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Instructional Focus Document
Algebra II
TITLE : Unit 11: Linear, Quadratic, and Exponential Data Models SUGGESTED DURATION : 5 days

Unit Overview

Introduction
This unit bundles student expectations that address analyzing sets of data using technology to determine if the data is best represented using linear, quadratic, or exponential models and applying the selected models to make predictions and critical judgments in terms of the data. Concepts are incorporated into both mathematical and real-world problem situations. According to the Texas Education Agency, mathematical process standards including application, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

Prior to this Unit
In Algebra I Units 03, 08, and 09, students were introduced to linear, quadratic, and exponential functions. In Algebra II Units 05 and 09, students analyzed quadratic and exponential functions. Linear functions were interspersed throughout Algebra II.

During this Unit
Students analyze and compare linear, quadratic, and exponential data sets using graphs, tables, verbal descriptions, and technology to determine which function can be selected to best model the data. Students use regression methods available through technology to write the appropriate regression function (linear, quadratic, or exponential) to model the data. Students apply the regression model to predict and make decisions and critical judgments in terms of the data.

After this Unit
In Units 12 and 13, students will review and continue to apply linear, quadratic, and exponential functions. In subsequent mathematics courses, students will also continue to apply these concepts when linear, quadratic, and exponential functions and equations arise in problem situations.

Additional Notes
In Algebra II, analysis of sets of data to select an appropriate regression equation and application of that regression equation to make predictions and critical judgments are identified as STAAR Readiness Standard 2A.8C and STAAR Supporting Standards 2A.8A and 2A.8B. These standards are subsumed under STAAR Reporting Category 2: Describing and Graphing Functions and Their Inverses. This unit is supporting the development of Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning B1; II. Algebraic Reasoning A1, B1, C1, D1, D2; III. Geometric Reasoning B2, C1; VII. Functions A2, B1, B2; VIII. Problem Solving and Reasoning; IX. Communication and Representation; X. Connections.

Research
According to the National Council of Teachers of Mathematics (2011), Developing Essential Understanding of Functions, Grades 9-12, understanding of the function concept is essential to describing and analyzing quantities which vary with respect to one another. According to research from the National Council of Teachers of Mathematics (2000), Principles And Standards For School Mathematics, high school algebra should provide students with insights into mathematical abstraction and structure. High school students’ algebra experience should enable them to create and use tabular, symbolic, graphical, and verbal representations and to analyze and understand patterns, relations, and functions with a higher degree of sophistication. Students should develop an understanding of the algebraic properties that govern manipulation of symbols in expressions, equations, and inequalities.

 

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. (2011). Developing essential understanding of expressions, equations, and functions, grades 9-12. 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/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9


  • Quantitative relationships model problem situations efficiently and can be used to make generalizations, predictions, and critical judgements in everyday life.
    • What patterns exist within different types of quantitative relationships and where are they found in everyday life?
    • Why is the ability to model quantitative relationships in a variety of ways essential to solving problems in everyday life?
  • Statistical displays often reveal patterns within data that can be analyzed to interpret information, inform understanding, make predictions, influence decisions, and solve problems in everyday life with degrees of confidence.
    • How does society use or make sense of the enormous amount of data in our world available at our fingertips?
    • How can data and data displays be purposeful and powerful?
    • Why is it important to be aware of factors that may influence conclusions, predictions, and/or decisions derived from data?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
  • Understanding how two quantities vary together (covariation) builds flexible functional reasoning in order to make predictions and critical judgments about the relationship.
    • What are the strengths and limitations of a particular function model for a problem situation?
    • How can functions be used to model problem situations efficiently?
    • How can it be determined if a relationship between two variables can be represented by a function?
    • How is function notation used to define and describe a function rule?
    • How is function notation used to make predictions and critical judgements about the relationship?
    • How can the most appropriate function model be determined for a set of data?
  • Different families of functions, each with their own unique characteristics, can be used to model problem situations to make predictions and critical judgments.
    • Linear functions are characterized by a constant rate of change and can be used to describe, model, and make predictions about situations.
    • Quadratic functions are characterized by a rate of change that changes at a constant rate and can be used to describe, model, and make predictions about problem situations.
    • Exponential functions are characterized by a rate of change that is proportional to the value of the function and can be used to describe, model, and make predictions about problem situations.
      • What kinds of mathematical and real-world situations can be modeled by …
        • linear functions?
        • quadratic functions?
        • exponential functions?
      • What graphs, key attributes, and characteristics are unique to …
        • linear functions?
        • quadratic functions?
        • exponential functions?
      • What patterns of covariation are associated with …
        • linear functions?
        • quadratic functions?
        • exponential functions?
      • How can the key attributes of linear, quadratic, and exponential functions be …
        • determined?
        • analyzed?
        • described?
      • How can key attributes be used to describe the behavior of linear, quadratic, and exponential functions?
      • What are the real-world meanings of the key attributes of linear, quadratic, and exponential function models?
      • How can key attributes be used to make predictions and critical judgments about the problem situation?
  • Functions can be represented in various ways with different representations of the function highlighting different characteristics and being more useful than other representations depending on the context.
    • How can functions be represented?
    • What is the purpose of representing functions in various ways?
    • How are function characteristics highlighted in different representations of the function?
    • What are the limitations of different function representations?
    • What connections can be made between multiple representations of a function?
  • Data
    • Data and Statistics
      • Data
      • Models
      • Conclusions and predictions
      • Regression methods
  • Associated Mathematical Processes
    • Application
    • Problem Solving Model
    • Tools and Techniques
    • Communication
    • Representations
    • Relationships
    • Justification
Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

  • Some students may think a scatterplot is linear because the points appear to be almost a line, rather than doing a regression analysis and comparing correlation coefficients. Parts of a quadratic relationship and parts of an exponential relationship may appear linear without in-depth analysis.
  • Some students may fail to put data in sequential order before checking first and second differences and common ratios.
  • Some students may check on first and second differences and fail to check common ratios when analyzing sequential data.
  • Some students may not put values in the correct order when calculating first and second differences (not y1y2, but y2y1).
  • Some students may not put values in the correct order when calculating the common ratio (not , but ).

Unit Vocabulary

  • Coefficient of determination (r2-value) – representation of the percent of data closest to the regression line and used to measure how well the regression line can be used as a prediction model
  • Correlation coefficient (r-value) – numeric value that assesses the strength of the linear relationship between two quantitative variables in a set of bivariate data
  • Regression equation – line of best fit representing a set of bivariate data

Related Vocabulary:

  • Common ratio
  • Exponential
  • First differences
  • Linear
  • Quadratic
  • Rate of change
  • Regression
  • Regression equation
  • Second differences
  • Sequential data
Unit Assessment Items System Resources Other Resources

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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.

System Resources may be accessed through Search All Components in the District Resources Tab.

Texas Higher Education Coordinating Board – Texas College and Career Readiness Standards

  

Texas Education Agency – Mathematics Curriculum

 

Texas Education Agency – STAAR Mathematics Resources

 

Texas Education Agency Texas Gateway – Revised Mathematics TEKS: Vertical Alignment Charts

 

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

 

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

 

Texas Education Agency Texas Gateway – Resources Aligned to Algebra II Mathematics TEKS

 

Texas Instruments – Graphing Calculator Tutorials


TEKS# SE# Unit Level Taught Directly TEKS Unit Level Specificity
 

Legend:

  • Knowledge and Skills Statements (TEKS) identified by TEA are in italicized, bolded, black text.
  • Student Expectations (TEKS) identified by TEA are in bolded, black text.
  • Student Expectations (TEKS) are labeled Readiness as identified by TEA of the assessed curriculum.
  • Student Expectations (TEKS) are labeled Supporting as identified by TEA of the assessed curriculum.
  • Portions of the Student Expectations (TEKS) that are not included in this unit but are taught in previous or future units are indicated by a strike-through.

Legend:

  • Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
  • Unit-specific clarifications are in italicized, blue text.
  • Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
2A.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
2A.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

Apply

MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE

Including, but not limited to:

  • Mathematical problem situations within and between disciplines
    • Everyday life
    • Society
    • Workplace

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • X. Connections
2A.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

Use

A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION

Including, but not limited to:

  • Problem-solving model
    • Analyze given information
    • Formulate a plan or strategy
    • Determine a solution
    • Justify the solution
    • Evaluate the problem-solving process and the reasonableness of the solution

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
2A.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

Select

TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, ESTIMATION, AND NUMBER SENSE AS APPROPRIATE, TO SOLVE PROBLEMS

Including, but not limited to:

  • Appropriate selection of tool(s) and techniques to apply in order to solve problems
    • Tools
      • Real objects
      • Manipulatives
      • Paper and pencil
      • Technology
    • Techniques
      • Mental math
      • Estimation
      • Number sense

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
2A.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Communicate

MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, GRAPHS, AND LANGUAGE AS APPROPRIATE

Including, but not limited to:

  • Mathematical ideas, reasoning, and their implications
    • Multiple representations, as appropriate
      • Symbols
      • Diagrams
      • Graphs
      • Language

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • IX. Communication and Representation
2A.1E Create and use representations to organize, record, and communicate mathematical ideas.

Create, Use

REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

  • Representations of mathematical ideas
    • Organize
    • Record
    • Communicate
  • Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
  • Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • IX. Communication and Representation
2A.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS

Including, but not limited to:

  • Mathematical relationships
    • Connect and communicate mathematical ideas
      • Conjectures and generalizations from sets of examples and non-examples, patterns, etc.
      • Current knowledge to new learning

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • X. Connections
2A.1G Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Display, Explain, Justify

MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION

Including, but not limited to:

  • Mathematical ideas and arguments
    • Validation of conclusions
      • Displays to make work visible to others
        • Diagrams, visual aids, written work, etc.
      • Explanations and justifications
        • Precise mathematical language in written or oral communication

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • IX. Communication and Representation
2A.8 Data. The student applies mathematical processes to analyze data, select appropriate models, write corresponding functions, and make predictions. The student is expected to:
2A.8A Analyze data to select the appropriate model from among linear, quadratic, and exponential models.
Supporting Standard

Analyze

DATA

Including, but not limited to:

  • Data collected from data collection devices
  • Data given in mathematical problem situations
  • Types of data
    • Linear
      • Constant rate of change (slope)
      • If independent values change sequentially, the dependent values have a common first difference.
    • Quadratic
      • Non-constant rate of change
      • If independent values change sequentially the dependent values have a common second difference.
    • Exponential
      • Non-constant rate of change
      • If independent values change sequentially the dependent values have a common ratio, .
    • Comparisons between sequential data as linear, quadratic, and exponential

To Select

THE APPROPRIATE MODEL FROM AMONG LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

Including, but not limited to:

  • Data collected from data collection devices
  • Data given in real-world problem situations
  • Data relationships
    • Linear
    • Quadratic
    • Exponential
  • Data representations
    • Data tables
    • Graphs/scatterplots
    • Verbal descriptions
    • Algebraic generalizations

Note(s):

  • Grade Level(s):
    • Algebra I introduced the linear, quadratic, and exponential functions.
    • Algebra II expands on transformations and applications of exponential functions.
    • 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.”
      • D1 – Interpret multiple representations of equations and relationships.
      • D2 – Translate among multiple representations of equations and relationships.
    • III. Geometric Reasoning
      • B2 – Identify the symmetries of a plane figure.
      • 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.
      • B2 – Algebraically construct and analyze new functions.
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
2A.8B Use regression methods available through technology to write a linear function, a quadratic function, and an exponential function from a given set of data.
Supporting Standard

Use

REGRESSION METHODS AVAILABLE THROUGH TECHNOLOGY TO WRITE A LINEAR FUNCTION, A QUADRATIC FUNCTION, AND AN EXPONENTIAL FUNCTION FROM A GIVEN SET OF DATA

Including, but not limited to:

  • Data collected from data collection devices
  • Data given in mathematical and real-world problem situations
  • Data relationships
    • Linear
    • Quadratic
    • Exponential
  • Regression equation – line of best fit representing a set of bivariate data
  • Correlation coefficient (r-value) – numeric value that assesses the strength of the linear relationship between two quantitative variables in a set of bivariate data
    • When the correlation coefficient, r, is given in regression calculations, it can be used to determine the strength of the regression model as a representation of mathematical and real-world problem situations.
    • The correlation coefficient, r, can only be used to analyze linear relationships or relationships that can be linearized such as exponential
    • Correlation coefficients closest to ±1 indicate the best model for mathematical and real-world problem situations.
    • Value of the correlation coefficient, –1 ≤ r ≤ 1
      • Perfect correlation, r = 1 or –1
      • Strong correlation, 0.68 < |r| < 1.00
      • Moderate correlation, 0.34 ≤ |r| ≤ 0.68
      • Weak, 0 < |r| < 0.34
      • No correlation, r = 0
  • Coefficient of determination (r2-value) – representation of the percent of data closest to the regression line and used to measure how well the regression line can be used as a prediction model
    • When the coefficient of determination, r2, is given in regression calculations, it can be used to determine the strength of the regression model to represent and make predictions in mathematical and real-world problem situations.
    • The coefficient of determination, r2, can be used to analyze and compare all types of relationships such as linear, quadratic, and exponential

Note(s):

  • Grade Level(s):
    • Algebra I introduced the linear, quadratic, and exponential functions.
    • Algebra I calculated, using technology, the correlation coefficient between two quantitative variables and interpreted this quantity as a measure of the strength of association.
    • 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
      • 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.
    • VII. Functions
      • 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.8C Predict and make decisions and critical judgments from a given set of data using linear, quadratic, and exponential models.
Readiness Standard

Predict, Make

DECISIONS AND CRITICAL JUDGMENTS FROM A GIVEN SET OF DATA USING LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

Including, but not limited to:

  • Mathematical and real-world problem situations modeled by linear, quadratic, and exponential functions and equations
  • Predictions, decisions, and critical judgments from function models
  • Justification of reasonableness of solutions in terms of mathematical and real-world problem situations
    • Mathematical justification
      • Substitution in original problem
      • Justification for predictions using the coefficient of determination, r2

Note(s):

  • Grade Level(s):
    • Algebra I introduced the linear, quadratic, and exponential functions.
    • Algebra I introduced the correlation coefficient as a measure of the strength of linear association.
    • Algebra I applied linear, quadratic, and exponential functions to model and make predictions in real-world problem situations.
    • 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.”
      • B1 – Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions (e.g. polynomials, radicals, rational expressions).
      • 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.
    • VII. Functions
      • 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
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.


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.
Click here to collapse or expand this section.
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 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
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
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 grade-level learning expectations across foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1, certain of these student expectations do not apply until the student has reached the stage of generating original written text using a standard writing system. The student is expected to:
ELPS.c.5A learn relationships between sounds and letters of the English language to represent sounds when writing in English
ELPS.c.5B write using newly acquired basic vocabulary and content-based grade-level vocabulary
ELPS.c.5C spell familiar English words with increasing accuracy, and employ English spelling patterns and rules with increasing accuracy as more English is acquired
ELPS.c.5D edit writing for standard grammar and usage, including subject-verb agreement, pronoun agreement, and appropriate verb tenses commensurate with grade-level expectations as more English is acquired
ELPS.c.5E employ increasingly complex grammatical structures in content area writing commensurate with grade-level expectations, such as:
ELPS.c.5F write using a variety of grade-appropriate sentence lengths, patterns, and connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired
ELPS.c.5G narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired.
Last Updated 08/01/2018
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