Austin ISD Instructional Planning Guide – Mathematics
3rd Six Weeks IPG – Nov. 10 - Dec. 17 (25 days; 2 days for 6 weeks review/test and 4 days for Final Exams)
©2009 Austin ISD
Algebra II
Discipline Based Concept
Pacing: 25 days
Concept description: Quadratic functions can be represented in different ways, and students should be able to translate among and make connections
between the various representations.
Unit: Quadratics
Unit Pacing: 25 days
Unit Overarching
Unit Vocabulary:
Quadratic functions have many applications in business models and science, and can also be used to determine the
path of an object that is thrown or projected.
Idea
Discipline Based Concept: Quadratic Functions


Unit Guiding
Questions


Arc Guiding
Questions
Quadratic and square root functions
Foundations
for Functions
Strand




What are some real-world applications of quadratic functions?
How can factoring, graphing, completing the square, and the quadratic formula be used to solve quadratic
equations and inequalities?
How are solutions to quadratic equations and inequalities represented in tables, graphs, and equations? How
are the different representations connected?
What are the similarities or differences between solving quadratic equations and solving quadratic
inequalities?
Arc : Quadratic Functions and Transformations
In what ways is the quadratic function similar to linear functions? How are they different?
How does the symbolic notation of quadratic transformations (horizontal shifts) connect to the graph?
How does the standard form compare to the vertex form of a quadratic function?
How can the standard and vertex forms of a quadratic function be used to graph the function?
TEKS
Knowledge & Skill
Student Expectation
2A.1The student uses
properties and attributes of
functions and applies
functions to problem situations
2A.1B The student is expected to collect
and organize data, make and interpret
scatter plots, fit the graph of a function to
the data, interpret the results, and
proceed to model, predict, and make
decisions and critical judgments.
2A.6 The student understands
that quadratic functions can
be represented in different
ways and translates among
their various representations.
2A.6B The student is expected to relate
representations of quadratic functions,
such as algebraic, tabular, graphical, and
verbal descriptions.
2A.8: The student formulates
equations and inequalities
based on quadratic functions,
uses a variety of methods to
solve them, and analyzes the
solutions in terms of the
situations.
2A.8A The student is expected to
analyze situations involving quadratic
functions and formulate quadratic
equations or inequalities to solve
problems.
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
Intended Learning: Students will be able to use quadratic functions
to model data and use quadratic models to analyze and make
predictions.
Team
Pattern Challenge
Holt 5.8 Curve
Fitting with
Quadratic Models
(for regression and
practice)
90
min.
Essential Questions:

What are types of patterns can be modeled by quadratic
functions?

How do you connect the pattern in a geometric model to a
rule for the pattern?

What is the difference in the regression equation when a
linear regression is chosen instead of quadratic for a set of
data?

How does one choose between which regression is
appropriate for a set of data?
Vocabulary: quadratic model, quadratic regression
MAlg2_3rdIA1a=lesson plan
MAlg2_3rdIA1a_TeamRoles
MAlg2_3rdIA1a_TeamPatternChallenge= Pattern Challenge
Activity
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
Page 1 of 5
ACM: Accelerated Curriculum for Mathematics
Algebra II
©2009 Austin ISD
Quadratic and square
root functions
Algebra and
Geometry
Quadratic and square root functions
Strand
Austin ISD Instructional Planning Guide – Mathematics
3rd Six Weeks IPG – Nov. 10 - Dec. 17 (25 days; 2 days for 6 weeks review/test and 4 days for Final Exams)
TEKS
Knowledge & Skill
Student Expectation
2A.7 The student interprets
and describes the effects of
changes in the parameters of
quadratic functions in applied
and mathematical situations.
2A.7A The student is expected to use
characteristics of the quadratic parent
function to sketch the related graphs and
connect between the y = ax2 + bx + c and
the y = a (x - h)2 + k symbolic
representations of quadratic functions.
2A.7B The student is expected to use the
parent function to investigate, describe,
and predict the effects of changes in a, h,
and k on the graphs of y = a (x - h)2 + k
form of a function in applied and purely
mathematical situations.
2A.6 The student understands
that quadratic functions can
be represented in different
ways and translates among
their various representations.
2A.4 The student connects
algebraic and geometric
representations of functions.
2A.6B The student is expected to relate
representations of quadratic functions,
such as algebraic, tabular, graphical, and
verbal descriptions.
TAKS
OBJ
Time/
Pace
DL: Shapes of
Quadrilaterals
5
(Alg1)
Holt 5-1 Using
Transformations to
Graph Quadratic
Functions (for
practice/homework)
90
min.
MAlg2_3rdIA1b1=lesson plan
MAlg2_3rdIA1b1_ Shapes of Quadratics
MAlg2_3rdIA1b1_ShapesofQuadratics_Lesson_Guide
MAlg2_3rdIA1b1_ShapesofQuadratics_Record_sheet
MAlg2_3rdIA1b1_ShapesofQuadratics_Task
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);
Closing distance
Grade 11 Lesson 8
Graphs,
Transformations,
and Solving
Equations
MAlg2_3rdIA1b2=lesson plan
45
min.
MAlg2_3rdIA1b2_StuPgs
Intended Learning: Students use the properties of quadratic
functions to identify similarities and differences between the
standard and vertex forms of quadratic functions and translate
between the forms.
2A.7B
2A.6B
(Alg1)
2A.4A
MAlg2_3rdIA1b2_matching cards
MAlg2_3rdIA1b2_QuadQuiz
2A.7
2A.4
Essential Questions:

How does the value of a affect the appearance and
location of the graph?

How does the value of the constant term c or k affect the
appearance and location of the graph?

How do h & k affect the appearance and location of the
graph?

How can you tell from the equation whether a quadratic
function has a maximum or minimum point on the graph?

Does the graph of every quadratic function have a yintercept? How can you determine the y-intercept by
looking at the equation?
Vocabulary: Vertex, Minimum , Maximum, quadratic function,
parabola, vertex form, standard form
2A.7A
2A.6
Teacher Tools
Intended Learning: Students will transform quadratic functions
and investigate the changes of a, h, and k in vertex form.
5
Algebra and Geometry
Resource
Algebra II
Holt 5.2 Properties
of Quadratic
Functions in
Standard Form
90
min.
Essential Questions:
 What applications use quadratic functions and how do
parabolas model real-life situations?
 What is the significance of the vertex and roots of a parabola
in real-life applications?
 What causes the parabola to change direction? How do h & k
effect the position of the parabola?
Vocabulary: axis of symmetry, standard form, minimum value,
maximum value, vertex form
MAlg2_3rdIA1c=lesson
MAlg2_3rdIA1c_warm_up_trans
MAlg2_3rdIA1c_alternate_opener_transp
MAlg2_3rdIA1c_Equation_Plotter_R&A2
MAlg2_3rdIA1c_InvestigateTransQuadFuncs
MAlg2_3rdIA1c_a2_ch05_02ppt = Holt 5.2 PowerPoint
MAlg2_3rdIA1c_tx_practice_b
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
Page 2 of 5
ACM: Accelerated Curriculum for Mathematics
Algebra II
Austin ISD Instructional Planning Guide – Mathematics
3rd Six Weeks IPG – Nov. 10 - Dec. 17 (25 days; 2 days for 6 weeks review/test and 4 days for Final Exams)
©2009 Austin ISD
Algebra II
Discipline Based Concept
Pacing: 25 days
Concept description: Quadratic functions can be represented in different ways, and students should be able to translate among and make connections
between the various representations.
Unit: Quadratics
Unit Pacing: 25 days
Unit Overarching
Unit Vocabulary:
Quadratic Functions have many applications in business models and science, and can also be used to determine
the path of an object that is thrown or projected.
Idea
Discipline Based Concept: Quadratic Functions


Unit Guiding
Questions


Arc Guiding
Questions
Foundations for
Functions
Strand




What are some real-world applications of quadratic functions?
How can factoring, graphing, completing the square, and the quadratic formula be used to solve quadratic
equations and inequalities?
How are solutions to quadratic equations and inequalities represented in tables, graphs, and equations?
How are the different representations connected?
What are the similarities or differences between solving quadratic equations and solving quadratic
inequalities?
Arc : Solving Quadratic Equations and Inequalities
How is solving quadratic equations similar to or different from solving quadratic inequalities?
What are the connections between the factors, solutions, intercepts, and zeroes of quadratic equations?
How do you determine the solution to a quadratic equation or inequality from a graph?
How are solutions of quadratic equations related to geometric applications?
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
Quadratic and Square Root
Functions
Resource
Time/
Pace
2A.8C The student is expected to
compare and translate between
algebraic and graphical solutions
of quadratic equations.
Teacher Tools
Intended Learning: Students will be able to use quadratic functions to model
real-world situations such as the height of a football, baseball, soccer ball or
some other type of object that is thrown or dropped.
2A.2A The student is expected to
use tools including factoring and
properties of exponents to simplify
expressions and to transform and
solve equations.
2A.8A
2A.8
TAKS
OBJ
Essential Questions:
Holt 5.3 Solving
Quadratic
Equations by
Graphing and
Factoring
90
min.

How can a student graph and/or factor quadratic equations to solve
equations?

What determines the solution(s) to quadratic equations when graphing?

What determines the solution(s) when factoring?

What is the significance of finding the zeros of a function?

What form represents a quadratic equation?
Vocabulary: Zero of a function, Root of a Function, Binomial, Trinomial,
Solutions
MAlg2_3rdIA2a= lesson
2A.8D The student is expected to
solve quadratic equations and
inequalities using graphs, tables,
and algebraic methods.
2A.6
2A.6C The student is expected to
determine a quadratic function
from its roots (real and complex) or
a graph.
MAlg2_3rdIA2a_Tech_Lab5_3
MAlg2_3rdIA2a_AccCurr_factors
MAlg2_3rdIA2a_Roots_Graphically
MAlg2_3rdIA2a_homework
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
Page 3 of 5
ACM: Accelerated Curriculum for Mathematics
Algebra II
©2009 Austin ISD
Algebra &
Geometry
Strand
TEKS
Knowledge & Skill
2A.5 The student knows the
relationship between the
geometric and algebraic
descriptions of conic sections.
Foundations for
Functions
2A.8
2A.2
2A.2
Quadratic and square root functions
2A.6
Austin ISD Instructional Planning Guide – Mathematics
3rd Six Weeks IPG – Nov. 10 - Dec. 17 (25 days; 2 days for 6 weeks review/test and 4 days for Final Exams)
Student Expectation
TAKS
OBJ
Resource
Time/
Pace
Teacher Tools
Intended Learning: Students will solve quadratic equations in order to find
the time needed for water to fall from the top of a waterfall.
2A.5E The student is expected to
use the method of completing the
square.
Holt 5.4
Completing the
Square
90
min.
2A.8D
2A.2A
2A.2A
2A.2B The student is expected to
use complex numbers to describe
the solutions of quadratic
equations.
2A.6A The student is expected to
determine the reasonable domain
and range values of quadratic
functions, as well as interpret and
determine the reasonableness of
solutions to quadratic equations
and inequalities.
2A.6B
Intended Learning: Students will be introduced to quadratic functions that
have no real zeros.
Holt 5.5
Complex
Numbers and
Roots
90
min.
2A.8
2A.8D
Review and
Quiz
2A.8B The student is expected to
analyze and interpret the solutions
of quadratic equations using
discriminants and solves quadratic
equations using the quadratic
formula.
Essential Questions:
 How does the solution method of completing the square differ from
solving by graphing and factoring quadratic equations?
 What is the importance of using square roots when completing the
square?
 Why is it important to use perfect squares when completing the square?
Vocabulary: Completing the Square
MAlg2_3rdIA2b= lesson
MAlg2_3rdIA2b_algebra_tiles
MAlg2_3rdIA2b_completing_square
MAlg2_3rdIA2b_problem_solving
MAlg2_3rdIA2b_practice_b
2A.8A
2A.8
Algebra II
45
min.
Essential Questions:
 How can the complex number be used when solving a quadratic
function?
 What occurs when a quadratic equation has no real solution?
 What form and for what purpose is the complex number “i” used in
solving quadratic equations?
 In complex numbers, which is the complex part and which is the real
part?
Vocabulary: Imaginary unit, imaginary number, complex numbers, real part,
imaginary part, complex conjugate.
MAlg2_3rdIA2c= lesson
MAlg2_3rdIA2c_warm up activity
MAlg2_3rdIA2c_alternate_exploration_trans
MAlg2_3rdIA2c_engagement activity
MAlg2_3rdIA2c_graphic_organizer_trans
MAlg2_3rdIA2c_lesson_quiz_trans
Review and Quiz over solving by graphing and factoring and completing the
square. Complex numbers and roots may be included at the teacher’s
discretion.
Intended Learning: This method will allow students how to solve quadratic
equations written in standard form.
Holt 5.6 The
Quadratic
Formula
90
min.
Essential Questions:
 How is the discriminant used when determining the type of solution for a
quadratic equation?
 The values of “a”, “b”, and “c” play what role in a quadratic equation
when written in standard form?
 What must occur before using the Quadratic Formula if an equation is
written in vertex form?
 What is the role of the discriminant and for what purpose does it play
when solving a quadratic equation?
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
Page 4 of 5
ACM: Accelerated Curriculum for Mathematics
Algebra II
©2009 Austin ISD
Strand
TEKS
Knowledge & Skill
Quadratic and square root functions
2A.8
Austin ISD Instructional Planning Guide – Mathematics
3rd Six Weeks IPG – Nov. 10 - Dec. 17 (25 days; 2 days for 6 weeks review/test and 4 days for Final Exams)
Student Expectation
Resource
Time/
Pace
Vocabulary: Discriminant
MAlg2_3rdIA2d= lesson
MAlg2_3rdIA2d_SolvingQuadraticEqsA
MAlg2_3rdIA2d_Quadratic_formula
MAlg2_3rdIA2d_Exploring_the_Discriminant
MAlg2_3rdIA2d_Quiz_Finding_Roots
MAlg2_3rdIA2d_homework
2A.8A
Intended Learning: The student will learn how tour companies and other
businesses use quadratic inequalities to make predictions of profits.
2A.8B
Holt 5.7 Solving
Quadratic
Inequalities
2A.6A
90
min.
2A.2
Teacher Tools
2A.8D The student is expected to
solve quadratic equations and
inequalities using graphs, tables,
and algebraic methods.
2A.8D
2A.6
TAKS
OBJ
Algebra II
2A.2A
Essential Questions:
 Why is there a procedure in place for solving quadratic inequalities?
 What are the rules to determine the appropriate portion of a parabola
to be graphed?
 When is the boundary of a parabola dashed or solid?
 How do you find critical values?
 Which x-values are tested in the original inequality?
 How can you determine which intervals belong to the solution set of an
inequality?
Vocabulary: Quadratic inequality in two-variables
MAlg2_3rdIA2e= lesson
MAlg2_3rdIA2e_warm_up_trans
MAlg2_3rdIA2e_alternate_exploration_trans
MAlg2_3rdIA2e_engagement activity
MAlg2_3rdIA2e_Additional Clarifying Activity
MAlg2_3rdIA2e_additional_examples_trans
MAlg2_3rdIA2e_graphic_organizer_trans
MAlg2_3rdIA2e_lesson_quiz_trans
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
Page 5 of 5
ACM: Accelerated Curriculum for Mathematics
Algebra II