INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
UNIT OVERVIEW
This unit bundles student expectations that address transformations, characteristics, and applications of absolute value functions. Absolute value equations and inequalities
are solved in mathematical problems. Absolute value equations are formulated for real-world problem situations, solved, and solutions justified in terms of the situation.
Concepts are incorporated into both mathematical and real-world problem situations. According to the Texas Education Agency, mathematical process standards including
application, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills
so that students are prepared to use mathematics in everyday life, society, and the workplace.
Prior to this unit, in Algebra I Units 01 – 04 and Unit 11 and Algebra II Unit 01, students transformed and analyzed linear functions and solved linear equations and inequalities.
During this unit, students graph the absolute value parent function, f(x) = |x|, and analyze the key attributes such as domain, range, intercepts, symmetries, and maximum and
minimum. Students analyze the effect on the graph 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, and investigate parameter changes and key attributes in terms of mathematical and real-world problem situations. Students solve absolute value linear equations and
inequalities in mathematical problems. Students also formulate absolute value linear equations that model real-world situations, solve the equations, and justify the solutions in
terms of the problem situation. After this unit, in Algebra II Unit 12, and in subsequent mathematics courses, students will continue to apply these concepts when absolute value functions, equations, and
inequalities arise in problem situations.
In Algebra II, analyzing and graphing absolute value functions are identified in STAAR Readiness Standards 2A.2A and STAAR Supporting Standard 2A.6C; and subsumed
under STAAR Reporting Category 2: Describing and Graphing Functions and Their Inverses and STAAR Reporting Category 6: Other Functions, Equations, and Inequalities.
Solving and applying absolute value equations and inequalities are identified in STAAR Readiness Standards 2A.6E, and STAAR Supporting Standards 2A.6D, 2A.6F; and
subsumed under STAAR Reporting Category 6: Other Functions, Equations, and Inequalities. This unit is supporting the development of Texas College and Career Readiness
Standards (TxCCRS): I. Numeric Reasoning B1; II. Algebraic Reasoning A1, C1, D1, D2; III. Geometric Reasoning B1, C1; VII. Functions A1, A2, B1, B2, C1, C2; VIII.
Problem Solving and Reasoning; IX. Communication and Representation; X. Connections.
According to research from the National Council of Teachers of Mathematics (NCTM), “Using a variety of representations can help make functions more understandable to a
wider range of students than can be accomplished by working with symbolic representations alone” (2009, p. 41). This unit places particular emphasis on multiple
representations. State and national mathematics standards support such an approach. The Texas Essential Knowledge and Skills repeatedly require students to relate
representations of functions, such as algebraic, tabular, graphical, and verbal descriptions. This skill is mirrored in the Principles and Standards for School Mathematics
(NCTM, 1989). Specifically, this work calls for instructional programs that enable all students to understand relations and functions and select, convert flexibly among, and use
various representations for them. More recently, the importance of multiple representations has been highlighted in Curriculum Focal Points for Prekindergarten through Grade
8 Mathematics (NCTM, 2007). According to this resource, students should be able to translate among verbal, tabular, graphical, and algebraic representations of functions and
describe how aspects of a function appear in different representations as early as Grade 8. Also, in research summaries such as Classroom Instruction That Works:
Last Updated 05/20/2015
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Page 1 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
Research-Based Strategies for Increasing Student Achievement (2001), such concept development is even cited among strategies that increase student achievement.
Specifically, classroom use of multiple representations, referred to as nonlinguistic representations, and identifying similarities and differences has been statistically shown to
improve student performance on standardized measures of progress (Marzano, Pickering & Pollock, 2001).
Marzano, R. J., Pickering, D. J., & Pollock, J. E. (2001). Classroom instruction that works: Research-based strategies for increasing student achievement. Alexandria, VA:
Association for Supervision and Curriculum Development.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.
National Council of Teachers of Mathematics. (2002). Navigating through algebra in grades 9 – 12. Reston, VA: National Council of Teachers of Mathematics, Inc.
National Council of Teachers of Mathematics. (2007). Curriculum focal points for prekindergarten through grade 8 mathematics. Reston, VA: National Council of Teachers of
Mathematics, Inc.
National Council of Teachers of Mathematics. (2009). Focus in high school mathematics: Reasoning and sense making. Reston, VA: National Council of Teachers of
Mathematics, Inc.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from
http://www.thecb.state.tx.us/collegereadiness/crs.pdf
OVERARCHING UNDERSTANDINGS AND QUESTIONS
Equations and inequalities can model problem situations and be solved using various methods.
Why are equations and inequalities used to model problem situations?
How are equations and inequalities used to model problem situations?
What methods can be used to solve equations and inequalities?
Why is it essential to solve equations and inequalities using various methods?
How can solutions to equations and inequalities be represented?
How do the representations of solutions to equations and solutions to inequalities compare?
Functions can be classified into different families with each function family having its own unique graphs, attributes, and relationships.
Why are functions classified into families of functions?
How are functions classified as a family of functions?
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Page 2 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
What graphs, key attributes, and characteristics are unique to each family of functions?
What patterns of covariation are associated with the different families of functions?
How are the parent functions and their families used to model real-world situations?
Transformation(s) of a parent function create a new function within that family of functions.
Why are transformations of parent functions necessary?
How do transformations affect a function?
How can transformations be interpreted from various representations?
Why does a transformation of a function create a new function?
How do the attributes of an original function compare to the attributes of a transformed function?
Function models for problem situations can be determined by collecting and analyzing data using a variety of representations and applied to make predictions and critical
judgments in terms of the problem situation.
Why is it important to determine and apply function models for problem situations?
What representations can be used to analyze collected data, and how are the representations interrelated?
Why is it important to analyze various representations of data, when determining appropriate function models for problem situations? How can function models be used to evaluate one or more elements in their domains?
How do the key attributes and characteristics of the function differ from the key attributes and characteristics of the function model for the problem situation?
How does technology aid in the analysis and application of modeling and solving problem situations?
PERFORMANCE ASSESSMENT(S)
OVERARCHING CONCEPTS
UNIT CONCEPTS
Algebraic Reasoning
UNIT UNDERSTANDINGS
Absolute value functions have unique graphs and attributes.
Algebra II Unit 02 PA 01
Multiple Representations
1) Given the functions f(x) = |x| and g(x) = |3(x + 1)| –
Functions
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What representations can be used to represent an absolute
value function?
What are the key attributes of an absolute value function and
Page 3 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
PERFORMANCE ASSESSMENT(S)
6
a) Graph and label f(x) and g(x) on a coordinate
plane.
b) Determine the effects of the parameter changes
on the graph of f(x) = |x| when replaced by g(x) = |3(x + 1)| – 6.
c) Identify and analyze the key attributes
including domain, range, intercepts, symmetries,
and maximum/minimum values of f(x) and g(x).
2) An architect is creating a design for the front
elevation of a building on a new software program. The
outline of the building is modeled using functions. The
function the architect uses to model one of the dormers
is d(x) = –1.5|(x – 4)| + 9.
OVERARCHING CONCEPTS
UNIT CONCEPTS
Attributes of Functions
Non-Linear Functions
Geometric Reasoning
Transformations
Associated Mathematical Processes
Application
Tools and Techniques
Problem Solving Model
Communication
Representations
Relationships Justification
SUGGESTED DURATION : 10 days
UNIT UNDERSTANDINGS
how can they be determined from various representations?
Transformations of the absolute value parent function, f(x) = |x|, can be
used to determine graphs and equations of representative absolute
value functions in problem situations.
What are the effects of changes on the graph of f(x) = |x| when
f(x) is replaced by af(x), for specific positive and negative values
of a?
What are the effects of changes on the graph of f(x) = |x| when
f(x) is replaced by f(bx), for specific positive and negative values
of b?
What are the effects of changes on the graph of f(x) = |x| when
f(x) is replaced by f(x – c), for specific positive and negative
values of c?
What are the effects of changes on the graph of f(x) = |x| when
f(x) is replaced by f(x) + d, for specific positive and negative
values of d?
a) At what point is the vertex of the dormer
located? Does this represent a maximum or
minimum of the function model?
b) What is the line of symmetry of the dormer?
c) Write a summary of the effects of the
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Page 4 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
PERFORMANCE ASSESSMENT(S)
OVERARCHING CONCEPTS
UNIT CONCEPTS
SUGGESTED DURATION : 10 days
UNIT UNDERSTANDINGS
parameter changes on f(x) = |x| that occur when
graphing the function for the dormer.
Standard(s): 2A.1A , 2A.1B , 2A.1C , 2A.1D , 2A.1E , 2A.1F , 2A.1G , 2A.2A , 2A.6C
ELPS.c.1A , ELPS.c.1C , ELPS.c.2D , ELPS.c.3B
, ELPS.c.3H , ELPS.c.4H , ELPS.c.5B , ELPS.c.5G
Algebraic Reasoning
Algebra II Unit 02 PA 02
1) Solve the following absolute value equations and
justify the solutions graphically.
a) 2|5x + 6| – 4 = 18
Equations
Expressions
Inequalities
Multiple Representations
Solve
Solution Representations
b) –32 + 5|3x – 2| = –7
Functions
c) |2x – 3| + 4 = 3
2) Solve the following absolute value inequalities and
justify the solutions graphically.
a) 3|2x – 3| + 12 ≤ 27
b) 3 – 2|4x – 6| < –3
Attributes of Functions
Non-Linear Functions
Associated Mathematical Processes
Application
Tools and Techniques
Problem Solving Model
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Absolute value functions can be used to model real-world problem
situations by analyzing collected data, key attributes, and various
representations in order to interpret and make predictions and critical
judgments.
What representations can be used to display absolute value
function models?
What key attributes identify an absolute value parent function
model?
What are the connections between the key attributes of an
absolute value function model and the real-world problem
situation?
How can absolute value function representations be used to
interpret and make predictions and critical judgments in terms
of the problem situation?
Equations and inequalities can be used to model and solve real-world
problem situations.
Page 5 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
PERFORMANCE ASSESSMENT(S)
OVERARCHING CONCEPTS
UNIT CONCEPTS
Communication
Representations
Relationships Justification
c) 5|7x + 1| – 10 > –15
d) 3|x – 4| + 2 < –1
3) Mrs. Keech’s physics students have been assigned
a laboratory activity to experimentally determine the
acceleration due to gravity by dropping a ball from a set
height and collecting data with a motion detector. After
students make their experimental determination, they
are to analyze the validity of their findings by
calculating the experimental Percent Error (PE) using
the formula below.
PE = SUGGESTED DURATION : 10 days
UNIT UNDERSTANDINGS
How are absolute value equations used to model problem
situations?
How are absolute value inequalities used to model problem
situations?
What methods can be used to solve absolute value equations?
What methods can be used to solve absolute value inequalities?
What causes extraneous solutions in absolute value equations?
How can extraneous solutions be identified in graphs, tables,
and algebraic calculations?
• 100 Mrs. Keech has told students to use 9.8067 m/s2 as
the actual value of the acceleration due to gravity and
will use the following chart to assign grades for the
activity.
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Page 6 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
PERFORMANCE ASSESSMENT(S)
OVERARCHING CONCEPTS
UNIT CONCEPTS
SUGGESTED DURATION : 10 days
UNIT UNDERSTANDINGS
a) Formulate an absolute value function to
represent the percent error as a function of
experimental value for the acceleration due to
gravity activity.
b) Create a graph of the function representing the
percent error as a function of experimental value
for the acceleration due to gravity activity.
c) In their experiment, Carol and Rey determine
an experimental value of 11.1056 m/s2 for the
acceleration due to gravity. What grade will they
earn?
d) Which experimental value(s) would result in
exactly a 10% error?
e) In order to pass physics, Trevor needs to make
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Page 7 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
PERFORMANCE ASSESSMENT(S)
OVERARCHING CONCEPTS
UNIT CONCEPTS
SUGGESTED DURATION : 10 days
UNIT UNDERSTANDINGS
at least a C on this activity. In which interval(s)
would Trevor’s experimental values for the
acceleration due to gravity need to fall for Trevor to
pass the class?
f) In professional laboratories a percent error of no
more than 30% is allowed or the results are
considered invalid. In which interval(s) would the
experimental values for the acceleration due to
gravity need to fall for this activity to be
considered invalid in a professional laboratory?
Standard(s): 2A.1A , 2A.1B , 2A.1C , 2A.1D , 2A.1E , 2A.1F , 2A.1G , 2A.6D , 2A.6E , 2A.6F
ELPS.c.1C , ELPS.c.1E , ELPS.c.2D , ELPS.c.3H
, ELPS.c.4H , ELPS.c.4K , ELPS.c.5B , ELPS.c.5G
MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS
Misconceptions:
Some students may think that |x| can equal a negative number such as |x| = –1 rather than the fact that it is the x inside the absolute that can equal –1.
Some students may think that only gives |x| = 2 rather than x = 2 and x = –2.
Underdeveloped Concepts:
Some students may not understand why they must switch the second inequality when separating an absolute value inequality; |x| < 2 Last Updated 05/20/2015
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x < 2 and x > –2.
Page 8 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
UNIT VOCABULARY
Continuous function – function whose values are continuous or unbroken over the specified domain
Discrete function – function whose values are distinct and separate and not connected; values are not continuous. Discrete functions are defined by their domain.
Domain – set of input values for the independent variable over which the function is defined
Extraneous solution – solution derived by solving the equation algebraically that is not a true solution of the equation and will not be valid when substituted back into the
original equation
Inequality notation – notation in which the solution is represented by an inequality statement
Interval notation – notation in which the solution is represented by a continuous interval(s)
Range – set of output values for the dependent variable over which the function is defined
Reflectional symmetry – symmetry in which one half of the image is a mirror image of the other over a line of reflection
Relative maximum – largest y-coordinate, or y-value, a function takes over a given interval of the curve
Relative minimum – smallest y-coordinate, or y-value, a function takes over a given interval of the curve
Set notation – notation in which the solution is represented by a set of values
x-intercept(s) – x-coordinate of a point at which the relation crosses the x-axis, meaning the y coordinate equals zero, (x, 0)
y-intercept(s) – y-coordinate of a point at which the relation crosses the y-axis, meaning the x coordinate equals zero, (0, y)
Zeros – the value(s) of x such that the y value of the relation equals zero
Related Vocabulary:
Absolute value
Function notation
Representations of solutions
Restricted domain
Simplify
Stretch/compress
Transformation
Translate
Vertex
Vertical/horizontal shift
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Page 9 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
UNIT ASSESSMENT ITEMS
Unit Assessment Items that have been published by
your district may be accessed through Search All
Components in the District Resources tab.
Assessment items may also be found using the
Assessment Creator if your district has granted access
to that tool.
SUGGESTED DURATION : 10 days
SYSTEM RESOURCES
OTHER RESOURCES
Mathematics Algebra II TEKS Supporting
Information
Mathematics Algebra II TEKS Supporting
Information (with TEKS Resource System
comments)
Mathematics Concepts Tree
STAAR Algebra II Mathematics Enhanced Blue
Print
Texas Education Agency – Mathematics Algebra II
TEKS Supporiting Information
Texas Education Agency – Texas College and
Career Readiness Standards
Texas Education Agency – Algebra I Reference
Materials
Texas Education Agency - Revised Mathematics
TEKS: Vertical Alignment Charts
Texas Instruments - Graphing Calculator Tutorials
Texas Education Agency – Mathematics Curriculum
Texas Education Agency – Assessment
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Bold black text in italics: Knowledge and
Skills Statement (TEKS)
Bold black text: Student Expectation (TEKS)
Bold red text in italics: Student Expectation
identified by TEA as a Readiness Standard for
STAAR
Bold green text in italics: Student Expectation
identified by TEA as a Supporting Standard for
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Blue text: Supporting information / Clarifications from TCMPC (Specificity)
Blue text in italics: Unit-specific clarification
Black text: Texas Education Agency (TEA); Texas College and Career Readiness Standards
(TxCCRS)
Page 10 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
STAAR
Strike-through: Indicates portions of the Student
Expectation that are not included in this unit but
are taught in previous or future unit(s)
2A.1
Mathematical process standards. The student uses
mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
2A.1A
Apply mathematics to problems arising in
everyday life, society, and the workplace.
Apply
MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE
Including, but not limited to:
Mathematical problem situations within and between disciplines
Everyday life
Society
Workplace
Note(s): The mathematical process standards may be applied to all content standards as appropriate.
TxCCRS:
X. Connections
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Page 11 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
2A.1B
Use a problem-solving model that incorporates
analyzing given information, formulating a plan
or strategy, determining a solution, justifying the
solution, and evaluating the problem-solving
process and the reasonableness of the solution.
Use
A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION,
FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION,
AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE
SOLUTION
Including, but not limited to:
Problem-solving model
Analyze given information
Formulate a plan or strategy
Determine a solution
Justify the solution
Evaluate the problem-solving process and the reasonableness of the solution
Note(s): The mathematical process standards may be applied to all content standards as appropriate.
TxCCRS:
VIII. Problem Solving and Reasoning
2A.1C
Select tools, including real objects,
manipulatives, paper and pencil, and technology
as appropriate, and techniques, including mental
math, estimation, and number sense as
appropriate, to solve problems.
Select
TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY
AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, ESTIMATION, AND NUMBER
SENSE AS APPROPRIATE, TO SOLVE PROBLEMS
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Page 12 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Including, but not limited to:
Appropriate selection of tool(s) and techniques to apply in order to solve problems
Tools
Real objects
Manipulatives
Paper and pencil
Technology
Techniques
Mental math
Estimation
Number sense
Note(s): The mathematical process standards may be applied to all content standards as appropriate.
TxCCRS:
VIII. Problem Solving and Reasoning
2A.1D
Communicate mathematical ideas, reasoning,
and their implications using multiple
representations, including symbols, diagrams,
graphs, and language as appropriate.
Communicate
MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE
REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, GRAPHS, AND LANGUAGE AS
APPROPRIATE
Including, but not limited to:
Mathematical ideas, reasoning, and their implications
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Page 13 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Multiple representations, as appropriate
Symbols
Diagrams
Graphs
Language
Note(s): The mathematical process standards may be applied to all content standards as appropriate.
TxCCRS:
IX. Communication and Representation
2A.1E
Create and use representations to organize,
record, and communicate mathematical ideas.
Create, Use
REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
Representations of mathematical ideas
Organize
Record
Communicate
Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being
communicated
Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas
Note(s): Last Updated 05/20/2015
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Page 14 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
The mathematical process standards may be applied to all content standards as appropriate.
TxCCRS:
IX. Communication and Representation
2A.1F
Analyze mathematical relationships to connect
and communicate mathematical ideas.
Analyze
MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
Mathematical relationships
Connect and communicate mathematical ideas
Conjectures and generalizations from sets of examples and non-examples,
patterns, etc.
Current knowledge to new learning
Note(s): The mathematical process standards may be applied to all content standards as appropriate.
TxCCRS:
X. Connections
2A.1G
Display, explain, or justify mathematical ideas
and arguments using precise mathematical
language in written or oral communication.
Display, Explain, Justify
MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN
WRITTEN OR ORAL COMMUNICATION
Including, but not limited to:
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Page 15 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Mathematical relationships
Connect and communicate mathematical ideas
Conjectures and generalizations from sets of examples and non-examples,
patterns, etc.
Current knowledge to new learning
Note(s): The mathematical process standards may be applied to all content standards as appropriate.
TxCCRS:
IX. Communication and Representation
2A.2
Attributes of functions and their inverses. 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:
2A.2A
Graph the functions f(x)=, f(x)=1/x, f(x)=x3, f(x)= ,
f(x)=bx, f(x)=|x|, and f(x)=logb (x) 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.
Graph
THE FUNCTIONS f(x) = |x|
Including, but not limited to:
Readiness Standard
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Representations of functions, including graphs, tables, and algebraic generalizations
Page 16 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Absolute value, f(x) = |x|
Connections between representations of families of functions
Comparison of similarities and differences of families of functions
Analyze
THE KEY ATTRIBUTES OF THE FUNCTIONS SUCH AS DOMAIN, RANGE, INTERCEPTS,
SYMMETRIES, ASYMPTOTIC BEHAVIOR, AND MAXIMUM AND MINIMUM GIVEN AN INTERVAL,
WHEN APPLICABLE
Including, but not limited to:
Domain and range of the function
Domain – set of input values for the independent variable over which the function is
defined
Continuous function – function whose values are continuous or unbroken over the
specified domain
Discrete function – function whose values are distinct and separate and not
connected; values are not continuous. Discrete functions are defined by their
domain.
Range – set of output values for the dependent variable over which the function is defined
Representation for domain and range
Verbal description
Inequality notation – notation in which the solution is represented by an inequality
statement
Set notation – notation in which the solution is represented by a set of values
Braces are used to enclose the set.
Solution is read as “The set of x such that x is an element of …”
Interval notation – notation in which the solution is represented by a continuous
interval
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Page 17 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Parentheses indicate that the endpoints are open, meaning the endpoints
are excluded from the interval.
Brackets indicate that the endpoints are closed, meaning the endpoints
are included in the interval.
Domain and range of the function versus domain and range of the contextual situation
Key attributes of functions
Intercepts/Zeros
x-intercept(s) – x coordinate of a point at which the relation crosses the x-axis,
meaning the y coordinate equals zero, (x, 0)
Zeros – the value(s) of x such that the y value of the relation equals zero
y-intercept(s) – y coordinate of a point at which the relation crosses the y-axis,
meaning the x coordinate equals zero, (0, y)
Symmetries
Reflectional symmetry – symmetry in which one half of the image is a mirror
image of the other over a line of reflection
Rotational symmetry – symmetry that occurs if a figure can be rotated less than
360° around a central point and still looks the same as the original. The number of
times a figure fits into itself in one complete rotation is called the order of
rotational symmetry.
Asymptotic behavior – behavior such that as x approaches infinity, f(x) approaches a
given value
Vertical asymptote – vertical line approached by the curve as the function
approaches positive or negative infinity. Vertical asymptotes are never crossed by
the curve.
Horizontal asymptote – horizontal line approached by the curve as the function
approaches positive or negative infinity. Horizontal asymptotes may be crossed
by the curve.
Maximum and minimum (extrema)
Relative maximum – largest y-coordinate, or value, a function takes over a given
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
interval of the curve
Relative minimum – smallest y-coordinate, or value, a function takes over a given
interval of the curve
Use key attributes to recognize and sketch graphs
Application of key attributes to real-world problem situations
Note(s):
Grade Level(s):
The notation represents the set of real numbers, and the notation represents the
set of integers.
Algebra I studied parent functions f(x) = x, f(x) = x2, and f(x) = b x and their key
attributes.
Precalculus will study polynomial, power, trigonometric, inverse trigonometric, and
piecewise defined functions, including step functions.
Various mathematical process standards will be applied to this student expectation as
appropriate.
TxCCRS:
III. Geometric Reasoning
B1 – Identify and apply transformations to figures.
C1 – Make connections between geometry and algebra.
VII. Functions
A1 – Recognize whether a relation is a function.
A2 – Recognize and distinguish between different types of functions.
B1 – Understand and analyze features of a function.
VIII. Problem Solving and Reasoning
IX. Communication and Representation
X. Connections
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
2A.6
Cubic, cube root, absolute value and rational
functions, equations, and inequalities. 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:
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. Supporting Standard
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
Including, but not limited to:
General form of the absolute value function
Absolute value
f(x) = |x|
Representations with and without technology
Graphs
Tables
Verbal descriptions
Algebraic generalizations
Effects on the graph of f(x) = |x| when parameters a, b, c, and d are changed in f(x) = a|b(x – c)|
+ d
Effects on the graph of f(x) = |x|, when f(x) is replaced by af(x) with and without
technology
a ≠ 0
|a| > 1, the graph stretches vertically
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
0 < |a| < 1, the graph compresses vertically
Opposite of a reflects vertically over the x-axis
Effects on the graph of f(x) = |x|, when f(x) is replaced by f(bx) with and without
technology
b ≠ 0
|b| > 1, the graph compresses horizontally
0 < |b| < 1, the graph stretches horizontally
Opposite of b reflects horizontally over the y-axis
Effects on the graph of f(x) = |x|, when f(x) is replaced by f(x – c) with and without
technology
c = 0, no horizontal shift
Horizontal shift left for values of c < 0 by |c| units
For f(x + 2) → f(x – (–2)), c = –2, and the function moves to the left two
units.
Horizontal shift right for values of c > 0 by |c| units
For f(x – 2), c = 2, and the function moves to the right two units
Effects on the graph of f(x) = |x|, when f(x) is replaced by f(x) + d with and without
technology
d = 0, no vertical shift
Vertical shift down for values of d < 0 by |d| units
Vertical shift up for values of d > 0 by |d| units
Connections between the critical attributes of transformed function and f(x) = |x|
Determination of parameter changes given a graphical or algebraic representation
Determination of a graphical representation given the algebraic representation or
parameter changes
Determination of an algebraic representation given the graphical representation or
parameter changes
Descriptions of the effects on the domain and range by the parameter changes
Effects of multiple parameter changes
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Mathematical problem situation
Real-world problem situation
Note(s):
Grade Level(s):
Algebra I determined effects on the graphs of the parent functions, f(x) = x and f(x)
= x2 when f(x) is replaced by af(x), f(x) + d, f(x – c), f(bx) for specific values
of a, b, c, and d.
Algebra II introduces the absolute value function and its transformations.
Various mathematical process standards will be applied to this student expectation as
appropriate.
TxCCRS:
III. Geometric Reasoning
B1 – Identify and apply transformations to figures.
C1 – Make connections between geometry and algebra.
VII. Functions
A2 – Recognize and distinguish between different types of functions.
B1 – Understand and analyze features of a function.
VIII. Problem Solving and Reasoning
IX. Communication and Representation
X. Connections
2A.6D
Formulate absolute value linear equations. Supporting Standard
Formulate
ABSOLUTE VALUE LINEAR EQUATIONS
Including, but not limited to:
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Data collection activities with and without technology
Data modeled by absolute value functions
Real-world problem situations
Real-world problem situations modeled by absolute value functions
Data tables
Technology methods
Transformations of f(x) = |x|
Note(s):
Grade Level(s):
Grade 6 defined absolute value and identified the absolute value of a number.
Algebra II introduces the absolute value equation and its applications.
Various mathematical process standards will be applied to this student expectation as
appropriate.
TxCCRS:
VII. Functions
B1 – Understand and analyze features of a function.
B2 – Algebraically construct and analyze new functions.
C2 – Develop a function to model a situation.
VIII. Problem Solving and Reasoning
IX. Communication and Representation
X. Connections
2A.6E
Solve absolute value linear equations. Readiness Standard
Solve
ABSOLUTE VALUE LINEAR EQUATIONS
Including, but not limited to:
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Methods for solving absolute value linear equations with and without technology
Graphs
Algebraic methods
Solving process
Transform the equation so that absolute expression is on one side of the
equation and all other variable terms and constants are on the other side of
the equation.
Separate the equation into two parts divided by “or”:
Expression inside the absolute value equal to the other side of the
equation
Expression inside the absolute value equal to the opposite of the
other side of the equation
|x| = 5 → x = 5 or x = –5
Extraneous solution – solution derived by solving the equation algebraically
that is not a true solution of the equation and will not be valid when
substituted back into the original equation
Solving absolute value equations involves separating the absolute value into
both the possible positive value inside the absolute and the possible
negative value inside the absolute. In the case of |x| = 2, The x value can
be either positive or negative 2. However, this is not a reversible situation,
|x| = 2 but |x| –2.
Justification of solutions with and without technology
Graphs
Substitution of solutions into original functions
Extraneous solutions
Real-world problem situations modeled by absolute value functions
Justification of reasonableness of solutions in terms of the real-world problem situations
or data collections
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Page 24 of 32
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Note(s):
Grade Level(s):
Grade 6 defined absolute value and identified the absolute value of a number.
Algebra II introduces the absolute value equation and its applications.
Various mathematical process standards will be applied to this student expectation as
appropriate.
TxCCRS:
I. Numeric Reasoning
B1 – Perform computations with real and complex numbers.
II. Algebraic Reasoning
A1 – Explain and differentiate between expressions and equations using words
such as “solve,” “evaluate,” and “simplify.”
C1 – Recognize and use algebraic (field) properties, concepts, procedures, and
algorithms to solve equations, inequalities, and systems of linear equations.
D1 – Interpret multiple representations of equations and relationships.
D2 – Translate among multiple representations of equations and relationships.
III. Geometric Reasoning
C1 – Make connections between geometry and algebra.
VIII. Problem Solving and Reasoning
IX. Communication and Representation
X. Connections
2A.6F
Solve absolute value linear inequalities. Supporting Standard
Solve
ABSOLUTE VALUE LINEAR INEQUALITIES
Including, but not limited to:
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Methods for solving absolute value linear inequalities with and without technology
Graphs
Algebraic methods
Solving process
Isolation of absolute expression on one side of the inequality
Separation of the inequality into two parts
Greater than (>) or greater than or equal to (≥)
First part: expression inside the absolute value set greater
than or greater than or equal to other side of the inequality
Second part: expression inside the absolute value set less
than or less than or equal to the opposite of the other side of
the inequality
Parts separated by “or”
Representation of solutions Symbolic notation
Interval notation
Graphical notation
Less than (<) or less than or equal to (≤)
First part: expression inside the absolute value set less than
or less than or equal to other side of the inequality
Second part: expression inside the absolute value set
greater than or greater than or equal to the opposite of the
other side of the inequality
Parts separated by “and”
Representation of solutions
Symbolic notation
Interval notation
Graphical notation
Justification of solutions of absolute value inequalities with and without technology
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Graphs
Substitution of solutions into original functions
Removal of extraneous solutions
Note(s):
Grade Level(s):
Grade 6 defined absolute value and identified the absolute value of a number.
Algebra II introduces absolute value inequalities.
Various mathematical process standards will be applied to this student expectation as
appropriate.
TxCCRS:
II. Algebraic Reasoning
A1 – Explain and differentiate between expressions and equations using words
such as “solve,” “evaluate,” and “simplify.”
C1 – Recognize and use algebraic (field) properties, concepts, procedures, and
algorithms to solve equations, inequalities, and systems of linear equations.
D1 – Interpret multiple representations of equations and relationships.
D2 – Translate among multiple representations of equations and relationships.
III. Geometric Reasoning
C1 – Make connections between geometry and algebra.
VIII. Problem Solving and Reasoning
IX. Communication and Representation
X. Connections
ELPS#
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
The English Language Proficiency Standards (ELPS), as required by 19 Texas Administrative Code, Chapter 74, Subchapter A, §74.4, outline English language
proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement ELPS as an integral part of
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
ELPS#
SUGGESTED DURATION : 10 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
each subject in the required curriculum.
School districts shall provide instruction in the knowledge and skills of the foundation and enrichment curriculum in a manner that is linguistically accommodated
commensurate with the student’s levels of English language proficiency to ensure that the student learns the knowledge and skills in the required curriculum.
School districts shall provide content-based instruction including the cross-curricular second language acquisition essential knowledge and skills in subsection (c) of the
ELPS in a manner that is linguistically accommodated to help the student acquire English language proficiency.
http://ritter.tea.state.tx.us/rules/tac/chapter074/ch074a.html#74.4 Choose appropriate ELPS to support instruction.
ELPS.c.1
The ELL uses language learning strategies to develop an awareness of his or her own learning processes in all content areas. In order for the ELL
to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be
linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency.
The student is expected to:
ELPS.c.1A
use prior knowledge and experiences to understand meanings in English
ELPS.c.1B
monitor oral and written language production and employ self-corrective techniques or other resources
ELPS.c.1C
use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and
grade-level vocabulary
ELPS.c.1D
speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying
ideas by defining or describing when exact English words are not known)
ELPS.c.1E
internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept
and language attainment
ELPS.c.1F
use accessible language and learn new and essential language in the process
ELPS.c.1G
demonstrate an increasing ability to distinguish between formal and informal English and an increasing knowledge of when to use each one
commensurate with grade-level learning expectations
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
ELPS#
SUGGESTED DURATION : 10 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
ELPS.c.1H
develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for patterns in language, and
analyzing sayings and expressions commensurate with grade-level learning expectations.
ELPS.c.2
The ELL listens to a variety of speakers including teachers, peers, and electronic media to gain an increasing level of comprehension of newly
acquired language in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language
acquisition in listening. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all
instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the
student's level of English language proficiency. The student is expected to:
ELPS.c.2A
distinguish sounds and intonation patterns of English with increasing ease
ELPS.c.2B
recognize elements of the English sound system in newly acquired vocabulary such as long and short vowels, silent letters, and consonant
clusters
ELPS.c.2C
learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions
ELPS.c.2D
monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed
ELPS.c.2E
use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language
ELPS.c.2F
listen to and derive meaning from a variety of media such as audio tape, video, DVD, and CD ROM to build and reinforce concept and
language attainment
ELPS.c.2G
understand the general meaning, main points, and important details of spoken language ranging from situations in which topics, language,
and contexts are familiar to unfamiliar
ELPS.c.2H
understand implicit ideas and information in increasingly complex spoken language commensurate with grade-level learning expectations
ELPS.c.2I
demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken
messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level
needs.
ELPS.c.3
The ELL speaks in a variety of modes for a variety of purposes with an awareness of different language registers (formal/informal) using vocabulary
with increasing fluency and accuracy in language arts and all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced
high stage of English language acquisition in speaking. In order for the ELL to meet grade-level learning expectations across the foundation and
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
ELPS#
SUGGESTED DURATION : 10 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded)
commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.3A
practice producing sounds of newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters to pronounce
English words in a manner that is increasingly comprehensible
ELPS.c.3B
expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing
people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using
routine language needed for classroom communication
ELPS.c.3C
speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as
more English is acquired
ELPS.c.3D
speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency
ELPS.c.3E
share information in cooperative learning interactions
ELPS.c.3F
ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and
expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during
extended speaking assignments
ELPS.c.3G
express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on
a variety of social and grade-appropriate academic topics
ELPS.c.3H
narrate, describe, and explain with increasing specificity and detail as more English is acquired
ELPS.c.3I
adapt spoken language appropriately for formal and informal purposes
ELPS.c.3J
respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and
language attainment.
ELPS.c.4
The ELL reads a variety of texts for a variety of purposes with an increasing level of comprehension in all content areas. ELLs may be at the
beginning, intermediate, advanced, or advanced high stage of English language acquisition in reading. In order for the ELL to meet grade-level
learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
ELPS#
SUGGESTED DURATION : 10 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
(communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1,
certain of these student expectations apply to text read aloud for students not yet at the stage of decoding written text. The student is expected to:
ELPS.c.4A
learn relationships between sounds and letters of the English language and decode (sound out) words using a combination of skills such as
recognizing sound-letter relationships and identifying cognates, affixes, roots, and base words
ELPS.c.4B
recognize directionality of English reading such as left to right and top to bottom
ELPS.c.4C
develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used
routinely in written classroom materials
ELPS.c.4D
use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to
enhance comprehension of written text
ELPS.c.4E
read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned
ELPS.c.4F
use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm
understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly
challenging language
ELPS.c.4G
demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding
to questions, and taking notes commensurate with content area and grade level needs
ELPS.c.4H
read silently with increasing ease and comprehension for longer periods
ELPS.c.4I
demonstrate English comprehension and expand reading skills by employing basic reading skills such as demonstrating understanding of
supporting ideas and details in text and graphic sources, summarizing text, and distinguishing main ideas from details commensurate with
content area needs
ELPS.c.4J
demonstrate English comprehension and expand reading skills by employing inferential skills such as predicting, making connections between
ideas, drawing inferences and conclusions from text and graphic sources, and finding supporting text evidence commensurate with content
area needs
ELPS.c.4K
demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and
performing critical analyses commensurate with content area and grade-level needs.
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 02: Absolute Value Functions, Equations, and Inequalities
ELPS#
SUGGESTED DURATION : 10 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
ELPS.c.5
The ELL writes in a variety of forms with increasing accuracy to effectively address a specific purpose and audience in all content areas. ELLs may
be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in writing. In order for the ELL to meet gradelevel learning expectations across foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated
(communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1,
certain of these student expectations do not apply until the student has reached the stage of generating original written text using a standard
writing system. The student is expected to:
ELPS.c.5A
learn relationships between sounds and letters of the English language to represent sounds when writing in English
ELPS.c.5B
write using newly acquired basic vocabulary and content-based grade-level vocabulary
ELPS.c.5C
spell familiar English words with increasing accuracy, and employ English spelling patterns and rules with increasing accuracy as more English
is acquired
ELPS.c.5D
edit writing for standard grammar and usage, including subject-verb agreement, pronoun agreement, and appropriate verb tenses
commensurate with grade-level expectations as more English is acquired
ELPS.c.5E
employ increasingly complex grammatical structures in content area writing commensurate with grade-level expectations, such as:
ELPS.c.5F
write using a variety of grade-appropriate sentence lengths, patterns, and connecting words to combine phrases, clauses, and sentences in
increasingly accurate ways as more English is acquired
ELPS.c.5G
narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired.
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