©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
4th Six Weeks IPG- January 8th – February 22nd (32 days; 2 days for 6 weeks review/test; 2 days for MoY)
Major Concept #1: Conic Sections
Overarching
Idea
Teacher
Guiding
Questions
Matrix
#
Matrix
Strand
341
Geometric Models
341

How does each conic section relate to a cone?

What is the definition of each conic section?

How is the change in parameters shown in the translations, reflections and rotations of the graphs?
TEKS
Knowledge & Skill
Student Expectation
Use conic sections to
model motion, such as the
graph of velocity vs.
positions of a pendulum
and motions of planets.
(P.5A)
Use properties of conic
sections to describe
physical phenomena such
as the reflective properties
of light and sound. (P.5B)
TAKS
OBJ
Resource
LH
(Section 10-2)
Introduction to
Conics:
Parabolas
Time/
Pace
3 days
(P.5A)
(P.5)
342
(P.5B)
341
(P.5A)
(P.5)
342
10 DAYS
Characteristics of conic sections
The student uses conic
sections, their
properties, and
parametric
representations as well
as tools and technology,
to model physical
situations. (P.5)
342
Pre-Calculus
(P.5B)
LH: Pre-Calculus with Limits, Larson-Hostetler, Houghton-Mifflin, 2007
PTII: Precalculus TEXTEAMS Institute Part II
LH
(Section 10-3)
Ellipses and
Circles
LH
(Section 10-4)
Hyperbolas
3 days
4 days
includes
days for
review
and/or
test
Teacher Tools
Vocabulary: conics, conic section, directrix,
focus, focal chord, latus rectum, parabola,
tangent
Teacher notes: The visual models on page 735
are also represented in the Animated
Precalculus video tutorials for this chapter and
can be accessed at
http://college.hmco.com/mathematics/larson/pre
calculus_limits/1e2/ins_resources/ap.html.
Use the following login information:
Username: larpclim1e
Password: sequence
Vocabulary: ellipse, foci, vertices, center, major
axis, minor axis, eccentricity
Teacher notes: Students study the key
characteristics of ellipses and solve problems.
The apogee and perigee of the orbit of the
moon around the earth is explored in the
application example of an ellipse on page 748.
An Elliptical Orbiter interactive animation tool
can be found at http://distanceed.math.tamu.edu/Precalculus_home/Module5/
module5.htm. Several other problems involving
standard P.5B are also found at this link.
Vocabulary: hyperbola, branches, transverse
axis, conjugate axis, asymptote
Teacher Notes: Application problems related to
sound and orbits of comets are described on
page 758 of the text with additional examples on
the link to the website above.
Pre-Calculus Page 1 of 4
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©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
4th Six Weeks IPG- January 8th – February 22nd (32 days; 2 days for 6 weeks review/test; 2 days for MoY)
Major Concept #2: Vectors
Overarching
Idea
Teacher
Guiding
Questions
336
241
336
Equations,
Functions, and
Function Models
Geometric Models
335

What is a vector?

How do you add and multiply vectors?

How do you write a vector as a sum of two vector components?
TEKS
Knowledge & Skill
The student uses
functions and their
properties, tools and
technology, to model
and solve meaningful
problems. (P.3)
The student uses
vectors to model
physical situations. (P.6)
Student Expectation
Solve problems from
physical situations using
trigonometry, including
the use of Law of Sines,
Law of Cosines, and
area formulas, and
incorporate radian
measure where needed.
(P.3E)
Use the concept of
vectors to model
situations defined by
magnitude and direction.
(P.6A)
Analyze and solve
vector problems
generated by real-life
situations. (P.6B)
Equations,
Functions, and
Function Models
241
Matrix
Strand
5 DAYS
The use of a line with both direction and distance.
(P.3)
(P.3E)
Geome
tric
Models
Matrix
#
Pre-Calculus
(P.6)
(P.6B)
LH: Pre-Calculus with Limits, Larson-Hostetler, Houghton-Mifflin, 2007
PTII: Precalculus TEXTEAMS Institute Part II
TAKS
OBJ
Resource
LH
(Section 6-3)
Vectors in a
Plane
LH
(Section 6-4)
Vectors and Dot
Products
Time/
Pace
Teacher Tools
2 days
Vocabulary: directed line segment, initial
point, terminal point, magnitude, Vector v in
the plane, standard position, zero vector, unit
vector, standard unit vectors, direction angle
Teacher Notes: The Student Notetaking
Guide includes sentence starters for students
to identify the important concepts related to
the component forms of vectors, basic vector
operations, and the direction angles of
vectors.
There are also Digital lessons for each
chapter and some sections that can be
downloaded and customized to fit your needs
at
http://college.hmco.com/mathematics/larson/p
recalculus_limits/1e/ins_resources.html.
3 days
includes
days for
review
and/or
test
Vocabulary: dot product, angle between two
nonzero vectors, orthogonal, vector
components, work, force
Technology: See Technology note on page
463.
Teacher Notes: There are connections to
science concepts of force and work included
in Examples 7 and 8.
Pre-Calculus Page 2 of 4
LTF/A2: Laying the Foundation, Connecting Algebra 2 LTF/PC: Laying the Foundation, Connecting Pre-Calculus
APTI: Algebra II/Precalculus TEXTEAMS Part I
©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
4th Six Weeks IPG- January 8th – February 22nd (32 days; 2 days for 6 weeks review/test; 2 days for MoY)
Major Concept #3: Parametric Equations
Overarching
Idea
Teacher
Guiding
Questions
Matrix
#
Matrix
Strand
239
260
230
239
Equations, Functions, and Function Models
230
Pre-Calculus
5 DAYS
Parametric equations can be used to simulate a body or object in motion and make predictions or solve problems.

How can equations be written to describe the motion of a point in a plane?

How can problems involving circular motion be solved using parametric equations?
TEKS
Knowledge & Skill
The student uses conic
sections, their properties,
and parametric
representations as well as
tools and technology, to
model physical situations.
(P.5)
Student Expectation
Convert between
parametric and
rectangular forms of
functions and
equations to graph
them. (P.5C)
Use parametric
functions to simulate
problems involving
motion.
(P.5D)
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)
Determine the
domain and range of
functions using
graphs, tables, and
symbols. (P.1B)
(P.5)
(P.5C)
(P.5)
(P.5D)
LH: Pre-Calculus with Limits, Larson-Hostetler, Houghton-Mifflin, 2007
PTII: Precalculus TEXTEAMS Institute Part II
TAKS
OBJ
Time/
Pace
Teacher Tools
1-2 days
Vocabulary: parameter, parametric
equations, plane curve, eliminating the
parameter, cycloid
Teacher Notes: Revisit parametric equations
if they were taught in the 2nd six weeks as a
lead into polar coordinates and graphing.
PTII: IV.1.1
Activity: Avoiding
the Crash
1-2 days
The purpose of this activity is to let students
see an application of parametric equations.
Before introducing the terminology however,
have participants complete the first chart
about the relative positions of the two
planes. A quick reminder about the distance
formula might be needed to complete the
last box of the chart. Graphing the situation
parametrically will give us a picture of the
flights of the two planes.
Place the calculator in parametric mode and
enter the expressions that were developed
in the chart. If necessary, explain that
parametric graphing involves defining each
of the graph coordinates x and y in terms of
a third variable or parameter, usually t.
PTII: IV.1.1
Activity 3: Free
Falling Bodies
2 days
includes
days for
review
and/or
test
For the problems in this activity, students
need to be reminded of the formula for the
height of a freely falling body. Show the
transparency and describe the meaning of
the equation. Model the first problem.
Resource
LH
(Section 10-6)
Parametric
Equations
Pre-Calculus Page 3 of 4
LTF/A2: Laying the Foundation, Connecting Algebra 2 LTF/PC: Laying the Foundation, Connecting Pre-Calculus
APTI: Algebra II/Precalculus TEXTEAMS Part I
©2007 Austin Independent School District
Austin ISD Instructional Planning Guide – Mathematics
4th Six Weeks IPG- January 8th – February 22nd (32 days; 2 days for 6 weeks review/test; 2 days for MoY)
Major Concept #4: Polar Coordinates
Overarching
Idea
Teacher
Guiding
Questions
Matrix
#
Matrix
Strand
341
Geometric
Models
271
Attributes of Functions
275
Pre-Calculus
8 DAYS
The relationship between the polar and Cartesian coordinate systems describes the position of a point in a plane using distance
and angle rather than x- and y-coordinates.

What is relationship between the polar and Cartesian coordinate system?

How are points changed from one system to the other?
TEKS
Knowledge & Skill
Student Expectation
The student interprets the
meaning of the symbolic
representations of
functions and operations
on functions to solve
meaningful problems.
(P.2)
Investigate identities
graphically and verify
them symbolically,
including logarithmic
properties,
trigonometric
identities, and
exponential
properties. (P.2C)
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)
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)
(P5)
(P.5A)
LH: Pre-Calculus with Limits, Larson-Hostetler, Houghton-Mifflin, 2007
PTII: Precalculus TEXTEAMS Institute Part II
TAKS
OBJ
Resource
LH
(Section 10-7)
Polar Coordinates
LH
(Section 10-8)
Graphs of Polar
Equations
LH
(Section 10-9)
Polar Equations of
Conics
Time/
Pace
Teacher Tools
2 days
Vocabulary: polar coordinate system pole (or
origin), polar axis, polar coordinates
Teacher Notes: Animated lessons with
checks for understanding are available for
students and teachers. Teachers can access
this resource at
http://college.hmco.com/mathematics/larson/
precalculus_limits/1e2/ins_resources/ap.htm
l?state=TX.
2 days
Vocabulary: symmetry, intercepts,
asymptotes, periods, shifts
Teacher Notes: There is a series of
animated video lessons available at the link
above for this section of Polar Coordinates.
The Student Notetaking Guide includes
polar graphs and special polar graphs so
that students can record important
information from instruction or the video
tutorials. Students could review the tutorials
for additional help when completing
homework assignments.
4 days
includes
days for
review
and/or
test
Vocabulary: directrix, focus, pole
Teacher Notes: There is a series of
animated video lessons available at the link
above for this section of Polar Coordinates.
Students could review the tutorials for
additional help when completing homework
assignments.
Pre-Calculus Page 4 of 4
LTF/A2: Laying the Foundation, Connecting Algebra 2 LTF/PC: Laying the Foundation, Connecting Pre-Calculus
APTI: Algebra II/Precalculus TEXTEAMS Part I