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INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
UNIT OVERVIEW
This unit bundles student expectations that address the exploration of linear and nonlinear data and their representations and relationships. Data includes models of linear,
quadratic, exponential, and inverse functions. Functional relationships are the basis of algebra and will be the focus of Algebra 1 throughout the course. The exploration of
functions through data collection and analysis is a foundation for this study and is introduced at the beginning of Algebra 1.
Prior to this unit, in Grade 8, students were introduced to arithmetic sequences, mathematical relationships, and multiple forms of representations.
During this unit, those topics are extended to include the development of the concept of function by an exploration of the representations and characteristics of functions to be
studied in Algebra 1. Graphing calculator technology is incorporated to collect and analyze data throughout the unit.
After this unit, students will continue to apply these skills, as linear and quadratic functions will be explored with greater depth and complexity in subsequent Algebra 1 units.
Focusing on relationships, properties, and attributes of functions in algebra is emphasized in the Texas College and Career Readiness Standards (TxCCRS): I. Numeric
Reasoning B1; II. Algebraic Reasoning A1, D1, D2; III. Geometric Reasoning C2; IV. Measurement Reasoning D1; VI. Statistical Reasoning A1, B1, B2, B4, C1, C2, C3; VII.
Functions A1, A2, B1, B2, C1, C2; VIII. Problem Solving and Reasoning B2, C2; IX. Communication and Representation A1, A3, B1, B2, C1; X. Connections A1; and STAAR
Readiness Standards: A.1D, A.1E, A.2B, A.2D, and A.4A. Independent and dependent variables, functionality, symbols, data patterns, and functional notation are addressed
in STAAR Supporting Standards: A.1A, A.1B, A.3A, A.3B, and A.4C. Inverse functions and exponential functions are addressed in STAAR Supporting Standards: A.11B and
A.11C.
TEKS Resource System takes a functional approach to Algebra as supported by the National Council of Teachers of Mathematics (NCTM), the Texas Education Agency
(TEA) in the math professional development modules and Algebra 1 EOC Success, and other mathematics research. According to Navigating through Algebra in Grades 9 –12 (2002), “much of what has traditionally been Algebra 1 in secondary schools is expected content for the middle grades. It is imperative then that a broadening anddeepening of mathematics content take place in high school. New topics…such as classes of functions and using technology on symbolic expressions are emerging in thehigh school curriculum” (NCTM, p. v). Additionally, Algebra in a Technological World (1995) states, the high school algebra curriculum should undergo “a shift in perspectivefrom algebra as skills for transforming, simplifying, and solving symbolic expressions to algebra as a way to express and analyze relationships” (NCTM, p. v). By beginningformal algebra with real-life situations that are naturally algebraic, students understand that formal algebra is not only a manipulation of symbols, but also a logical way to
approach mathematical situations in an effort to make sense of them. Experiencing real-life functional situations and their characteristics helps build algebraic habits of mind
(Driscoll, 1999). Through careful instruction, teachers connect real-life with algebraic representation and build conceptual understanding before delving into algebraic
manipulation. If students completely develop solving equations using symbolic manipulation before they develop a solid conceptual foundation for their work, they will be unable
to do more than symbolic manipulation (National Research Council, 1998).
Driscoll, M. (1999). Fostering algebraic thinking: A guide for teachers grades 6 – 10. Portsmouth, VA: Heinemann.
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 1 of 23
National Council of Teachers of Mathematics. (1995). Curriculum and evaluation standards for school mathematics: Algebra in a technological world. 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 Research Council. (1998). High school mathematics at work: Essays and examples for the education of all students. Washington, DC: National Academy Press.
Texas Education Agency. (2009). Texas college and career readiness standards. Austin, TX: Author.
PERFORMANCE ASSESSMENT(S)OVERARCHING CONCEPTS
UNIT CONCEPTSUNIT UNDERSTANDINGS
Algebra I Unit 01 PA 01
Create a graphic organizer that includes a table, graph,
verbal description, and algebraic generalization for a
linear function in a problem situation and a graphic
organizer for a quadratic function in a problem situation
such as the following:
Susan asked her father for a no-interest loan of
$8,500 so that she could purchase a used car.
She told her father that she would repay the loan
at a rate of $250 per month. How much will be
remaining on her loan after one year? When will
she have paid off the loan?
Study the figures below of one-inch square tiles
that are being used to determine the relationship
between side length and area. How many tiles
will be required to build a figure if the side length
is 8? What is the side length of a figure requiring
Foundations for Functions –
Relationships; Representations;
Properties and Attributes
Functional relationships for problem situations (linear and quadratic)
can be determined by collecting data and analyzing its properties and
attributes using a variety of representations, in order to interpret and
make predictions and critical judgments.
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 2 of 23
PERFORMANCE ASSESSMENT(S)OVERARCHING CONCEPTS
UNIT CONCEPTSUNIT UNDERSTANDINGS
121 tiles?
For each situation, write an analysis of the relationships
between the representations and a description of the
attributes (relation/function, independent/dependent,
domain/range, discrete/continuous, function notation,
etc.). Use the representations to make predictions and
critical judgments in the problem situation.
Standard(s): A.1A , A.1B , A.1D , A.1E , A.2B , A.2D ,
A.3A , A.3B , A.4A , A.4C ELPS.c.1C , ELPS.c.3D ,
ELPS.c.3H , ELPS.c.5B
Functional relationships for problem situations (inverse and
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 3 of 23
PERFORMANCE ASSESSMENT(S)OVERARCHING CONCEPTS
UNIT CONCEPTSUNIT UNDERSTANDINGS
Algebra I Unit 01 PA 02
Create a graphic organizer that includes a table, graph,
verbal description, and algebraic generalization for an
inverse function in a problem situation and a graphic
organizer for an exponential function in a problem
situation such as the following:
Jolene was commissioned by Welco Systems to
type a 1,000 page report by Thursday. They are
paying her $400 for the job. Since Jolene is not
sure if she can finish on time, she is getting
some people to help her type. She does not
want to use more than 10 people to help with the
job. She will split the $400 evenly between
everyone who types, including herself. If four
people type the report, how much will each
person make? If each person receives $50.00,
how many people did Jolene hire to help her
type?
The amount of a certain medication left in the
blood stream decreases by 25% after each
successive hour. After an initial dosage of 10
mg, Allen wants to analyze the amount of
medication in his bloodstream over
time.Approximately how many mg were left in
Allen’s bloodstream after 4 hours? After how
exponential) can be determined by collecting data and analyzing its
properties and attributes using a variety of representations in order to
interpret and make predictions and critical judgments.
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 4 of 23
PERFORMANCE ASSESSMENT(S)OVERARCHING CONCEPTS
UNIT CONCEPTSUNIT UNDERSTANDINGS
much elapsed time would Allen have
approximately mg in his bloodstream?
For each situation, write an analysis of the relationships
between the representations and a description of the
attributes (relation/function, independent/dependent,
domain/range, discrete/continuous, function notation,
etc.). Use the representations to make predictions and
critical judgments in the problem situation.
Standard(s): A.1A , A.1B , A.1D , A.1E , A.2B , A.2D ,
A.3A , A.3B , A.4A , A.4C , A.11B , A.11C ELPS.c.1C
, ELPS.c.3D , ELPS.c.3H , ELPS.c.5B
MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS
Misconceptions:
Some students may think that all relations are functions.
Some students may think that variables as letters represent an object as opposed to representing the number or quantity of objects.
UNIT VOCABULARY
Function – relation in which each element of the input (domain) is paired with exactly one element of the output (range)
Relation – a set of ordered pairs (pairing of a set of inputs (domain) with a set of outputs (range)
Representations – concrete models, tables, graphs, verbal descriptions, and algebraic generalization of data
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 5 of 23
SYSTEM RESOURCES OTHER RESOURCES
Algebra I Transition Alignment Guide (TAG) Tool Algebra 1 End of Course Success: Vocabulary: Objective 2 Lesson 1 – DescribingGraphs, Comparing Domains and Ranges, Domain and Range, On Your Own:
Domain and Range, Puzzler #1 & #2; CCRS: Objective 5 Lesson 2 – Box of Rice,On Your Own: How Long Will It Take?, Let’s Take Another Look: Area, Variations ona Theme Card Sort
Fostering Algebraic Thinking: Introduction and Analyzing Written Student Work,
Introductory Session – Postage Stamp, Closing Session – Peasant Algorithm,Session 1 – Crossing the River, Session 2 Sum of Consecutive Numbers, Session 3– The Staircase Problem, Session 4 – Golden Apples; Asking Questions ofStudents, Session 1 – The Candles Problem, Session 2 – Towering Numbers,Session 3 – Toothpick Squares, Session 4 – More Postage Stamps; DocumentingPatterns of Student Thinking, Session 1 – Marcy’s Dots, Session 4 – More PostageStamps; Listening to Students, Session 1 – Carnival Bears, Session 2 – Differenceof Squares, Session 3 – Lots of Squares, Session 4 – More Postage StampsTEA STAAR Mathematics
Resources: http://www.tea.state.tx.us/student.assessment/staar/math/
TEA STAAR Released Test
Questions: http://www.tea.state.tx.us/student.assessment/staar/testquestions/
TEXTEAMS: Algebra 1: 2000 and Beyond: I – Foundations of Functions; 1.Developing Mathematical Models, 1.1 Variables and Functions, Act 1 (Examples of
Dependent Relationships), Act. 2 (Independent and Dependent Variables), 1.2
Valentine’s Day Idea; Act. 1 (Valentine’s Day Idea), Act. 2 (Using Tables to Find theMore Economical Offer), Act. 3 (Using Graphs to Find the Better Idea), Act. 4 (New
Rose Offers), Act. 5 (Using Tables for New Rose Offers), Act. 6 (Using Graphs for
New Rose Offers); 2. Using Patterns to Identify Relationships, 2.1 Identifying
Patterns, Act. 1 (Painting Towers), Act. 2 (Building Chimneys), Act. 3 (Constructing
Trucks), Act. 4 (Generating Patterns), Student Act. (Perimeter of Rectangles), 2.2
Identifying More Patterns, Act. 1 (Building Blocks), Act. 2 (Starting Staircases), Act.
3 (Too Many Triangles); III – Nonlinear Functions; 3. Exponential Functions and
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 6 of 23
Equations, 3.1 Exponential Equations, Act. 1 (Paper Folding), Act. 2 (Measure with
Paper), Act. 3 (Regions), Act. 4 (How Big Is a Region?), Student Act. (Recursion
Again), 3.2 Exponential Growth and Decay, Act. 1 (Exponential Growth), Act. 2
(Exponential Decay), Student Act. (On the Wall), 3.3 Exponential Models, Act. 1
(Population Growth), Act. 2 (Cooling Down); 4. Interpreting Relationships Between
Data Sets, 4.1 Bounce It!, Act. 1(Collect the Data), Act. 2 (A Bounce), Act. 3
(Bounce Height vs. Bounce Number), Act. 4 (Bounce Height vs. Drop Height),
Student Act. 1 (Pattern Blocks), Student Act. 2 (Throw Up!), Student Act. 3
(Radioactive Decay), Student Act. 4 (Pendulum Decay)
TEKS UNIT LEVEL SPECIFICITY
Legend:
Bold black text in italics: Knowledge and
Skills Statement (TEKS)
Bold black text: Student Expectation (TEKS)
Bolded red text in italics: Student
Expectation identified by TEA as a
Readiness Standard for STAAR
Bolded 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)
Legend:
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)
TEKS#
SE#
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 7 of 23
TEKS UNIT LEVEL SPECIFICITYTEKS#
SE#
A.1 Foundations for functions. The student understands
that a function represents a dependence of one
quantity on another and can be described in a
variety of ways. The student is expected to:
A.1A Describe independent and dependent quantities
in functional relationships.
Supporting Standard
Understand, Describe, Represent
INDEPENDENT AND DEPENDENT QUANTITIES IN FUNCTIONAL RELATIONSHIPS
Including, but not limited to:
Identification of independent and dependent quantities in real-world problem situations
Verbal descriptions of dependency relationships
Representations of relationships between independent and dependent quantities in functional
relationships with and without technology
Verbal descriptions
Algebraic generalizations (including equation and function notation)
TxCCRS Note:
VII. Functions B1 – Understand and analyze features of a function.
A.1B Gather and record data and use data sets to
determine functional relationships between
quantities.
Supporting Standard
Represent, Describe, Gather, Record, Use, Determine
FUNCTIONAL RELATIONSHIPS OF DATA SETS
Including, but not limited to:
Data involving measurement activities, models, simulations, and real-world problem situations
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 8 of 23
TEKS UNIT LEVEL SPECIFICITYTEKS#
SE#
Data representing linear and nonlinear models
Representations of functional relationships with and without technology
Models
Concrete
Pictorial
Tables
Graphs
Verbal descriptions
Algebraic generalizations (including equation and function notation)
Connections between representations of functional relationships with and without technology
Analysis of data for predictions and conclusions (TxCCRS)
Comparisons between functional and non-functional relations (TxCCRS)
TxCCRS Note:
II. Algebraic Reasoning D1 – Interpret multiple representations of equations and relationships.VI. Statistical Reasoning B1 – Determine types of data.VI. Statistical Reasoning C1 – Make predictions and draw inferences using summary statistics.VII. Functions A1 – Recognize whether a relation is a function.VII. Functions A2 – Recognize and distinguish between different types of functions.VII. Functions B2 – Algebraically construct and analyze new functions.VII. Functions C2 – Develop a function to model a situation.
A.1D Represent relationships among quantities using
concrete models, tables, graphs, diagrams, verbal
descriptions, equations, and inequalities.
Readiness Standard
Represent
RELATIONSHIPS AMONG QUANTITIES
Including, but not limited to:
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 9 of 23
TEKS UNIT LEVEL SPECIFICITYTEKS#
SE#
Sets of related data
Representations of relationships with and without technology
Models
Concrete
Pictorial (e.g., mappings)
Tables
Graphs
Verbal descriptions
Algebraic generalizations (including equation and function notation)
Equations
y = 2x + 3 or f(x) = 2x + 3
Connections between representations of relationships with and without technology
Analysis of data for predictions and conclusions (TxCCRS)
Identification of certain relations as functions (TxCCRS)
Note:
In middle school, students generate different representations of data from other representations.
(TEKS 8.4A)
TxCCRS Note:
II. Algebraic Reasoning D1 – Interpret multiple representations of equations and relationships.II. Algebraic Reasoning D2 – Translate among multiple representations of equations and relationships.VI. Statistical Reasoning B2 – Select and apply appropriate visual representations of data.VII. Functions A1 – Recognize whether a relation is a function.VII. Functions B1 – Understand and analyze features of a function.VII. Functions B2 – Algebraically construct and analyze new functions.
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 10 of 23
TEKS UNIT LEVEL SPECIFICITYTEKS#
SE#
VII. Functions C2 – Develop a function to model a situation.IX. Communication and Representation B1 – Model and interpret mathematical ideas and conceptsusing multiple representations.
IX. Communication and Representation B2 – Summarize and interpret mathematical informationprovided orally, visually, or in written form within the given context.
IX. Communication and Representation C1– Communicate mathematical ideas, reasoning, and theirimplications using symbols, diagrams, graphs, and words.
A.1E Interpret and make decisions, predictions, and
critical judgments from functional relationships.
Readiness Standard
Interpret, Make
DECISIONS, PREDICTIONS, AND CRITICAL JUDGMENTS FROM FUNCTIONAL RELATIONSHIPS
Including, but not limited to:
Data sets and real-world problem situations
Representations of functional relationships with and without technology
Tables
Graphs, including situational
Verbal descriptions
Algebraic generalizations
Connections between representations of functional relationships with and without technology
Analysis of data representations for predictions and conclusions with and without technology
Note:
In middle school, students predict, find, and justify solutions using various representations.
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 11 of 23
TEKS UNIT LEVEL SPECIFICITYTEKS#
SE#
TxCCRS Note:
II. Algebraic Reasoning D1 – Interpret multiple representations of equations and relationships.VI. Statistical Reasoning C1 – Make predictions and draw inferences using summary statistics.
A.2 Foundations for functions. The student uses the
properties and attributes of functions. The student
is expected to:
A.2B Identify mathematical domains and ranges and
determine reasonable domain and range values
for given situations, both continuous and discrete.
Readiness Standard
Use, Identify, Determine
REASONABLE MATHEMATICAL DOMAINS AND RANGES
Including, but not limited to:
Comparison of discrete and continuous domains
Representations of domains and ranges with and without technology
Tables
Graphs, including situational
Verbal descriptions
Algebraic generalizations (including equation and function notation)
Notation of domain and range
Lists of domain and range in sets (including f(x) for y)
Verbal
Ex: Domain is all real numbers; domain is all real numbers greater than five.
Ex: Range is all real numbers less than zero; range is all real numbers.
Symbolic
Ex: domain (e.g., x > 0; -3 < x < 4; Ø; R)Ex: range (e.g., y ≤ 0; 7 < y ≤ 4; 5 < f(x) ≤ 2; Ø; R)
Determination of scales for graphs and windows on graphing calculators using domain and
range
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 12 of 23
TEKS UNIT LEVEL SPECIFICITYTEKS#
SE#
Contextual domain and range of real-world problem situation
Comparison of the domain and range of the problem situation versus the domain and range of
the representative mathematical function
TxCCRS Note:
VII. Functions B1 – Understand and analyze features of a function.VIII. Problem Solving and Reasoning C2 – Use a function to model a real world situation.
A.2D Collect and organize data, make and interpret
scatterplots (including recognizing positive,
negative, or no correlation for data
approximating linear situations), and model,
predict, and make decisions and critical
judgments in problem situations.
Readiness Standard
Use, Collect, Organize
DATA
Including, but not limited to:
Data sets and real-world problem situations
Data with and without the use of data collection technology (e.g., graphing calculators,
CBR/CBL, and computers)
Representations of data with and without technology
Tables
Graphs, including scatterplots
Verbal descriptions
Algebraic generalizations (including equation and function notation)
Make, Interpret
SCATTERPLOTS AND REPRESENTATIVE FUNCTIONS FOR DATA
Including, but not limited to:
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 13 of 23
TEKS UNIT LEVEL SPECIFICITYTEKS#
SE#
Data sets and real-world problem situations
General trends in the data
Data analysis with and without the use of technology (e.g., graphing calculators, CBR/CBL, and
computers)
Representations of data with and without technology
Tables
Graphs, including scatterplots
Verbal descriptions
Algebraic generalizations (including equation and function notation)
Make, Model, Predict
DECISIONS AND CRITICAL JUDGMENTS IN PROBLEM SITUATIONS
Including, but not limited to:
Data sets and real-world problem situations
General trends in the data with and without technology
Data with and without the use of data collection technology (e.g., graphing calculators,
CBR/CBL, and computers)
Representations of data with and without technology
Tables
Graphs, including scatterplots
Verbal descriptions
Algebraic representations (including equation and function notation)
Predictions and critical judgments in terms of the scatterplots and representative functions
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
Last Updated 06/10/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISDpage 14 of 23
TEKS UNIT LEVEL SPECIFICITYTEKS#
SE#
TxCCRS Note:
II. Algebraic Reasoning D1 – Interpret multiple representations of equations and relationships.II. Algebraic Reasoning D2 – Translate among multiple representations of equations and relationships.III. Geometric Reasoning C2 – Make connections between geometry, statistics, and probability.IV. Measurement Reasoning D1 – Compute and use measures of center and spread to describe data.VI. Statistical Reasoning A1 – Plan a study.VI. Statistical Reasoning B1 – Determine types of data.VI. Statistical Reasoning B2 – Select and apply appropriate visual representations of data.VI. Statistical Reasoning B4 – Describe patterns and departure from patterns in a set of data.VI. Statistical Reasoning C1 – Make predictions and draw inferences using summary statistics.VI. Statistical Reasoning C2 – Analyze data sets using graphs and summary statistics.VI. Statistical Reasoning C3 – Analyze relationships between paired data using spreadsheets,graphing calculators, or statistical software.
VII. Functions A2 – Recognize and distinguish between different types of functions.VII. Functions B2 – Algebraically construct and analyze new functions.VII. Functions C1 – Apply known function models.VII. Functions C2 – Develop a function to model a situation.VIII. Problem Solving and Reasoning B2 – Use various types of reasoning.IX. Communication and Representation B1 – Model and interpret mathematical ideas and conceptsusing multiple representations.
IX. Communication and Representation B2 – Summarize and interpret mathematical informationprovided orally, visually, or in written form within the given context.
IX. Communication and Representation C1– Communicate mathematical ideas, reasoning, and theirimplications using symbols, diagrams, graphs, and words.
X. Connections A1 – Connect and use multiple strands of mathematics in situations and problems.
A.3 Foundations for functions. The student understands
how algebra can be used to express generalizations
and recognizes and uses the power of symbols to
represent situations. The student is expected to:
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
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TEKS UNIT LEVEL SPECIFICITYTEKS#
SE#
A.3A Use symbols to represent unknowns and
variables.
Supporting Standard
Use
SYMBOLS
Including, but not limited to:
Representation of an unknown quantity in a problem situation
Representation of a quantity that “varies” in a data table process columnRepresentations of patterns in data collections
Representations of data collections or problem situations with and without technology
Models
Pictorial (e.g., diagrams of the problem situation)
Verbal descriptions
Algebraic generalizations
Verbal expressions translated to algebraic expressions using symbols
Problem situation as an expression or equation
Express, Represent
UNKNOWNS AND VARIABLES
Including, but not limited to:
Representation of an unknown quantity in a problem situation
Representation of a quantity that “varies” in a data table process columnRepresentations of data collections or problem situations with and without technology
Models
Pictorial (e.g., diagrams of the problem situation)
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
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TEKS UNIT LEVEL SPECIFICITYTEKS#
SE#
Verbal descriptions
Algebraic generalizations
Verbal expressions translated to algebraic expressions using symbols
Problem situation as an expression or equation
Note:
In middle school, students use symbols to represent arithmetic sequences.
TxCCRS Note:
VII. Functions B2 – Algebraically construct and analyze new functions.VII. Functions C2 – Develop a function to model a situation.IX. Communication and Representation A1 – Use mathematical symbols, terminology, and notation torepresent given and unknown information in a problem.
IX. Communication and Representation A3 – Use mathematics as a language for reasoning, problemsolving, making connections, and generalizing.
A.3B Look for patterns and represent generalizations
algebraically.
Supporting Standard
Understand, Use, Express, Recognize, Represent
PATTERNS AS ALGEBRAIC GENERALIZATIONS
Including, but not limited to:
Hands-on data collection activities
Problem situations with data collection
Representations of patterns in data collections or problem situations with and without
technology
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
TITLE : Unit 01: The Study of Functions SUGGESTED DURATION : 17 days
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TEKS UNIT LEVEL SPECIFICITYTEKS#
SE#
Models
Concrete
Pictorial (e.g., diagrams of a problem situation)
Tables
Graphs
Verbal descriptions
Algebraic generalizations (including equation and function notation)
Algebraic generalizations connected to relationships in patterns
Note:
In middle school, students represent arithmetic sequences algebraically.
In geometry, students will represent numeric and geometric patterns to develop algebraic
expressions.
TxCCRS Note:
VII. Functions B2 – Algebraically construct and analyze new functions.VII. Functions C2 – Develop a function to model a situation.
A.4 Foundations for functions.
The student understands the importance of the
skills required to manipulate symbols in order to
solve problems and uses the necessary algebraic
skills required to simplify algebraic expressions
and solve equations and inequalities in problem
situations. The student is expected to:
A.4A Find specific function values, simplify polynomial
expressions, transform and solve equations, and Find
INSTRUCTIONAL FOCUS DOCUMENTAlgebra I
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TEKS UNIT LEVEL SPECIFICITYTEKS#
SE#
factor as necessary in problem situations.
Readiness Standard
FUNCTION VALUES
Including, but not limited to:
Evaluation of mathematical expressions
Simplification of numeric expressions by order of operations
Evaluation of algebraic expressions when given specific values for variables
Evaluation of functions
Function notation
Ex: If f(x) = 2x – 1, find f(2).
Ex: If f(x) = 2x – 1 and f(x) = 5, find x.
Function values using technology (e.g., the table or trace features on the graphing calculator)
Specific range values at given domains from various representations (e.g., tables, graphs, or
algebraic generalizations)
Specific domain values at given ranges from various representations (e.g., tables, graphs, or
algebraic generalizations)
TxCCRS Note:
I. Numeric Reasoning B1 – Perform computations with real and complex numbers. (Algebra 1 onlyrequires the students to compute with real numbers.)
II. Algebraic Reasoning A1 – Explain and differentiate between expressions and equations using wordssuch as “solve”, “evaluate”, and “simplify”.II. Algebraic Reasoning B1 – Recognize and use algebraic (field) properties, concepts, procedures,and algorithms to combine, transform, and evaluate expressions (e.g., polynomials, radicals, rational
expressions).
II. Algebraic Reasoning C1 – Recognize and use algebraic (field) properties, concepts, procedures,and algorithms to solve equations, inequalities, and systems of linear equations.
A.4C Connect equation notation with function notation,
such as y = x + 1 and f(x) = x + 1. Use, Connect
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Supporting StandardFUNCTION NOTATION
Including, but not limited to:
Comparison of characteristics of equation notation and function notation
Domain of each type of notation is x
Range of equation notation is y; range of function notation is f(x)
Benefits of function notation
Function aligned to specific situation by descriptive letter (e.g., cost function as C(x) =
30x + 100)
Indication of domain input to evaluate in the function (e.g., C(2) = 30(2) + 100)
Note:
Finding function values using function notation is addressed and has been tested under TEKS
A.4A.
TxCCRS Note:
VII. Functions B1 – Understand and analyze features of a function.
A.11 Quadratic and other nonlinear functions. The
student understands there are situations modeled
by functions that are neither linear nor quadratic
and models the situations. The student is expected
to:
A.11B Analyze data and represent situations involving
inverse variation using concrete models, tables, Understand, Model, Analyze, Represent
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graphs, or algebraic methods.
Supporting Standard INVERSE VARIATION
Including, but not limited to:
Problem situation and/or data sets involving inverse relationships with and without technology
Representations of data with and without technology
Concrete models
Tables
Graphs
Algebraic generalizations (including equation and function notation)
Analysis of representations of inverse variation with and without technology
Reasonableness of solutions in terms of the situation
Note:
In Algebra 2, students will extend the study of rational functions and equations.
TxCCRS Note:
II. Algebraic Reasoning D2 – Translate among multiple representations of equations and relationships.VII. Functions B1 – Understand and analyze features of a function.VII. Functions B2 – Algebraically construct and analyze new functions.VII. Functions C2 – Develop a function to model a situation.VIII. Problem Solving and Reasoning C2 – Use a function to model a real world situation.IX. Communication and Representation B1 – Model and interpret mathematical ideas and conceptsusing multiple representations.
IX. Communication and Representation B2 – Summarize and interpret mathematical informationprovided orally, visually, or in written form within the given context.
IX. Communication and Representation C1– Communicate mathematical ideas, reasoning, and theirimplications using symbols, diagrams, graphs, and words.
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A.11C Analyze data and represent situations involving
exponential growth and decay using concrete
models, tables, graphs, or algebraic methods.
Supporting Standard
Understand, Model, Analyze, Represent
EXPONENTIAL GROWTH AND DECAY
Including, but not limited to:
Problem situation and/or data sets involving exponential growth and decay with and without
technology
Representation of data with and without technology
Concrete models
Tables
Graphs
Algebraic generalizations (including equation and function notation)
Analysis of representations of exponential growth and decay with and without technology
Comparison between exponential growth and decay with and without technology
Reasonableness of solutions in terms of the situation
Note:
In Algebra 2, students will extend the study of exponential functions and equations.
TxCCRS Note:
II. Algebraic Reasoning D2 – Translate among multiple representations of equations and relationships.VII. Functions B1 – Understand and analyze features of a function.VII. Functions B2 – Algebraically construct and analyze new functions.VII. Functions C2 – Develop a function to model a situation.VIII. Problem Solving and Reasoning C2 – Use a function to model a real world situation.IX. Communication and Representation B1 – Model and interpret mathematical ideas and concepts
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using multiple representations.
IX. Communication and Representation B2 – Summarize and interpret mathematical informationprovided orally, visually, or in written form within the given context.
IX. Communication and Representation C1– Communicate mathematical ideas, reasoning, and theirimplications using symbols, diagrams, graphs, and words.
The English Language Proficiency Standards (ELPS), as required by 19 Texas Administrative Code, Chapter 74, Subchapter A, §74.4, outline English languageproficiency 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.
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# SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
Last Updated 06/10/2014
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