Algebra II
2016-17 ~ Unit 2
Title
Suggested Time Frame
1st Six Weeks
Suggested Duration: 16 Days
Guiding Questions
Absolute Value – Functions, Equations, and Inequalities
*CISD Safety Net Standards: 2A.2A
Big Ideas/Enduring Understandings
•
•
Functions can be used to show various forms of information,
both conceptual and real world, to help understand what is
being expressed.
Absolute value expresses the distance between two points and
is the same no matter from which direction the information is
viewed.
•
•
Why would one choose to use an equation, a graph, or a table to
solve a problem?
If a person was to drive their car in reverse, would they remove
miles from their odometer? Why or why not?
Vertical Alignment Expectations
TEA Vertical Alignment Document
Sample Assessment Question
COMING SOON………………………………….
The resources included here provide teaching examples and/or meaningful learning experiences to address the District Curriculum. In order to address the TEKS to the proper
depth and complexity, teachers are encouraged to use resources to the degree that they are congruent with the TEKS and research-based best practices. Teaching using only the
suggested resources does not guarantee student mastery of all standards. Teachers must use professional judgment to select among these and/or other resources to teach the
district curriculum. Some resources are protected by copyright. A username and password is required to view the copyrighted material. District Specificity/Examples TEKS
clarifying examples are a product of the Austin Area Math Supervisors TEKS Clarifying Documents.
Algebra II ~ Unit 2
Updated April 7, 2016
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Ongoing TEKS
Algebra II
2016-17 ~ Unit 2
Mathematical Process Standards - The student uses mathematical processes to acquire and demonstrate mathematical understanding. The
student is expected to:
1A apply mathematics to problems arising in everyday life, society, and the workplace;
Apply
Mathematical Practices
1) Make sense of problems and persevere in
solving them.
2) Reason abstractly and quantitatively.
3) Construct viable arguments and critique
the reasoning of others.
4) Model with mathematics.
5) Use appropriate tools strategically.
6) Attend to precision.
7) Look for and make use of structure.
8) Look for and express regularity in repeated
reasoning.
1D Communicate mathematical ideas, reasoning, and their implications using multiple
Communicate:
representations, including symbols, diagrams, graphs, and language as appropriate;
Have the students:
1) Keep a journal
2) Participate in online forums for the
classroom like Schoology or Edmoto.
3) Write a summary of their daily notes as
part of the assignments.
1E Create and use representations to organize, record, and communicate mathematical
Create, Use
ideas;
The students can:
1) Create and use graphic organizers for
things such as parent functions. This
organizer can have a column for a) the name
of the functions, b) the parent function
equation, c) the graph, d) the domain, e) the
range, f) any asymptotes.
Algebra II ~ Unit 2
Updated April 7, 2016
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Algebra II
2016-17 ~ Unit 2
1F analyze mathematical relationships to connect and communicate mathematical ideas;
Knowledge and Skills
with Student
Expectations
2A.6E
2A.2A
2A.6C
2A.6D
2A.6F
Algebra II ~ Unit 2
Updated April 7, 2016
This organizer can be filled out all at once, or
as you go through the lessons. They could
even use this on assessments at the
teacher’s discretion.
ANALYZE
District Specificity/ Examples
•
•
Major Points
Analyzing Functions
Absolute Value Functions and Equations
Vocabulary
•
•
•
•
•
•
•
Coefficient
Domain
Function
Interval
Quadratic
Function
Range
Transformation
Suggested Resources
Resources listed and categorized to indicate
suggested uses. Any additional resources
must be aligned with the TEKS.
Text Resources
• HMH Algebra II Text Book
Lessons:
• Domain, Range, and End
Behavior
• Characteristics of
Functions
• Transformations of
Function Graphs
• Inverses of Functions
• Graphing Absolute Value
Functions
• Solving Absolute Value
Equations
Page 3 of 14
2A.2
Linear Functions,
Equations, and
Inequalities
The student applies
mathematical
processes
to understand that
functions have distinct
key
attributes and
understand the
relationship
between a function
and its inverse. The
student is expected to:
*CISD Safety Net*
2A.2A
graph the functions , f (x) =
√x, f (x) = 1/x
f(x) = x3 , f(x) = 3√x , f(x) =
xb , f(x) = |x| ,
and f(x) = logbx where b is
2, 10, and e, and,
when applicable, analyze
the key attributes
such as domain, range,
intercepts,
symmetries, asymptotic
behavior, and
maximum and minimum
given an interval
Algebra II ~ Unit 2
Updated April 7, 2016
Algebra II
2016-17 ~ Unit 2
Websites:
• https://my.hrw.com
• https://www.khanacadem
y.org/
• http://illuminations.nctm.
org/
• Region XI: Livebinder
2A.2A
Graph
* This could work here as well as in the example above. The
graphs would be stressed at this standard.
Parent Functions Chart
The students can:
1) Create and use graphic organizers for things such as parent
functions. This organizer can have a column for a) the name
of the functions, b) the parent function equation, c) the graph,
d) the domain, e) the range, f) any asymptotes.
This organizer can be filled out all at once, or as you go through
the lessons. They could even use is on assessments at the
teacher’s discretion.
Page 4 of 14
Algebra II
2016-17 ~ Unit 2
2A.2B
graph and write the
inverse of a
function using notation
such as f -1 (x);
2A.2D
use the composition of two
functions,
including the necessary
restrictions on the
domain, to determine if the
functions are
inverses of each other.
2A.6
Cubic, Cube Root,
Absolute Value and
Rational Functions,
Equations, and
Inequalities.
2A.2B
Graph, Write
The students should be given several graphs that may or may
not be “functions”. In teams, the students will: a) identify points
on the given graph, b) identify the domain and range
of the given graphs, c) switch the x and y values, d) graph the
results using the “new” points, e) write the domain and range
of the result. The teacher can guide them to the idea that the
inverse is the original graph reflected about the line y = x.
2A.2D
Use, Determine
Remind the students of composition of functions from Algebra 1.
Explain what composition of functions is and how to do the
work. Then give them several examples grouped into two groups: 1)
These functions are inverses of each other, and 2) these
functions are not inverses of each other. Ask them to determine
what the inverses have in common that the non-inverse
functions do not have in common. Lead them to the understanding
that if two functions are inverses of each other, then f(g(x)) = x and
g(f(x)) = x. If there is any other result, than the functions are not
inverses of each other.
2A.6E
Finding the Inverse
Algebraically
See A&M Consolidated 05-06
Spring Unit 1
Topic 1-1 and 1-2
Verifying Inverses
See A&M Consolidated 05-06
Spring Unit 1 Topic 1-3
See A&M Consolidated 05-06
Fall Unit 1
Topic 1-5
Solving an Absolute Value Equation
Algebra II ~ Unit 2
Updated April 7, 2016
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The student applies
mathematical
processes
to understand that
cubic, cube root,
absolute
value and rational
functions, equations,
and inequalities can be
used to model
situations,
solve problems, and
make predictions. The
student is expected to
Solve and graph: |2x − 1| = 5
2A.6E
solve absolute value linear
equations;
Solving a Multi-Step Absolute Value
Equation
Solve and graph:
3|x + 2| - 1 = 8
Algebra II ~ Unit 2
Updated April 7, 2016
Algebra II
2016-17 ~ Unit 2
Solving Absolute Value
Equations Practice
Solving Absolute Value
Equations Graphically
Khan Academy Tutorial
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Algebra II
2016-17 ~ Unit 2
Extraneous Solutions
What is the solution |3x + 2| = 4x + 5
Check for extraneous solutions.
2A.6C
analyze the effect on the
graphs of f(x)
= |x| when f(x) is replaced
by af(x), f(bx),
f(x-c), and f(x) + d for
specific positive and
negative real values of a, b,
c, and d;
2A.6C
Analyze
Example 1: Vertical and Horizontal
Transformations of Absolute Value functions
Use the graph of f (x) = |x| to graph
g (x) = |x + 3| and h(x) = |x| + 2 .
The graph of h(x) = |x| + 2 is the graph of
f (x) = |x| shifted up 2 units.
The graph of g (x) = |x + 3| is the graph of
f (x) = |x| shifted 3 units to the left.
Transformations Tutorial
Transformations of Absolute
Value Functions Practice
Algebra II ~ Unit 2
Updated April 7, 2016
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Algebra II
2016-17 ~ Unit 2
2A.6D
formulate absolute value
linear equations;
2A.6D
Example:
The solutions of =|x| 3 are the two points
that are 3 units from zero. The solution is a
disjunctions: x = 3 or x = − 3 .
2A.6F
solve absolute value linear
inequalities;
See A&M Consolidated 05-06
Fall Unit 1
Topic 1-5 and Topic 1-7
2A.6F
Solving Absolute Value Inequality |x| < a
x > − a and x < a or
Algebra II ~ Unit 2
Updated April 7, 2016
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−a<x<a
Algebra II
2016-17 ~ Unit 2
Absolute Value Inequalities
Tutorial from Khan Academy
Example:
The solutions of |x| < 3 are the points that are less than 3 units
from zero.
The solution is the conjunction: − 3 < x < 3.
Solving the Absolute Value Inequality
( |x| < a)
Solve and Graph:
Solving Absolute Value Inequality |x| > a
x < − a OR x > a
Example:
The solutions of |x| > 3 are the points that are more than 3 units
from zero.
Algebra II ~ Unit 2
Updated April 7, 2016
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Algebra II
2016-17 ~ Unit 2
The solution is the disjunction: x <− 3 OR x > 3.
Solving the Absolute Value Inequality ( |x| > a )
Solve and graph:
2A.7
Number and Algebraic
Methods
The student applies
mathematical
processes
to simplify and perform
operations on
Algebra II ~ Unit 2
Updated April 7, 2016
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Algebra II
2016-17 ~ Unit 2
expressions and to
solve equations. The
student is expected to:
2A.7I
write the domain and
range of a function
in interval notation,
inequalities, and set
notation.
2A.7I
Students should know:
Domain and Range Matching
Activity
Set Notation :
What is domain and range?
Domain and Range of a graph
Interval Notation:
Interval Notation Tutorial
Set Builder Notation
Example:
Algebra II ~ Unit 2
Updated April 7, 2016
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Write the domain and range in interval notation, inequalities
and set notation.
2A.8
Data
The student applies
mathematical
processes
to analyze data, select
appropriate models,
write corresponding
functions, and make
predictions. The
student is expected to:
2A.8B
use regression methods
available through
technology to write a linear
function, a quadratic
function, and an
exponential function from
a given set of data;
Algebra II ~ Unit 2
Updated April 7, 2016
2A.8B
Algebra II
2016-17 ~ Unit 2
How to do linear regression
on the graphing calculator
video
Printable Calculator
Instructions
Linear Regression Activity
Linear Regression Activities
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Algebra II
2016-17 ~ Unit 2
Algebra II ~ Unit 2
Updated April 7, 2016
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Algebra II
2016-17 ~ Unit 2
Quadratic Regression Tutorial
Pass the ball activity
Exponential Worksheet with
Answers
Step by Step Exponential
Regression Steps
M&M's and Rhinos
More M&M's
NSA Exponential Growth and
Decay Activities
From the graphs, it looks like the quadratic functions is the best
fit for the data set.
Algebra II ~ Unit 2
Updated April 7, 2016
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