instructional focus document algebra i · additionally, algebra in a technological world (1995)...

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.







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





about:/module/standards/0/107308/standard.ashx
















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.







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





















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





about:/module/content/search/item/676359/viewdetail.ashx

http://www.tea.state.tx.us/student.assessment/staar/math/

http://www.tea.state.tx.us/student.assessment/staar/testquestions/

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#





about:/module/standards/Tools/Browse?StandardId=107307

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


Data involving measurement activities, models, simulations, and real-world problem situations









SE#

Data representing linear and nonlinear models

Representations of functional relationships with and without technology

Models

Concrete

Pictorial

Tables

Graphs

Verbal descriptions


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








SE#

Sets of related data

Representations of relationships with and without technology

Models

Concrete

Pictorial (e.g., mappings)

Tables

Graphs

Verbal descriptions


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.






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


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.







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


Comparison of discrete and continuous domains

Representations of domains and ranges with and without technology

Tables

Graphs, including situational

Verbal descriptions


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








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



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


Make, Interpret

SCATTERPLOTS AND REPRESENTATIVE FUNCTIONS FOR DATA








SE#


General trends in the data

Data analysis with and without the use of technology (e.g., graphing calculators, CBR/CBL, and

computers)


Tables


Verbal descriptions


Make, Model, Predict

DECISIONS AND CRITICAL JUDGMENTS IN 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)


Tables


Verbal descriptions

Algebraic representations (including equation and function notation)

Predictions and critical judgments in terms of the scatterplots and representative functions






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.



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:







SE#

A.3A Use symbols to represent unknowns and

variables.

Supporting Standard

Use

SYMBOLS


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


Verbal expressions translated to algebraic expressions using symbols

Problem situation as an expression or equation

Express, Represent

UNKNOWNS AND VARIABLES


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)







SE#

Verbal descriptions


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


Hands-on data collection activities

Problem situations with data collection

Representations of patterns in data collections or problem situations with and without

technology







SE#

Models

Concrete

Pictorial (e.g., diagrams of a problem situation)

Tables

Graphs

Verbal descriptions


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








SE#

factor as necessary in problem situations.

Readiness Standard

FUNCTION VALUES


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







SE#

Supporting StandardFUNCTION NOTATION


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








SE#

graphs, or algebraic methods.

Supporting Standard INVERSE VARIATION


Problem situation and/or data sets involving inverse relationships with and without technology


Concrete models

Tables

Graphs


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.








SE#

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


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


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







SE#

using multiple representations.



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.






http://ritter.tea.state.tx.us/rules/tac/chapter074/ch074a.html#74.4

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