INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
UNIT OVERVIEW
This unit bundles student expectations that address transformations, characteristics, and applications of cubic and cube root functions, including inverse relationships between
cube root and cubic functions. This unit also includes solving equations involving rational exponents and formulating, solving, and justifying the solutions to cube root equations.
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 II Unit 01, students investigated parent functions and their attributes. Students also analyzed inverse functions using various representations. In
Algebra II Unit 04, students used the rules of exponents to solve equations involving rational exponents.
During this unit, students describe and analyze the inverse relationship between the cubic and cube root functions and graph and write the inverse functions using notation
such as f -1 (x). Students graph the functions f(x) = x³ and f(x) = and analyze key attributes such as domain, range, intercepts, symmetries, and maximum and minimum
given an interval. Students analyze the effect on the graphs of f(x) = x³ and f(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. Students investigate parameter changes and key attributes in terms of real-world problem situations. Students solve equations involving rational
exponents that have real solutions, focusing on cubic and cube root equations. Students formulate and solve equations involving cubic and cube root equations for real-world
situations and justify the solutions in terms of the problem situations.
After this unit, in Algebra II Unit 12, students will review cubic and cube root functions and equations and their real-world applications. In subsequent courses in mathematics,
these concepts will continue to be applied to problem situations involving cubic and cube root functions and equations.
In Algebra II, graphing, analyzing key attributes, and describing the inverse relationship of cubic and cube root functions are identified in STAAR Readiness Standards 2A.2A
and 2A.2C and subsumed under STAAR Reporting Category 2: Describing and Graphing Functions and Their Inverses. Solving equations involving rational exponents is
identified in STAAR Readiness Standards 2A.7H and subsumed under STAAR Reporting Category 1: Number and Algebraic Methods. Graphing and writing cubic and cube
root functions as inverses of each other is identified in STAAR Supporting Standard 2A.2B and subsumed under STAAR Reporting Category 2: Describing and Graphing
Functions and Their Inverses. Analyzing transformations of cubic and cube root functions is identified in STAAR Supporting Standard 2A.6A and subsumed under STAAR
Reporting Category 6: Other Functions, Equations, and Inequalities. Solving cube root equations is identified in STAAR Supporting Standard 2A.6B and subsumed under
STAAR Reporting Category 6: Other Functions, Equations, and Inequalities. This unit supports 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; VIII. Problem Solving and Reasoning; IX.
Communication and Representation; X. Connections.
According to the National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics (2000), students should develop an understanding of
the algebraic properties that govern manipulation of symbols in expressions, equations, and inequalities. According to Navigating through Algebra in Grades 9 – 12, “High
school students continue to develop fluency with mathematical symbols and become proficient in operating on algebraic expressions in solving problems. Their facility with
Last Updated 08/17/2016
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Page 1 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
representation expands to include equations, inequalities, systems of equations, graphs, matrices, and functions, and they recognize and describe the advantages and
disadvantages of various representations for a particular situation. Such facility with symbols and alternative representations enables them to analyze a mathematical situation,
choose an appropriate model, select an appropriate solution method, and evaluate the plausibility of their solutions” (NCTM, 2002, p. 3). Research from the National Council of
Teachers of Mathematics (NCTM) also states, “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, 2000). 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: Research-Based Strategies for Increasing Student
Achievement (2001), such concept development is cited among strategies that increase student achievement. Specifically, classroom use of multiple representations, referred
to as nonlinguistic representations, and identifying similarities and differences have been statistically shown to improve student performance on standardized measures of
progress (Marzano, Pickering & Pollock).
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 can model problem situations and be solved using various methods.
Why are equations used to model problem situations?
How are equations used to model problem situations?
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Page 2 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
What methods can be used to solve equations?
Why is it essential to solve equations using various methods?
How can solutions to equations be represented?
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?
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?
Inverses of functions create new functions.
What relationships and characteristics exist between a function and its inverse?
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.
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Page 3 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
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
Cubic and cube root functions have unique graphs and attributes.
Algebra II Unit 07 PA 01
Multiple Representations
1. Given the functions f(x) = x³ and g(x) = – 4
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) = x³ when replaced by g(x) =
– 4.
c. Identify and analyze the key attributes of f(x)
and g(x), including domain, range, intercepts,
and symmetries.
Functions
Attributes of Functions
Inverses of Functions
Non-Linear Functions
Geometric Reasoning
Transformations
Associated Mathematical Processes
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What representations can be used to represent cubic and cube
root functions?
What are the key attributes of cubic and cube root functions and
how can they be determined from various representations?
The inverse of a function can be determined from multiple
representations.
How can the inverse of a function be determined from the graph
of the function?
How can the inverse of a function be determined from a table of
coordinate points of the function?
How can the inverse of a function be determined from the
equation of the function?
Page 4 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
PERFORMANCE ASSESSMENT(S)
d. Write f –1(x) and g–1(x) in function notation, and
graph and label the inverse functions. Analyze
the representations and write a summary
describing the relationships between the
functions and their inverses.
2. Given the functions h(x) = + 1
and m(x) = –2
OVERARCHING CONCEPTS
UNIT CONCEPTS
Tools and Techniques
Problem Solving Model
Communication
Representations
Relationships Justification
SUGGESTED DURATION : 10 days
UNIT UNDERSTANDINGS
How are a function and its inverse distinguished symbolically?
How do the attributes of inverse functions compare to the
attributes of original functions?
Transformations of the cubic function, f(x) = x³, and cube root function,
f(x) = , can be used to determine graphs and equations of
representative cubic and cube root functions in problem situations.
What are the effects of changes on the graphs of f(x) = x³ and
f(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 graphs of f(x) = x³ and
f(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 graphs of f(x) = x³ and
f(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 graphs of f(x) = x³ and
f(x) = , when f(x) is replaced by f(x) + d, for specific positive
and negative values of d?
a. Graph and label h(x) and m(x) on a coordinate
plane.
b. Determine the effects of the parameter changes
on the graph of h(x) = when replaced by m(x)
= –2
+ 1.
c. Identify and analyze the key attributes including
domain, range, intercepts, and symmetries of
h(x) and m(x).
d. Write h–1(x) and m–1(x) in function notation, and
graph and label the inverse functions.
Standard(s): 2A.1B , 2A.1C , 2A.1D , 2A.1E , 2A.1F , 2A.1G , 2A.2A , 2A.2B , 2A.2C , 2A.6A
ELPS.c.1C , ELPS.c.2D , ELPS.c.3B , ELPS.c.3D
, ELPS.c.4G , ELPS.c.4H , ELPS.c.5B
Numeric Reasoning
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Equations can be used to model and solve mathematical and real-world
Page 5 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
PERFORMANCE ASSESSMENT(S)
SUGGESTED DURATION : 10 days
OVERARCHING CONCEPTS
UNIT CONCEPTS
Algebra II Unit 07 PA 02
UNIT UNDERSTANDINGS
problem situations.
Exponents
1. Solve the following equations and justify the
solutions.
a. Algebraic Reasoning
+ 6 = 22
Equations
Solve
b. 2x – 1 = –
c. –125 + (x + 4)3 = 120 d. 2 = e. 36 – 4
Functions
Attributes of Functions
Non-Linear Functions
+ 5
= 24
2. A 20-inch by 15-inch sheet of cardboard is used to
create an open-topped box by cutting out squares
from each corner and folding the sides up. The side
length of the cut out squares is represented by x.
a. Formulate a function to model the volume of the
created box in terms of x, the side length of the
cut out squares.
Associated Mathematical Processes
Application
Tools and Techniques
Problem Solving Model
Communication
Representations
Relationships Justification
b. Identify the domain and range of the model
function and the domain and range of the
problem situation in inequality, set, and interval
notation. How do the domain and range of the
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How are real-world problem situations identified as ones that
can be modeled by cube root equations?
How are cube root equations used to model problem situations?
What methods can be used to solve cube root equations?
What are the advantages and disadvantages of various methods
used to solve cube root equations?
What methods can be used to justify the reasonableness of
solutions to cube root equations?
Cubic and cube root 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 cubic and cube
root function models?
What key attributes identify the cubic and cube root parent
function models?
What are the connections between the key attributes of cubic
and cube root function models and the real-world problem
situation?
How can cubic and cube root function representations be used
to interpret and make predictions and critical judgments in
terms of the problem situation?
Page 6 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
PERFORMANCE ASSESSMENT(S)
OVERARCHING CONCEPTS
UNIT CONCEPTS
SUGGESTED DURATION : 10 days
UNIT UNDERSTANDINGS
model function and the domain and range of the
problem situation compare?
c. What are the x- and y-intercepts of the model
function? Are they included in the domain and
range of the problem situation? Justify your
reasoning.
d. What is the maximum volume of a box that can
be created with this sheet of cardboard? What
are the dimensions of this box? What attribute
of the graph of the function represents this
solution? Justify your reasoning.
3. Wind turbines used to generate electricity are
sprouting up all over Texas. The power produced by
a wind turbine can be calculated by the formula, P
= where P is the amount of power in
kilowatts, C is the power coefficient, A is the
circular area swept by the blade in m2, ρ is the
density of the air in kg/m3, and v is the velocity of
the wind in m/s. At sea level, the density of the air
is 1.225 kg/m3. At a wind farm on the gulf coast,
each blade of the wind turbines is 50 meters long.
The turbine has a power coefficient of 0.35.
Approximately what wind velocity, rounded to the
nearest whole number, would be needed for the
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Page 7 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
OVERARCHING CONCEPTS
UNIT CONCEPTS
PERFORMANCE ASSESSMENT(S)
SUGGESTED DURATION : 10 days
UNIT UNDERSTANDINGS
wind turbine to generate 26,308 kilowatts of
electricity? Justify your reasoning.
4. Innovative Perfumes has hired a designer to create
a new style of container for its new fragrance. The
designer has decided on a decorative spherical
container. To determine the radius of the containers,
the designer uses the following formula: r = .
a. If Innovative Perfumes plans for one spherical
container to hold a volume of 2.5 cubic
centimeters, what would be the approximate
radius of the container, rounded to the nearest
tenth of a centimeter?
b. If the designer created a spherical container
with a radius of 2.5 cm, approximately how
many cubic centimeters of perfume would it
hold, rounded to the nearest tenth of a cubic
centimeter?
Standard(s): 2A.1A , 2A.1B , 2A.1C , 2A.1D , 2A.1E , 2A.1F , 2A.1G , 2A.2A , 2A.6B , 2A.7H
ELPS.c.1C , ELPS.c.1E , ELPS.c.2D , ELPS.c.3D
, ELPS.c.3F , ELPS.c.4H , ELPS.c.4K , ELPS.c.5B
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Page 8 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS
Misconceptions:
Some students may think that the cube root of a negative number is imaginary rather than understanding that the cube root of a negative number is just the negative
number.
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
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
Inverse of a function – function that undoes the original function. When composed f(f --1(x)) = x and f --1(f(x)) = x.
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 value, a function takes over a given interval of the curve
Relative minimum – smallest y-coordinate, or value, a function takes over a given interval of the curve
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.
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:
Cube root equation
Horizontal stretch
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Root
Page 9 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
Cube root function
Cubic function
Extraneous solution
Horizontal shift
SUGGESTED DURATION : 10 days
Horizontal compression
Parameter change
Properties of exponents
Rational exponents
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.
Solution
Vertical compression
Vertical shift
Vertical stretch
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 Alegbra II
TEKS Supporting 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
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Blue text: Supporting information / Clarifications from TCMPC (Specificity)
Page 10 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
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
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.
Blue text in italics: Unit-specific clarification
Black text: Texas Education Agency (TEA); Texas College and Career Readiness Standards
(TxCCRS)
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
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Note(s): The mathematical process standards may be applied to all content standards as appropriate.
TxCCRS:
X. Connections
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
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
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
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
Communicate
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
representations, including symbols, diagrams,
graphs, and language as appropriate.
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
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
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
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): 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
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
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:
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:
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
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) = x3, f(x) = Including, but not limited to:
Representations of functions, including graphs, tables, and algebraic generalizations
Readiness Standard
Cubic, f(x) = x3
Cube root, f(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, 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.
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
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
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.
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Maximum and minimum (extrema)
Relative maximum – largest y-coordinate, or value, a function takes over a given
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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Page 19 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
2A.2B
Graph and write the inverse of a function using
notation such as f -1(x). Graph, Write
Supporting Standard
THE INVERSE OF A FUNCTION USING NOTATION SUCH AS f –1 (x)
Including, but not limited to:
Inverse of a function – function that undoes the original function. When composed f(f –1(x))
= x and f –1(f(x)) = x.
Inverse functions
Cubic and cube root
Inverses of functions on graphs
Symmetric to f(x) = x Inverses of functions in tables
Interchange independent (x) and dependent (y) coordinates in ordered pairs
Inverses of functions in equation notation
Interchange independent (x) and dependent (y) variables in the equation, then solve for y
Inverses of functions in function notation
f –1(x) represents the inverse of the function f(x).
Note(s):
Grade Level(s):
Algebra II introduces inverse of a function.
Various mathematical process standards will be applied to this student expectation as
appropriate.
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Page 20 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
TxCCRS:
III. Geometric Reasoning
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.
B2 – Algebraically construct and analyze new functions.
VIII. Problem Solving and Reasoning
IX. Communication and Representation
X. Connections
2A.2C
Describe and analyze the relationship between a
function and its inverse (quadratic and square
root, logarithmic and exponential), including the
restriction(s) on domain, which will restrict its
range.
Readiness Standard
Describe, Analyze
THE RELATIONSHIP BETWEEN A FUNCTION AND ITS INVERSE
Including, but not limited to:
Relationships between functions and their inverses
All inverses of functions are relations.
Inverses of one-to-one functions are functions.
Inverses of functions that are not one-to-one can be made functions by restricting the
domain of the original function, f(x).
Characteristics of inverse relations
Interchange of independent (x) and dependent (y) coordinates in ordered pairs
Reflection over f(x) = x
Domain and range of the function versus domain and range of the inverse of the given function
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Cubic function and cube root function, f(x) = x3 and g(x) = Note(s):
Grade Level(s):
Algebra I determined if relations represented a function.
Algebra II introduces inverse of a function and restricting domain to maintain functionality.
Various mathematical process standards will be applied to this student expectation as
appropriate.
TxCCRS:
III. Geometric Reasoning
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.
B2 – Algebraically construct and analyze new functions.
VIII. Problem Solving and Reasoning
IX. Communication and Representation
X. Connections
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:
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Page 22 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
2A.6A
Analyze the effect on the graphs of f(x) = x3 and
( ) = when ( ) is replaced by ( ), ( ), ( –
fx
fx
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) = x3 AND f(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 cubic and cube root functions
Cubic
f(x) = x3
Cube root
f(x) = Representations with and without technology
Graphs
Tables
Verbal descriptions
Algebraic generalizations
Effects on the graphs of f(x) = x3 and f(x) = f(x) = when parameters a, b, c, and d are changed in
and f(x) = Effects on the graphs of f(x) = x3 and f(x) = , when f(x) is replaced by af(x) with and
without technology
a ≠ 0
|a| > 1, the graph stretches vertically
0 < |a| < 1, the graph compresses vertically
Opposite of a reflects vertically over the x-axis
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Effects on the graphs of f(x) = x3 and f(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 graphs of f(x) = x3 and f(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 graphs of f(x) = x3 and f(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) = x3 and f(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
Mathematical problem situation
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
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 cubic and cube root functions and their 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.6B
Solve cube root equations that have real roots. Supporting Standard
Solve
CUBE ROOT EQUATIONS THAT HAVE REAL ROOTS
Including, but not limited to:
Application of laws (properties) of exponents
Application of cube roots to solve cubic equations
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Applications of cubics to solve cube root equations
Reasonableness of solutions
Substitution of solutions into original problem
Graphical analysis
Mathematical problem situations
Real-world problem situations
Note(s):
Grade Level(s):
Algebra II introduces cubic and cube root functions and solving cube root equations.
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.7
Number and algebraic methods. The student
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
applies mathematical processes to simplify and
perform operations on expressions and to solve
equations. The student is expected to:
2A.7H
Solve equations involving rational exponents. Readiness Standard
Solve
EQUATIONS INVOLVING RATIONAL EXPONENTS
Including, but not limited to:
Laws (properties) of exponents
Product of powers (multiplication when bases are the same): am • an = am+n
Quotient of powers (division when bases are the same): = am-n
Power to a power: (am)n = amn
Negative exponent: a-n = Rational exponent: ; Equations when bases are the same: am = an → m = n
Solving equations with rational exponents
Isolation of base and power using properties of algebra
Exponentiation of both sides by reciprocal of power of base
Simplification to obtain solution
Verification of solution
Real-world problem situations modeled by equations involving rational exponents
Justification of reasonableness of solutions in terms of real-world problem situations
Note(s):
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Page 27 of 33
INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
SUGGESTED DURATION : 10 days
TEKS#
TEKS
UNIT LEVEL SPECIFICITY
SE#
Grade Level(s):
Prior grade levels simplified numeric expressions, including integral and rational
exponents.
Algebra II introduces equations involving rational exponents.
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.
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
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.
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
ELPS#
SUGGESTED DURATION : 10 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
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
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
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
ELPS#
SUGGESTED DURATION : 10 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
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
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
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
ELPS#
SUGGESTED DURATION : 10 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
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
(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
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
ELPS#
SUGGESTED DURATION : 10 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
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.
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,
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INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 07: Cubic and Cube Root Functions and Equations
ELPS#
SUGGESTED DURATION : 10 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
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.
Last Updated 08/17/2016
Last Updated 08/17/2016
Print Date 08/21/2016 Printed By Kendall Price, CORSICANA H IGH SCHOOL
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