Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Aug. 24 – Oct. 2 (29 of days; 2 days for 6 weeks review/test, 2 days for BOY)
©2009 Austin ISD
Algebra II
Discipline Based Concept: Foundation for Functions
Pacing:
Concept description: Using properties and attributes of functions and applying functions to problem situations
Unit Major Concept #1: Linear Functions
Unit Overarching
Idea
Unit Teacher
Guiding Questions
Finance, Banking, and Science use functions to represent data, understand relationships, and make predictions
about situations in our environment.

How can we use data relationships to make predictions?

When do we know two variables have a dependent relationship?

What kinds of data fit into linear relationships? What kinds of data are non-linear?

How do we establish the boundaries (domain, range) of collected data?
Unit Pacing:
Unit Vocabulary:
Arc: Characteristics of Parent functions






Arc Teacher
Guiding Questions
Foundations for functions
Foundations for functions
Matrix
Strand
TEKS
Knowledge & Skill
2A.1 The student uses
properties and
attributes of functions
and applies functions
to problem situations.
2A.4 The student
connects algebraic
and geometric
representations of
functions.
DL: Disciplinary Literacy
Algebra 2
What is a 1-to-1 relationship?
How is a rate of change related to “steepness” in a linear relationship?
How does a shifted y-intercept affect a graphed line?
Does modifying a slope value affect the appearance of a graphed line? How?
What is the difference between a shift and a stretch transformation?
What is significant about the slopes of reflected linear functions?
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
2A.1A The student is expected to
identify the mathematical
domains and ranges of functions
and determine reasonable
domain and range values for
continuous and discrete
situations;
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.,
Intended Learnings: Students will explore geometric patterns and their
connection to algebraic expressions. Students will create a process column for
determining the pattern or the linear function rule. Students will represent the rule
using function notation. When analyzing patterns, students will observe that
constant finite differences are characteristic of linear functions. Students will
represent functions concretely (with manipulative), verbally (in words),
numerically (by tables), graphically (by graphs), and symbolically (by
formulas).Students will utilize the TI calculator to create a data table and a graph
of a linear function. Students will also learn how to use the ‘trace function.
ETQ: Generating
Patterns 2.1.1
90 min
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);
ETQ: Ensuring Teacher Quality
Teacher Tools
AA: Algebra II Assessments
Essential Questions: Given a table of data, how do you know if it’s a linear
relationship; as opposed to quadratic, exponential, etc? What are different ways
to represent a functional relationship? After finding a function rule, how can you
determine the independent (domain) value when given a dependent (range)
value?
Vocabulary: Linear function, Domain, Range, Rate of Change, Constant,
Y-intercept, ordered pair, dependent, independent, x-axis, y-axis, scatter plot
See the following attachments in the lesson “Foundational Activity: Slope and YIntercept” for more details:
MAlg21stIA1a = lesson plan
MAlg21stIA1a _patterns2.1.1=teacher key & student resources
MAlg21stIA1a Numerical Fluency 1_13 = teacher resources
MAP: Maximizing Algebra II Performance SATEC: San Antonio Technology in Education Coalition
Page 1 of 7
7/20/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Aug. 24 – Oct. 2 (29 of days; 2 days for 6 weeks review/test, 2 days for BOY)
©2009 Austin ISD
Strand
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Algebra II
Teacher Tools
Intended Learnings: Students will explore five ways to represent functions:
Foundations for functions
concretely, verbally, numerically, graphically and symbolically.
2A.1
2A.3 The student
formulates systems of
equations and
inequalities from
problem situations,
uses a variety of
methods to solve
them, and analyzes
the solutions in terms
of the situations.
Essential Questions: What are the relationships between the equation, the data
in the table, and the important features of the graph?
Vocabulary: Slope, x-intercept, slope intercept form, interval
2A.1A
2A.3B Use algebraic methods,
graphs, tables, or matrices, to
solve systems of equations or
inequalities.
Tape Activity
45 min
Teacher Notes:
This activity is designed for a group of four students. The teacher may initially
assign the duties to the group members or they can assign duties themselves.
Depending on space in the classroom, more than one graph can be generated.
The domain and range can be -5 to +5 or -10 to +10, which will be determined by
space availability.
Variation to lesson- Teachers may use chart tablet or bulletin board paper if
utilizing the floor is not feasible.
See the following attachments in the lesson “Tape Activity: Explore graphing a
line given an equation” for more details:
Algebra and Geometry
MAlg21stIA1b = lesson plan
2A.4
2A.4A
Holt 2-3
and
Closing the
Distance TAKS
Exit Level
45 min
MAlg21stIA1b_Numerical Fluency 11 = teacher resources
Intended Learnings: Determine if the function is linear. Be able to graph
a linear function using a variety of methods.
Essential Questions: What are the relationships between the equation, the data
in the table, and the important features of the graph?
Which representation is appropriate in which situations?
What characteristics would determine if the function is linear?
How would you graph a line given
a) the slope and a point
b) the x-intercept and y- intercept
c) the equation in slope intercept form?
Vocabulary: horizontal and vertical lines, vertical line test
Teacher Notes: Emphasize the multiple representations of the data (table, graph,
equation)
See the following attachments in the lesson “Graphing Linear Functions” for more
details:
MAlg21stIA1c = lesson plan
MAlg21stIA1c _commute work play trans = teacher resources
MAlg21stIA1c _work and play student = student resources
MAlg21stIA1c _function card sort = teacher resources
DL: Disciplinary Literacy
Algebra 2
ETQ: Ensuring Teacher Quality
AA: Algebra II Assessments
MAP: Maximizing Algebra II Performance SATEC: San Antonio Technology in Education Coalition
Page 2 of 7
7/20/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Aug. 24 – Oct. 2 (29 of days; 2 days for 6 weeks review/test, 2 days for BOY)
©2009 Austin ISD
Strand
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Algebra II
Teacher Tools
Intended Learnings: Use slope-intercept form and point-slope form to write
linear equations.
Algebra and Geometry
Essential Questions: How would you write the equation of a line given:
2A.5 The student
understands that linear
functions can
be represented in
different ways and
translates among their
various
representations.
2A.5C The student is expected
to use, translate, and make
connections among algebraic,
tabular, graphical, or verbal
descriptions of linear functions.
Holt 2-4
90 min
a.
b.
c.
d.
e.
f.
A graph
Table
A point and slope
Two points
Parallel to a given line and a given point
Perpendicular to a given line and a given point
Why are different scales used in graphs? How do you determine the graphing
scale for data you wish to represent?
Vocabulary: Point-slope form
Algebra and Geometry
See the following attachments in the lesson “Writing Linear Functions” for more
details:
MAlg21stIA1d = lesson plan
MAlg21stIA1d_accelerated math teachers ed. = teacher resources
MAlg21stIA1d_accelerated math student ed. = student resources
Intended Learnings: Use linear functions to solve real world problems.
Essential Questions: How would you use linear functions to solve real world
problems?
2A.5
DL: Disciplinary Literacy
Algebra 2
2A.5C
Write Linear
Functions to
Solve Real
Applications
Vocabulary: There are no new vocabulary words. Review previous vocabulary.
90 min
See the following attachments in the lesson “Use Linear Functions to Solve Real
World Applications” for more details:
MAlg21stIA1e = lesson plan
MAlg21stIA1e_accelerated math teachers ed. = teacher resources
MAlg21stIA1e_accelerated math student = student resources
ETQ: Ensuring Teacher Quality
AA: Algebra II Assessments
MAP: Maximizing Algebra II Performance SATEC: San Antonio Technology in Education Coalition
Page 3 of 7
7/20/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Aug. 24 – Oct. 2 (29 of days; 2 days for 6 weeks review/test, 2 days for BOY)
©2009 Austin ISD
Algebra II
Discipline Based Concept: Foundation for Functions
Pacing:
Concept description: Using properties and attributes of functions and applying functions to problem situations
Unit Major Concept #1: Linear Functions
Unit Overarching
Idea
Unit Teacher
Guiding Questions
Finance, Banking, and Science use functions to represent data, understand relationships, and make predictions
about situations in our environment.

How can we use data relationships to make predictions?

When do we know two variables have a dependent relationship?

What kinds of data fit into linear relationships? What kinds of data are non-linear?

How do we establish the boundaries (domain, range) of collected data?
Unit Pacing:
Unit Vocabulary:
Arc: Equations and Inequalities




Arc Teacher
Guiding Questions
Foundations for functions
Foundations for functions
Strand
TEKS
Knowledge & Skill
2A.2 The student
understands the
importance of the skills
required to manipulate
symbols in order to
solve problems and
uses the necessary
algebraic skills
required to simplify
algebraic expressions
and solve equations
and inequalities in
problem situations.
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
Intended Learnings: Students will solve linear equations and inequalities using
a variety of methods.
Essential Questions: How are equations used to represent real-life situations?
How are algebraic operations useful in solving equations in relevant applications?
2A.2A Use tools … to simplify
expressions and to transform
and solve equations
Holt 2.1
45 min
Vocabulary: equation(ecaucion), inequality(desigualdad), solution set of an
equation, identity (identidad)
See the following attachments in the lesson “Solving equations & inequalities ” for
more details:
MAlg21stIA1f = lesson plan
MAlg21stIA1f_PwrPt2.1EqsIneqs = teacher resources
MAlg21stIA1f_holt exploration 2.1 = teacher resources
Intended Learnings: The student will solve linear inequalities using
concrete models, graphs, and properties of equality.
2A.2.
DL: Disciplinary Literacy
Algebra 2
How do we know when an inequality includes a particular point?
When is an inequality applicable to a real world situation?
When and why do we change the direction of an inequality symbol?
How are absolute value and inequality function equations related to a linear parent function?
2A.2A
ETQ: Ensuring Teacher Quality
Holt 2-5 &
Linear
Inequalities in
Two Variables
Lesson Plan
AA: Algebra II Assessments
Essential Questions: Explain what the shaded area represents. How many
possible solutions are there to a linear inequality?
45 min
Vocabulary: linear inequality, solution, boundary line
See the following attachments in the lesson “Linear Inequalities in Two
Variables” for more details:
Mlg21stIA1g= lesson plan
Mlg21stIA1g_inequality card sort= teacher resources
Mlg21stIA1g_activities= student resources
Mlg21stIA1g_key to activities= teacher resources
MAP: Maximizing Algebra II Performance SATEC: San Antonio Technology in Education Coalition
Page 4 of 7
7/20/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Aug. 24 – Oct. 2 (29 of days; 2 days for 6 weeks review/test, 2 days for BOY)
©2009 Austin ISD
Discipline Based Concept: Foundation for Functions
Algebra II
Pacing:
Concept description: Using properties and attributes of functions and applying functions to problem situations
Unit Major Concept #1: Linear Functions
Unit Overarching
Idea
Unit Teacher
Guiding Questions
Finance, Banking, and Science use functions to represent data, understand relationships, and make predictions
about situations in our environment.

How can we use data relationships to make predictions?

When do we know two variables have a dependent relationship?

What kinds of data fit into linear relationships? What kinds of data are non-linear?

How do we establish the boundaries (domain, range) of collected data?
Algebra and geometry
Algebra and geometry.
Arc: Transformations
Arc Teacher
Guiding Questions


Unit Pacing:
Unit Vocabulary:
How do different types of transformations affect the graph and equation of a linear function? a quadratic function? a piecewise functions?
How are the ordered pairs or values in the table of a function affected by a transformation
Intended Learnings: Students will explore how the graph and rule of a function
is affected by a horizontal shift, vertical shift, reflection across the x-axis, and
reflection across the y-axis? Student will also explore how a stretch or
compression can affect the function rule and its graph. Students will transform
linear functions numerically and graphically. Students will solve problems
involving linear transformations.
2A.4 The student
connects algebraic
and geometric
representations of
functions.
2A.4A
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;
TEXTEAMS:
Introducing
Transformations
180
min
Essential Questions How can you verify if an image is an accurate translation of
a pre-image? How can you represent a transformation in coordinate notation?
How can you represent a transformation in function notation? How is range
affected by compression dilations?
How is range affected by stretch dilations?
Vocabulary: Transformation, horizontal shift, vertical shift, reflect across y-axis/xaxis, translate, dilation, stretch, compress.
See the following attachments in the lesson “Introducing Transformations” for more
details:
MAlg21stIA1h= lesson plan
MAlg21stIA1h_transformations 1.1 = teacher and student resources
MAlg21stIA1h_alternate transformations = teacher and student resources
Intended Learnings: The student will transform linear functions and solve
problems involving linear transformations. The student will be able to show an
algebraic representation of a parent function and its transformation, a graphic
representation of a parent function and its transformation and a table form of a
parent function and its transformation.
2A.4
2A.4A
2A.4B
Holt 2-6
45 min
Essential Questions: How does a reflection change the function rule? How
does a stretch or compression affect the function rule? How does a reflection
affect the graph? How does a stretch or compression affect the graph? Does
slope change when a linear function is translated? How does graphing the
parent function along with its transformation help identify the transformation?
Vocabulary: parent function, reflection, translation, stretches, compressions
See the following attachments in the lesson “Transforming Linear Functions”
for more details:
MAlg21stIA1i = lesson plan
DL: Disciplinary Literacy
Algebra 2
ETQ: Ensuring Teacher Quality
AA: Algebra II Assessments
MAP: Maximizing Algebra II Performance SATEC: San Antonio Technology in Education Coalition
Page 5 of 7
7/20/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Aug. 24 – Oct. 2 (29 of days; 2 days for 6 weeks review/test, 2 days for BOY)
©2009 Austin ISD
Discipline Based Concept: Foundations for Functions
Concept description: Using properties and attributes of functions and applying functions to problem situations
Unit Major Concept # 1: Linear Functions
Unit Overarching
Idea
Unit Teacher
Guiding Questions
Finance, Banking, and Science use functions to represent data, understand relationships, and make
predictions about situations in our environment

How can we use data relationships to make predictions?

When do we know two variables share a dependent relationship?

What kinds of data fit into linear relationships? What kinds of data are non-linear?

How do we establish the boundaries (domain, range) of collected data?
Algebra II
Pacing:
Unit Pacing:
Unit Vocabulary:
Arc: Absolute Value functions

What linear equations make up each part of an absolute value graph? How are these equations related to the absolute value equation?
Arc Teacher

How do different transformations effect the absolute value equation?
Guiding Questions
Foundations for functions
Matrix
Strand
TEKS
Knowledge & Skill
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
Intended Learnings: Students will investigate various parameter changes to the
absolute value parent function and make generalizations about how specific
parameter functions affect the graph of the parent function.
2A.1A
Essential Questions: What are the effects of parameter changes on the
2A.1
2A.4 The student
connects algebraic and
geometric
representations of
functions.
2A.4A The student is
expected to extend parent
functions with parameters
such as f(x) = a/x and
describe the effects of the
parameter changes on the
graph of parent functions.
MAP: Absolute
Value Functions
Distance from the
Firehouse
absolute value functions? What are the connections among the graphical and
algebraic solutions of absolute value equations and inequalities?
135
min
Vocabulary: absolute value parent function, restricted domain
See the following attachments in the lesson “Distance to the Fire Station”
for more details:
MAlg21stIA2a= lesson plan
MAlg21stIA2a_Numerical Fluency 1-8 = teacher resources
MAlg21stIA2a_distance to the fire station = teacher and student resources
Intended Learnings: Students will be able to graph and transform absolute
value-functions. Students will connect the (h, k) translation of absolute value
functions to the (h, k) translation of quadratic functions.
Algebra and Geometry
Essential Questions: How can you sketch the graph of the transformation of an
2A.4
DL: Disciplinary Literacy
Algebra 2
Holt 2-9
2A.4A , 2A.4B
45 min
absolute value function without making a table of values?
How does a vertical translation affect the graph of an absolute value function?
How does a horizontal translation affect the graph of an absolute value
function? How is a vertical stretch and compression of an absolute value
function similar to a vertical stretch or compression of a linear function? How is
it different? Is the vertex of an absolute value always a minimum point?
Vocabulary: absolute-value functions, vertical translation, horizontal translation,
(h, k) translation, stretch, compression, reflection
See the following attachments in the lesson “Absolute Value Functions”
for more details:
MAlg21stIA2b= lesson plan
ETQ: Ensuring Teacher Quality
AA: Algebra II Assessments
MAlg21stIA2b_Numerical Fluency 1-12 = teacher resources
MAP: Maximizing Algebra II Performance SATEC: San Antonio Technology in Education Coalition
Page 6 of 7
7/20/09
Austin ISD Instructional Planning Guide – Mathematics
1st Six Weeks IPG- Aug. 24 – Oct. 2 (29 of days; 2 days for 6 weeks review/test, 2 days for BOY)
©2009 Austin ISD
Algebra II
Discipline Based Concept: Foundation for Functions
Concept description: Using properties and attributes of functions and applying functions to problem situations
Unit Major Concept #1: Linear Functions
Unit Overarching
Finance, Banking, and Science use functions to represent data, understand relationships, and make
Idea
predictions about situations in our environment
 How can we use data relationships to make predictions?
Unit Teacher
 When do we know two variables have a dependent relationship?
Guiding Questions
 What kinds of data fit into linear relationships? What kinds of data are non-linear?
 How do we establish the boundaries (domain, range) of collected data?
Pacing:
Unit Pacing:
Unit Vocabulary:
Arc: Inverse Functions
Arc Teacher
Guiding Questions
Algebra and
geometry
Foundations for
functions
Matrix
Strand



What is the difference between a function and its inverse?
Describe the significance of the ‘Y=X’ line?
How are the domain and range of a function and its resulting inverse related?
TEKS
Knowledge & Skill
2A.1. The student uses
properties and attributes
of functions and applies
functions to problem
situations.
2A.4 The student
connects algebraic and
geometric
representations of
functions.
Student Expectation
2A.1A The student is
expected to identify the
mathematical domains and
ranges of functions and
determine reasonable domain
and range values for
continuous and
discrete situations;
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
Intended Learnings: Students will be able to find the inverse of a given function;
be able to describe inverse relations and functions using graphs, tables, and
algebraic methods.
MAP: Inverses of
Functions
135
min
2A.4A
2A.4B
2A.4C
Essential Questions: How can you tell whether two functions are inverses of
each other? When is the inverse of a function not also a function? How can you
find the inverse of a function? If we know how to find the inverse of a linear
function, how can we find the inverse of a quadratic function?
Vocabulary: Inverse function, inverse relation
See the following attachments in the lesson “Inverse of Functions ”
for more details:
MAlg21stIA3a= lesson plan
MAlg21stIA3a_inverse of functions = teacher & student resources
Algebra and
Geometry
MAlg21stIA3a_Numerical Fluency 1-18 = teacher resources
Intended Learnings: Students will be able to graph, recognize, and find
inverses of relations and functions.
2A.4 The student
connects algebraic and
geometric
representations of
functions.
2A.4C The student is
expected to describe and
analyze the relationship
between a function and its
inverse.
Holt 7-2
Holt Technology
Lab
90 min
Essential Questions: What does it mean “to mirror each other”?
What are two ways to”mirror” points?
What are functions that undo each other?
Vocabulary: Inverse function, inverse relation
See the following attachments in the lesson “Inverses of relations and functions”
for more details:
MAlg21stIA3b = lesson plan
BOY Benchmark
Review and
1st 6-week
assessment
DL: Disciplinary Literacy
Algebra 2
ETQ: Ensuring Teacher Quality
AA: Algebra II Assessments
90 min
90 min
MAP: Maximizing Algebra II Performance SATEC: San Antonio Technology in Education Coalition
Page 7 of 7
7/20/09