Austin ISD Instructional Planning Guide – Mathematics template
5th Six Weeks IPG – Feb. 22-Apr. 16 (34 days; 1 day for ELA TAKS, 2 days for 6 weeks review/test)
©2010 Austin ISD
Algebra II
Discipline Based Concept: Logarithmic and Rational Functions
Pacing:
Concept description: Inverse relationships produce other functions that can model data to solve problems and to predict trends.
Unit #1: Logarithmic Functions
Unit Overarching Idea
Define logarithms by exploring and describing the relationship between exponential functions and their inverses.

Unit Guiding Questions
Arc Guiding Questions
Exponential and Logarithmic Functions
Algebra and Geometry
Strand


How can the inverse relationships between exponential and logarithmic functions be used to develop an understanding of
logarithmic equations?
How can multiple representations be used to solve logarithmic equations?
How are logarithmic functions used to model real-world data?



Arc: Inverse Relationships
How can graphs of exponential functions and their inverses be used to develop an understanding of logarithmic functions?
How can the graphing calculator be used to verify properties of logarithmic functions?
How is 10x = c related to log c?
TEKS
Knowledge & Skill
2A.4: The student connects
algebraic and geometric
representations of functions.
2A.11: The student
formulates equations and
inequalities based on
exponential and logarithmic
functions, uses a variety of
methods to solve them, and
analyzes the solutions in
terms of the situation.
Legend: TEXTEAMS: Algebra II Part 2
Student Expectation
2A.4A: The student is expected
to identify and sketch graphs of
parent functions, including linear
(f(x) = x), quadratic (f(x) = x2),
exponential (f(x) = ax), and
logarithmic (f(x) = logax)
functions, absolute value of x
(f(x) = |x|), square root of x (f(x) =
√x), and reciprocal of x (f(x) =
1/x);
2A.4B: The student is expected
to extend parent functions with
parameters such as a in f (x) =
a/x and describe the effects of
the parameter changes on the
graph of parent functions;
2A.11A: The student is expected
to develop the definition of
logarithms by exploring and
describing the relationship
between exponential functions
and their inverses;
2A.11C: The student is expected
to determine the reasonable
domain and range values of
exponential and logarithmic
functions, as well as interpret and
determine the reasonableness of
solutions to exponential and
logarithmic equations and
inequalities.
2A.11D: The student is expected
to determine the solutions of
exponential functions and
logarithmic equations using
graphs, tables and algebraic
methods.
TAKS
OBJ
Resource
Time/
Pace
Unit Pacing: 8 days
Unit Vocabulary: Logarithm,
common logarithm, logarithmic and
exponential functions, properties of
logarithms, asymptote, exponential
and logarithmic regression
Teacher Tools
Intended Learning: Students should be able to write equivalent forms for
exponential and logarithmic functions. Students should be able to write,
evaluate, and graph logarithmic functions.
Essential Questions:
Holt 7-3
Logarithmic
Functions
TEXTEAMS
Energy of
Earthquakes
90
min.
90
min.

What is a logarithm and how is it related to an exponential function?

What is the difference between an exponential equation and a
logarithmic equation? How are they similar?

What do you notice about the domain and range of an exponential
function and a logarithmic function?
Vocabulary: Logarithm, common logarithm, logarithmic function
MAlg2_5thIA1a = lesson
MAlg2_5thIA1a_log_as_inverse
MAlg2_5thIA1a_exploring_logs
MAlg2_5thIA1a_warmup
MAlg2_5thIA1a_log
MAlg2_5thIA1a_assessment
Intended Learning: The student will use a real-life data to model a logarithm.
Students will learn to use logarithms to scale large numbers. Students will
create logarithm scales so that they can see the characteristics of the graphs.
Essential Questions:

How do logarithms scales help you understand the characteristics
of graphs?

Why are logarithms useful in scaling earthquakes?

Why is a log-scale appropriate for the amount of energy released
from a volcano?
Vocabulary: Exponential functions, properties of logarithms, scaling
MAlg2_5thIA2a=lesson
MAlg2_5thIA2a_Energy of earthquakes Richter scale
MAlg2_5thIA2a_warmup
ETQ: Ensuring Teacher Quality AA: Algebra II Assessments MAP: Maximizing Algebra II Performance
SATEC: San Antonio Technology in Education Coalition
Algebra II
Page 1 of 7
ACM: Accelerated Curriculum for Mathematics
2/14/2010
Austin ISD Instructional Planning Guide – Mathematics template
5th Six Weeks IPG – Feb. 22-Apr. 16 (34 days; 1 day for ELA TAKS, 2 days for 6 weeks review/test)
©2010 Austin ISD
Arc Guiding Questions
Arc: Logarithmic Functions and Transformations
What situations are best modeled by logarithmic functions?
How are logarithmic functions applied in science to explain real-world situations?
How are transformations of logarithmic functions similar to or different from transformations of other functions?
How is function notation for logarithmic functions related to exponential function notation?
TEKS
Knowledge & Skill
Foundations
for Functions
Exponential and Logarithmic
Functions
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
2A .4
2A.4B
2A.11B: The student is expected
to use the parent functions to
investigate, describe, and predict
the effects of parameter changes
on the graphs of exponential and
logarithmic functions, describe
limitations on the domains and
ranges, and examine asymptotic
behavior.
2A .1 The student uses
properties and attributes of
functions and applies
functions to problem
situations.
Holt 7.7
Transforming
Exponential and
Logarithmic
Functions
90
min.
2A.1B The student is expected to
collect and organize data, make
and interpret scatterplots, fit the
graph of a function to the data,
interpret the results, and proceed
to model, predict, and make
decisions and critical judgments.
2A.11C
2A.11D
2A.11
2A.11F: The student is expected
to analyze a situation modeled by
an exponential function,
formulate an equation or
inequality, and solve the
problem.
Teacher Tools
Intended Learning: Students will be able to transform exponential and
logarithmic functions by changing parameters. Students will be able to
describe the effects of changes in the coefficients of exponential and
logarithmic functions.
2A.4A
Exponential and Logarithmic
Functions
Algebra and Geometry
Strand




Algebra II
Holt 7.8
Curve Fitting with
Exponential and
Logarithmic
Models
90
min.
Essential Questions:

How are transformations of exponential and logarithmic functions
similar or different?

How can you determine if the transformation is horizontal
translation, vertical translation, vertical stretch or compression,
horizontal stretch or compression, or a reflection?

How can you determine the asymptote of a function without drawing
the graph?

What is the difference between an exponential asymptote and
a logarithmic asymptote?

Which transformation of an exponential or logarithmic function will
cause the asymptote to move?
Vocabulary: asymptote
MAlg2_5thIA2b=lesson
MAlg2_5thIA2b_warmup
MAlg2_5thIA2b_engage
MAlg2_5thIA2b_explore
MAlg2_5thIA2b_explain
MAlg2_5thIA2b_organizer
MAlg2_5thIA2b_assessment
Intended Learning: Students will model data by using exponential and
logarithmic functions. Students will use exponential and logarithmic functions
to analyze and make predictions about the given data.
Essential Questions:

How can you determine if the data given is a linear model, a quadratic
model or an exponential model?

Can the common ratio of an exponential function be between 0 and 1?

Can the common ratio of an exponential function be negative?

What characteristics of any given data would make a logarithmic model
appropriate?

How can you use the graphing calculator and regression to find the equation
for a set of data?
Vocabulary: exponential regression, logarithmic regression
MAlg2_5thIA2c=lesson
MAlg2_5thIA2c_warmup
MAlg2_5thIA2c_engage
MAlg2_5thIA2c_explore
MAlg2_5thIA2c_explain
MAlg2_5thIA2c_elaborate
Legend: TEXTEAMS: Algebra II Part 2
ETQ: Ensuring Teacher Quality AA: Algebra II Assessments MAP: Maximizing Algebra II Performance
SATEC: San Antonio Technology in Education Coalition
Algebra II
Page 2 of 7
ACM: Accelerated Curriculum for Mathematics
2/14/2010
Austin ISD Instructional Planning Guide – Mathematics template
5th Six Weeks IPG – Feb. 22-Apr. 16 (34 days; 1 day for ELA TAKS, 2 days for 6 weeks review/test)
©2010 Austin ISD
Arc Guiding Questions
Strand




Arc: Solving Equations and Inequalities
How can finding a common base be used to solve exponential equations?
How can exponential equations be solved using the properties of exponents?
What is the Power Property of Logarithms and how can it be used to solve equations?
How do you determine if a solution to a logarithmic equation is reasonable?
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
2A.11D
2A.11E: The student is expected
to determine solutions of
exponential and logarithmic
inequalities using graphs and
tables.
2A.11
Teacher Tools
Intended Learning:
2A.11C
Exponential and Logarithmic Functions
Algebra II
-
Students will solve exponential and logarithmic equations and
inequalities
-
Students will solve problems involving exponential and logarithmic
equations
Essential Questions:
Holt 7.5
Exponential and
Logarithmic
Equations and
Inequalities
90 min
Days 1
&2
2A.11F
-
What are uses of exponential and logarithmic functions?
-
How can exponential and logarithmic functions be used to help
prepare and plan for financial security?
-
How can exponential and logarithmic functions be used to analyze
population growth or decay and make real-life decisions
surrounding population rates?
-
What methods can be used for exponential and logarithmic
equations and inequalities and how do you choose which method is
best?
Vocabulary:
-
exponential equations
-
logarithmic equations
MAlg2_5thIA3a=lesson
MAlg2_5thIA3aWU= warm up
Intended Learning:
Exponential and Logarithmic Functions
2A.11C
-
Students will solve exponential and logarithmic equations and
inequalities
-
Students will solve problems involving exponential and logarithmic
equations
2A.11D
Essential Questions:
2A.11E
2A.11
2A.11F
Holt 7.5
Exponential and
Logarithmic
Equations and
Inequalities
90 min
Days 3
&4
-
What are uses of exponential and logarithmic functions?
-
How can exponential and logarithmic functions be used to help
prepare and plan for financial security?
-
How can exponential and logarithmic functions be used to analyze
population growth or decay and make real-life decisions
surrounding population rates?
-
What methods can be used for exponential and logarithmic
equations and inequalities and how do you choose which method is
best?
Vocabulary: exponential equations, logarithmic equations
MAlg2_5thIA3b=lesson
MAlg2_5thIA3b_engage= engage activity
MAlg2_5thIA3b_warmup= warm up
Legend: TEXTEAMS: Algebra II Part 2
ETQ: Ensuring Teacher Quality AA: Algebra II Assessments MAP: Maximizing Algebra II Performance
SATEC: San Antonio Technology in Education Coalition
Algebra II
Page 3 of 7
ACM: Accelerated Curriculum for Mathematics
2/14/2010
©2010 Austin ISD
Strand
TEKS
Knowledge & Skill
Austin ISD Instructional Planning Guide – Mathematics template
5th Six Weeks IPG – Feb. 22-Apr. 16 (34 days; 1 day for ELA TAKS, 2 days for 6 weeks review/test)
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Algebra II
Teacher Tools
Intended Learning:
-
Students will solve exponential and logarithmic equations and
inequalities
-
Students will solve problems involving exponential and logarithmic
equations
2A.11C
Exponential and Logarithmic Functions
Essential Questions:
2A.11D
Holt 7. 6
The Natural Base,
e
2A.11
2A.11E
-
What are uses of exponential and logarithmic functions?
-
How can exponential and logarithmic functions be used to help
prepare and plan for financial security?
-
How can exponential and logarithmic functions be used to analyze
population growth or decay and make real-life decisions
surrounding population rates?
-
What methods can be used for exponential and logarithmic
equations and inequalities and how do you choose which method is
best?
135
min
Days
5, 6 &
7
Vocabulary:
-
exponential equations
-
logarithmic equations
MAlg2_5thIA3c=lesson
MAlg2_5thIA3c_explore
MAlg2_5thIA3c_explain
2A.11F
MAlg2_5thIA3c_explainalternate
MAlg2_5thIA3c_evaluate
MAlg2_5thIA3c_pwrpt
Legend: TEXTEAMS: Algebra II Part 2
ETQ: Ensuring Teacher Quality AA: Algebra II Assessments MAP: Maximizing Algebra II Performance
SATEC: San Antonio Technology in Education Coalition
Algebra II
Page 4 of 7
ACM: Accelerated Curriculum for Mathematics
2/14/2010
Austin ISD Instructional Planning Guide – Mathematics template
5th Six Weeks IPG – Feb. 22-Apr. 16 (34 days; 1 day for ELA TAKS, 2 days for 6 weeks review/test)
©2010 Austin ISD
Arc Guiding Questions
Strand




Algebra II
Arc: Probability
How do you determine the probability of compound events?
How is calculating the probability of dependent events similar to or different independent events?
What is the significance of the numbers 0 and 1 in determining probability?
How are circle graphs, histograms, and bar graphs similar and different? When is one graph a better representation of data than another?
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
Intended Learning:
Students will find the theoretical probability of an event. Students will find
the experimental probability of an event. Students will determine whether
the events are dependent or independent. Students will find the
probability independent and dependent events.
Essential Questions:
8.11A The student is expected to
find the probabilities of
dependent and independent
events.
Accelerated
Curriculum for
Mathematics
Grade 11
Exit TAKS
Probability and Statistics
8.11: The student applies
concepts of theoretical and
experimental probability to
make predictions.
90 min

What is the difference between theoretical probability and
experimental probability?

Compare independent and dependent events.

What is sample space?

What is an equally likely outcome?

What is a favorable outcome?
Vocabulary: probability, outcome, sample space, event, equally likely
outcomes, favorable outcomes, theoretical probability, experimental
probability, independent events, dependent events
8.11B The student is expected to
use theoretical probabilities and
experimental results to make
predictions and decisions.
MAlg2_5thIB1a=lesson
MAlg2_5thIB1a _accelerated math teachers ed. = teacher resources
MAlg2_5thIB1a _accelerated math student = student resources
8.12: The student uses
statistical procedures to
describe data.
8.13: The student evaluates
predictions and conclusions
based on statistical data.
8.12A The student is expected to
select the appropriate measure of
central tendency to describe a
set of data for a particular
purpose.
8.12C The student is expected to
construct circle graphs, bar
graphs and histograms, with and
without technology.
8.13B The student is expected to
recognize misuses of graphical or
numerical information and
evaluate predictions and
conclusions based on data
analysis.
Intended Learning:
Students will find the measures of central tendency and measures of
variation. Students will learn which type of graph best displays the given
data.
Essential Questions:
Accelerated
Curriculum for
Mathematics
Grade 11
Exit TAKS
90 min

What is statistics?

What is a circle graph? How do you calculate how many degrees
should be in a central angle of each section of a circle graph?

What is a histogram?

How are a bar graph and histogram alike? How are they different?

Explain the difference between mean, median and mode.

How do statisticians use Venn Diagrams?
Vocabulary: statistics, histogram, mean, mode, median, Venn Diagrams
MAlg2_5thIB1b=lesson
MAlg2_5thIB1b _accelerated math teachers ed. = teacher resources
MAlg2_5thIB1b _accelerated math student = student resources
Legend: TEXTEAMS: Algebra II Part 2
ETQ: Ensuring Teacher Quality AA: Algebra II Assessments MAP: Maximizing Algebra II Performance
SATEC: San Antonio Technology in Education Coalition
Algebra II
Page 5 of 7
ACM: Accelerated Curriculum for Mathematics
2/14/2010
Austin ISD Instructional Planning Guide – Mathematics template
5th Six Weeks IPG – Feb. 22-Apr. 16 (34 days; 1 day for ELA TAKS, 2 days for 6 weeks review/test)
©2010 Austin ISD
Discipline Based Concept: Logarithmic and Rational Functions
Algebra II
Pacing:
Concept description: Inverse relationships produce other functions that can model data to solve problems and to predict trends.
Unit #2: Rational Functions
Unit Overarching Idea
Situations modeled by functions with a variable in the denominator of a rational term have unique characteristics.
Unit Guiding Questions



How are rational expressions, fractions, and rational numbers related?
What are the differences between adding/subtracting and multiplying/dividing rational expressions?
When can rational functions be used to find solutions to specific problems?
Arc Guiding Questions



Arc: Rational Functions and Transformations
How are transformations of rational functions similar to or different from transformations of other functions?
What are the unique characteristics of the graph of a rational function?
How do transformations of rational functions affect the domain and range?
Strand
Unit Pacing: 6 days + 7 days
Unit Vocabulary: Inverse Variation,
Horizontal Asymptote, Vertical
Asymptote, hole, factors,
discontinuity, continuous function,
hyperbola, branches
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
Intended learning: Graph rational functions using transformations and
factoring techniques
Rational Functions
Algebra and Geometry
2A.4A
2A .4
Holt 8.4
Rational Functions
90
mins
2A.4B
2A.10 The student
formulates equations and
inequalities based on
rational functions, uses a
variety of methods to solve
them, and analyzes the
solutions in terms of the
situation.
Legend: TEXTEAMS: Algebra II Part 2
2A.10A: The student is expected
to use quotients of polynomials to
describe the graphs of rational
functions, predict the effects of
parameter changes, describe
limitations on the domains and
ranges and examine asymptotic
behavior;
2A.10B: The student is expected
to analyze various
representations of rational
functions with respect to problem
situations
2A.10C: The student is expected
to determine the reasonable
domain and range values of
rational functions, as well as
interpret and determine the
reasonableness of solutions to
rational equations and
inequalities;
Essential Questions:
What do asymptotes represent?
What are real-life applications of rational functions?
What is the end behavior of rational functions?
Vocabulary: Inverse Variation, Horizontal Asymptote, Vertical Asymptote,
hole (in a graph), factors, discontinuity, continuous function, hyperbola,
branches
MAlg2_5thIC1a= lesson
MAlg2_5th1C1a_noteexamples
MAgl2_5thIC1a_activity
MAgl2_5thIC1a_activitypictures
MAlg2_5thIC1a_practiceproblems
MAlg2_5thIC1a_warmup
MAgl2_5thIC1a_explore
Intended learning: Students will learn to simplify rational expressions and
graph them. Students will apply transformations to rational functions.
Essential Questions:
What do asymptotes represent?
What are real-life applications of rational functions?
What is the end behavior of rational functions?
Vocabulary: Inverse Variation, Horizontal Asymptote, Vertical Asymptote,
Holt 8.4
Rational Functions
90
mins
hole (in a graph), factors, discontinuity, continuous function, hyperbola,
branches
MAlg2_5thIC1b= lesson
MAlg2_5thIC1b_explore
MAlg2_5th1C1b_note
MAlg2_5thIC1b_practice
MAlg2_5thIC1b_warmup
MAgl2_5thIC1b_quiz
MAgl2_5thIC1b_summary
ETQ: Ensuring Teacher Quality AA: Algebra II Assessments MAP: Maximizing Algebra II Performance
SATEC: San Antonio Technology in Education Coalition
Algebra II
Page 6 of 7
ACM: Accelerated Curriculum for Mathematics
2/14/2010
©2010 Austin ISD
Austin ISD Instructional Planning Guide – Mathematics template
5th Six Weeks IPG – Feb. 22-Apr. 16 (34 days; 1 day for ELA TAKS, 2 days for 6 weeks review/test)
Algebra II
Suggested TAKS practice is included until TAKS is replaced by the Algebra II End-of-Course test for most high school juniors and seniors.
TEKS
Knowledge & Skill
Student Expectation
G4: The student uses a
variety of representations to
describe geometric
relationships and solve
problems.
G4.A: The student is expected to
select an appropriate
representation (concrete,
pictorial, graphical, verbal or
symbolic) in order to solve
problems.
TAKS
OBJ
Congruence and the
Geometry of Size
8
G8: The student uses tools
to determine measurements
of geometric figures and
extends measurement
concepts to find perimeter,
area, and volume in
problem situations.
Geometric
Structure
Geometric
Structure
Strand
G5: student uses a variety
of representations to
describe geometric
relationships & solve
problems
G8.D: The student is expected to
find surface areas and volumes
of prisms, pyramids, spheres
cones, cylinders, and composites
of these figures in problem
situations.
Congruence
and the
Geometry of
Size
Geometric
Structure
Congruence and the Geometry
of Size
G4
Closing the
Distance
Lesson 12
Legend: TEXTEAMS: Algebra II Part 2
60-90
mins
(1
block
day)
G5.D: The student is expected to
identify and apply patterns from
right triangles to solve meaningful
problems, including special right
triangles and triangles whose
sides are Pythagorean triples
Intended learning:
Identify how and when to use the different volume and SA formulas and to
apply them in problem situations (3d shapes and nets)
Essential Questions:
How do you determine which formula is appropriate for a given
context and/or figure?
What is the difference between surface area and volume?
How is this difference seen in the formulas for surface area and
volume?
What additional considerations must be made when finding surface
area and volume of a composite solid figure?
Vocabulary:
Intended learning:
To apply and use pyth thm and special right triangle formulas in triangles and
prob situations with triangles
Closing the
Distance
Lesson 10
G8.C: The student is expected to
derive, extend, and use the
Pythagorean theorem.
60-90
mins
(1
block
day)
G4.A
G8.D
Teacher Tools
Area, base, circular, circumference, composite solids, cylindrical,
diameter, dimensions, lateral surface area, radius, rate, rectangular,
rectangular prism, total surface area, volume
MAlg2_5thID1a= lesson
MAlg2_5th1D1aHW= obj 8 hw for practice
TAKS tests for
practice
questions
G8
Time/
Pace
-
6&8
G8
Resource
90
mins
Essential questions:
How can I extend the Pythagorean thm to special right triangles?
How can I use what I know about a 30-60-90 triangle to solve a realworld problem for a right triangle?
How can I use what I know about a 45-45-90 tirangle to solve a realworld problem for a right triangle?
Vocabulary: 30-60-90 triangle, 45-45-90 triangle, angle of depression, angle
of elevation, leg, hypotenuse , and Pythagorean thm
MAlg2_5thID1b= lesson
MAlg2_5thID1bHW= homework for practice
Intended learning:
To apply the effects of dimension change to find and calculate the new
perimeter, surface area, and volume
Essential Questions
How is the volume affected by changing the dimensions of a smaller
or larger figure?
How is the area affected as dimensions are altered?
How is the perimeter changed with dimensions being scaled up or
down?
What are the affects when not all dimensions are changed?
What is the real-world application for such changes in dimension
and capacities of shapes?
Vocabulary: Volume , Surface Area, Area, Dimensions, Scale Factor
Doubling/ tripling, scale factor squared, scale factor cubed, lateral
MAlg2_5thID1c= lesson
MAlg2_5thID1cWarmUp= warm up
MAlg2_5thID1cExplore= explore activity
MAlg2_5thID1cAssess= evaluate problems for assessment
MAlg2_5thID1cHW= homework (area practice)
ETQ: Ensuring Teacher Quality AA: Algebra II Assessments MAP: Maximizing Algebra II Performance
SATEC: San Antonio Technology in Education Coalition
Algebra II
Page 7 of 7
ACM: Accelerated Curriculum for Mathematics
2/14/2010