
(including radical),
exponential, logarithmic,
trigonometric, and
piecewise-defined
functions. (P.1)
Describe parent
functions symbolically
and graphically,
including f(x)=xn,
f(x)=ln x, f(x)=logax,
f(x)=1/x, f(x)=ex,
f(x)=|x|, f(x)=ax, f(x)=sin
x, f(x)=arcsin x, etc.
(P.1A)
LH
(Section
1.7)
(P.1)
(P.1A)
(P.1)
(P.1A)
Resource
Time/
Pace
Teacher Tools
1-2
days
Lesson on Transformations of Functions, pages 7478
Exercises on pages 79-83
LTF/A2
2-3
days
Transformations of Functions, pages 54-60
LTF/PC
1-2
days
Piecewise Functions, pages 42-44
The Laying the Foundations series is being used by the approval of the district to help students be more successful in Advance Placement courses by
beginning their preparation early through well-designed and focused Pre-AP program.
LH: Pre-Calculus with Limits, Larson-Hostetler, Houghton-Mifflin, 2007
PTII: Precalculus TEXTEAMS Institute Part II
Pre-Calculus Page 1 of 5
LTF/A2: Laying the Foundation, Connecting Algebra 2 LTF/PC: Laying the Foundation, Connecting Pre-Calculus
APTI: Algebra II/Precalculus TEXTEAMS Part I
7/3/09
©2009 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- August 24th – October 2nd (29 days; 2 days for 6 weeks review/test, 2 days for BoY)
Major Concept #2: Composition and Inverses of Functions
Overarching
Idea
Teacher
Guiding
Questions
276
Matrix
Strand
Attributes of Functions
Matrix
#
Pre-Calculus
5-6 DAYS
Composing Functions using arithmetic methods and connecting composition of functions to the inverses of functions.






What are the domains and ranges of functions?
How do domains change when functions are arithmetically combined or composed?
What does the domain and range represent in a problem situation?
What are inverse functions?
How do graphs of inverse functions relate?
Why are inverses functions one-to-one? What does it mean to be one-to-one?
TEKS
Knowledge & Skill
The student interprets the
meaning of the symbolic
representations of
functions and operations
on functions to solve
meaningful problems. (P.2)
(P.2)
Student Expectation
Perform operations
including composition on
functions, find inverses,
and describe these
procedures and results
verbally, numerically,
symbolically, and
graphically. (P.2B)
(P.2B)
LH: Pre-Calculus with Limits, Larson-Hostetler, Houghton-Mifflin, 2007
PTII: Precalculus TEXTEAMS Institute Part II
TAKS
OBJ
Resource
Time/
Pace
LH
(Section
1.8)
2-3
days
LH
(Section
1.9)
2-3
days
Teacher Tools
Lesson on Composition of Functions, pages 84-88
Exercises on pages 89-92
Group activities : Exercises 66-68 on page 92
Lesson on Inverses of Functions, pages 93-98
Exercises on pages 99-101
Pre-Calculus Page 2 of 5
LTF/A2: Laying the Foundation, Connecting Algebra 2 LTF/PC: Laying the Foundation, Connecting Pre-Calculus
APTI: Algebra II/Precalculus TEXTEAMS Part I
7/3/09
©2009 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- August 24th – October 2nd (29 days; 2 days for 6 weeks review/test, 2 days for BoY)
Major Concept #3: Regression Modeling
Overarching
Idea
Teacher
Guiding
Questions
240A
Matrix
Strand
Equations, Functions,
and Function Models
Matrix
#
Pre-Calculus
3-4 DAYS
Use of modeling methods to approximate data points.



What does the domain and range represent in each problem situation?
What is the reasonable domain of the problem? Why?
Which regression model best fits the given problem situation? Why?
TEKS
Knowledge & Skill
Student Expectation
The student uses functions
and their properties, tools
and technology, to model
and solve meaningful
problems. (P.3)
Use functions such as
logarithmic, exponential,
trigonometric, polynomial,
etc. to model real-life data.
(P.3B)
LH
(Section
1.10)
1-2
days
(P.3)
(P.3B)
Larson
1997
edition
1-2
days
LH: Pre-Calculus with Limits, Larson-Hostetler, Houghton-Mifflin, 2007
PTII: Precalculus TEXTEAMS Institute Part II
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
Lesson on Mathematical Modeling, pages 103-108
Exercises on pages 109-114
Modeling Activity : Auto Crumple Zones, Activity B
(http://www.utdanacenter.org/mathtoolkit/downloads/le
ssons/pc_models_ws2.pdf)
Pre-Calculus Page 3 of 5
LTF/A2: Laying the Foundation, Connecting Algebra 2 LTF/PC: Laying the Foundation, Connecting Pre-Calculus
APTI: Algebra II/Precalculus TEXTEAMS Part I
7/3/09
©2009 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- August 24th – October 2nd (29 days; 2 days for 6 weeks review/test, 2 days for BoY)
Major Concept #4: Radian Measures and Introduction to Right Triangle Trigonometry
Overarching
Idea
Teacher
Guiding
Questions
271
Matrix
Strand
Attributes of Functions
Matrix
#
Pre-Calculus
3 DAYS
Use radian and degree measure to evaluate trigonometric functions of any angle.


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

How do radian and degree measures of an angle relate?
How do you solve a right triangle?
What are coterminal angles and how are they different from reference angles?
How does the location of an angle affect its trigonometric value?
Why is the reference angle helpful in finding a trigonometric value?
TEKS
Knowledge & Skill
Student Expectation
(P.1)
Recognize and use
connections among
significant values of a
function (zeros, maximum
values, and minimum
values, etc.), points on the
graph of a function, and
the symbolic
representation of a
function. (P.1D)
(P.1)
(P.1)
(P.1D)
(P.1D)
LH: Pre-Calculus with Limits, Larson-Hostetler, Houghton-Mifflin, 2007
PTII: Precalculus TEXTEAMS Institute Part II
TAKS
OBJ
Resource
LH
(Section
4.1)
LH
(Section
4.3)
LH
(Section
4.4)
Time/
Pace
1 day
1 day
1 day
Teacher Tools
Lesson on Radian and Degree Measure, pages 282289
Exercises on pages 290-293
Lesson on Right Triangle Trigonometry, pages 301307
Exercises on pages 308-311
Lesson on Trigonometric Functions of Any Angle,
pages 312-317
Exercises on pages 318-320
Pre-Calculus Page 4 of 5
LTF/A2: Laying the Foundation, Connecting Algebra 2 LTF/PC: Laying the Foundation, Connecting Pre-Calculus
APTI: Algebra II/Precalculus TEXTEAMS Part I
7/3/09
©2009 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- August 24th – October 2nd (29 days; 2 days for 6 weeks review/test, 2 days for BoY)
Major Concept #5: Unit Circle
Overarching
Idea
Teacher
Guiding
Questions
271
Matrix
Strand
Attributes of Functions
Matrix
#
Pre-Calculus
5-6 DAYS
Know the values around the unit circle to be able to evaluate trigonometric values.



Why is it called a unit circle?
What does each point on the unit circle represent?
Are there patterns in the values around the unit circle?
TEKS
Knowledge & Skill
Student Expectation
P.1
(P.1D)
P.1
(P.1D)
LH: Pre-Calculus with Limits, Larson-Hostetler, Houghton-Mifflin, 2007
PTII: Precalculus TEXTEAMS Institute Part II
TAKS
OBJ
Resource
LH
(Section
4.2)
.pdf link
Time/
Pace
3-4
days
1-2
days
Teacher Tools
Lesson on The Unit Circle, pages 294-298
Exercises on pages 299-300
Activity : Students fill in the values around the unit
circle with radian and degree measures and the exact
values of 30,45,60 values
Unit circle template(http://www.picciotto.org/mathed/circle/circles/10cm-circle.pdf or AustinISD
Resources
Pre-Calculus Page 5 of 5
LTF/A2: Laying the Foundation, Connecting Algebra 2 LTF/PC: Laying the Foundation, Connecting Pre-Calculus
APTI: Algebra II/Precalculus TEXTEAMS Part I
7/3/09