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Instructional Focus Document
Precalculus
TITLE : Unit 11: Parametric Equations SUGGESTED DURATION : 7 days

Unit Overview

This unit bundles student expectations that address graphing parametric equations, using parametric equations to model and solve problem situations, and converting between parametric equations and rectangular relations. 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 02 – 04, 08, and 09, Algebra II Units 01, 02, and 05 – 11, and Precalculus Units 01, 03 – 05, and 08, students graphed various types of functions and their transformations, including linear, quadratic, exponential, absolute value, square root, cubic, cube root, rational, logarithmic, polynomial, power, trigonometric, and inverse trigonometric functions. Additionally, students analyzed the features of these functions, including domain and range. In Algebra I Units 01 and 07, students solved literal equations for specified variables. In Algebra II Unit 01 and Precalculus Unit 02, students used function composition to model and solve problems. In Geometry Unit 05, students used trigonometric ratios (including sine and cosine) to determine the lengths of sides and the measures of angles in right triangles. In Precalculus Unit 07, students extended the use of the trigonometric ratios to solve real-world problems, including those involving navigational bearings. In Precalculus Unit 10, students represented, used, and applied vectors and vector operations to model and solve problem situations.

During this unit, students graph parametric equations by hand using tables and explore the characteristics of these equations, including the effect of the parameter t and the direction of the graph over time. Students graph two sets of parametric equations on the same graph (in mathematical and real-world problem situations) and explore whether the two paths meet at the same time. Students compare parametric equations and their corresponding rectangular relations to determine what additional information is provided by parametric equations. Student graph parametric equations using graphing technology and analyze these graphs to model and solve problem situations. Students explore the effect of the t-step value on the graph of a parametric equation created using graphing technology. Students convert parametric equations into rectangular relations, and convert rectangular relations into parametric equations. Students model linear situations with parametric equations, including modeling linear motion and vector situations. Students use these parametric models to solve real-world problems. Students model projectile motion with parametric equations and then use these models to solve real-world problems.

After this unit, in Precalculus Unit 12, students will continue to study complex curves and relations that are not defined in terms of f(x). Specifically, students will use trigonometry to graph polar equations and convert between polar and rectangular coordinates. In Precalculus Unit 13, students will convert between parametric equations and rectangular relations for conic sections and use these representations to model and solve problems. In subsequent mathematics courses, students will continue to apply parametric equations as they arise in problem situations.

Algebraic reasoning serves an integral role in college readiness. Translating among multiple representations of equations and relationships and analyzing the features of functions are emphasized in the Texas College and Career Readiness Standards (TxCCRS): II. Algebraic Reasoning C1, D2; VII. Functions B1, C2; VIII. Problem Solving and Reasoning; IX. Communication and Representation; X. Connections.

According to the National Council of Teachers of Mathematics (2000), students in grades 9-12 should use algebraic symbols to represent and analyze mathematical situations. Specifically, students should represent functions and relations using a variety of symbolic representations, including parametric equations (NCTM, 2000). Parametric equations are useful for representing graphs of curves that cannot be represented as functions where y is defined in terms of x and for modeling situations involving motion along a path where position coordinates (x(t), y(t)) can be determined over time (Herman, 2006). Cooney, Beckmann, & Lloyd (2010) contend that parametric equations provide a way to create functions that map real numbers (for the parameter t) to specific points (x(t), y(t)) for rectangular relations where y is not a function of x. In this way, parametric equations provide an example of functions where the domain and range of the function do not have to be numbers (Cooney, Beckmann, & Lloyd, 2010). The study of parametric equations continues into calculus, where students analyze planar curves (including those given in parametric form, polar form, and vector form) as an important part of functional analysis and derivative studies (College Board, 2012). These planar curves can represent a number of real-world applications, including problems incorporating velocity and acceleration. Additionally, students in calculus will determine the length of a curve, including a curve represented with parametric equations (College Board, 2012).

 

College Board.  (2012). AP calculus course description. Retrieved from http://media.collegeboard.com/digitalServices/pdf/ap/ap-calculus-course-description.pdf.
Cooney, T., Beckmann, S., & Lloyd, G. (2010). Developing essential understanding of functions for teaching mathematics in grades 9-12. Reston, VA: National Council of Teachers of Mathematics, Inc.
Herman, M. (2006). Introducing parametric equations through graphing calculator explorations. Mathematics Teacher, 99(9), 637-640.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.

OVERARCHING UNDERSTANDINGS and QUESTIONS

Equations can be used to model and solve problem situations.

  • Why are equations used to model problem situations?
  • How are equations used to model problem situations?
  • What methods can be used to solve equations?
  • Why is it essential to solve equations using various methods?
  • How can solutions to equations be represented?

 

Relations are algebraic models that describe how two quantities relate to one another. Functions are a subset of relations.

  • What are types of relations?
  • How can relations be represented?
  • Why do some relations not define a function?
  • Why do some relations define a function?
  • Why can function models describe how two variable quantities change in relation to one another?
Performance Assessment(s) Overarching Concepts
Unit Concepts
Unit Understandings
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.

Algebraic Reasoning

  • Equations
  • Multiple Representations
  • Relations

 

Functions

  • Attributes of Functions
  • Linear Functions
  • Non-Linear Functions

 

Associated Mathematical Processes

  • Application
  • Tools and Techniques
  • Problem Solving Model
  • Communication
  • Representations
  • Relationships 
  • Justification

Parametric equations have unique characteristics and can be represented in multiple ways, including as rectangular relations.

  • What are the characteristics of parametric equations?
  • How do the characteristics of parametric equations and their corresponding rectangular relations compare?
  • How can parametric equations be used to represent functions and relations?
  • How can parametric equations be represented using tables?
  • How can parametric equations be represented using graphs?
  • How can parametric equations be represented algebraically?
  • How can parametric equations be converted into rectangular relations?
  • How can rectangular relations be converted into parametric equations?

 

Parametric equations can be used to model and solve mathematical real-world problem situations.

  • How are parametric equations used to model problem situations?
  • What type of problem situations can be modeled by parametric equations?
  • How can parametric equations be formulated to represent problem situations?
  • What methods can be used to solve problem situations involving parametric equations?
  • How is the reasonableness of solutions justified in problem situations?
  • Why must the reasonableness of solutions be justified in problem situations?

MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

  • Some students may incorrectly evaluate trigonometric functions if they use a calculator in the wrong angle mode.
  • Some students may incorrectly graph parametric equations if they use a calculator in the wrong angle mode.
  • When graphing parametric equations, some students may only graph the path of the parametric equations without noting specific t values along this path.
  • Some students may believe that two sets of parametric equations that trace out the same path are equivalent. However, students most also consider the role of the parameter t in determining the “speed” with which each set of parametric equations traces out the path.
  • Some students may believe that each rectangular relation has a unique set of corresponding parametric equations. Instead, each rectangular relation can be represented by an infinite set of parametric equations.

 

Underdeveloped Concepts:

  • Some students may struggle with writing multiple sets of parametric equations to represent a rectangular relation.
  • Some students may use the incorrect value for the acceleration due to gravity (either 32 ft/s2 or 9.8 m/s2) when formulating parametric equations to model projectile motion.
  • Some students may not understand how the t-step value affects the graph of parametric equations created using graphing technology.

Unit Vocabulary

 

Related Vocabulary:

  • Acceleration due to gravity
  • Convert
  • Direction
  • Function
  • Graph
  • Initial height
  • Initial velocity
  • Motion
  • Parameter
  • Parametric curve
  • Parametric equations
  • Path
  • Projectile motion
  • Rate of change
  • Rectangular relation
  • Relation
  • Starting point
  • Vectors
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 (select CCRS from Standard Set dropdown menu)

Texas Instruments – Graphing Calculator Tutorials

Texas Education Agency – STAAR Mathematics Resources

Texas Education Agency – Revised Mathematics TEKS: Vertical Alignment Charts

Texas Education Agency – Texas Response to Curriculum Focal Points for K-8 Mathematics Revised 2013

Texas Education Agency – Mathematics Curriculum

Texas Education Agency – Mathematics TEKS: Supporting Information

Texas Education Agency – Interactive Mathematics Glossary

The phase 2 College Readiness English Language Arts and Reading vertical alignment team found that the College Readiness Standards in English Language Arts and Reading are well aligned with the Texas Essential Knowledge and Skills.
TEKS# SE# TEKS Unit Level Specificity
 
  • Bold black text in italics: Knowledge and Skills Statement (TEKS)
  • Bold black text: Student Expectation (TEKS)
  • Strike-through: Indicates portions of the Student Expectation that are not included in this unit but are taught in previous or future unit(s)
  • 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)
P.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
P.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
P.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
P.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
P.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
P.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
P.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
P.1G Display, explain, and 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
P.3 Relations and geometric reasoning. The student uses the process standards in mathematics to model and make connections between algebraic and geometric relations. The student is expected to:
P.3A Graph a set of parametric equations.

Graph

A SET OF PARAMETRIC EQUATIONS

Including, but not limited to:

  • Characteristics of parametric graphs
    • Parameter (t)
    • Direction
  • Methods for graphing parametric equations
    • Constructing tables and plotting points
    • Using graphing calculator technology
      • Mode settings
        • Changing from “function” mode to “parametric” mode
        • Entering two equations for one graph (x(t) and y(t))
        • Window setting
          • Minimum and maximum values of t
          • Interval between t-values (“t-Step”)
    • Convert parametric equations to rectangular relations to graph
      • Algebraic methods
        • Solving one equation in a set of parametric equations (either x(t) or y(t)) for the parameter t
        • Substituting the expression for t into the other equation (either y(t) or x(t))
        • Graphing locus of points for the rectangular relation

Note(s):

  • Grade Level(s):
    • Algebra II graphed various types of functions, including their transformations and compositions.
    • Algebra II also analyzed the domains and ranges of functions, written in inequality, set notation, and interval notation.
    • Precalculus extends these ideas through the graphing of sets of parametric equations.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxCCRS:
    • II. Algebraic Reasoning
      • D2 – Translate among multiple representations of equations and relationships.
    • VII. Functions
      • B1 – Understand and analyze features of a function.
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections 
P.3B Convert parametric equations into rectangular relations and convert rectangular relations into parametric equations.

Convert

PARAMETRIC EQUATIONS INTO RECTANGULAR RELATIONS

Including, but not limited to:

  • Algebraic methods
    • Solving one equation in a set of parametric equations (either x(t) or y(t)) for the parameter t
    • Substituting the expression for t into the other equation (either y(t) or x(t))

 

Convert

RECTANGULAR RELATIONS INTO PARAMETRIC EQUATIONS

Including, but not limited to:

  • Rectangular relations into general parametric equations
    • Rectangular functions of the form y = f(x)
      • Letting x = t
      • Writing y as y = f(t)
    • Rectangular relations of the form x = f(y)
      • Letting y = t
      • Writing x as x = f(t)
    • Rectangular relations, given with specific information about x(t) or y(t)
      • Write an expression to describe x(t) or y(t)
      • Substitute the expression for x or y into the given rectangular relation
    • Rectangular relations of circles, ellipses, and hyperbolas
      • Circles
        • Applying the trigonometric identity sin2t + cos2t = 1 to parameterize a circle
      • Ellipses
        • Applying the trigonometric identity sin2t + cos2t = 1 to parameterize an ellipse
      • Hyperbolas
        • Applying the trigonometric identity sec2t – tan2t = 1 to parameterize a hyperbola

Note(s):

  • Grade Level(s):
    • Algebra I solved literal equations for a specified variable.
    • Algebra II used the composition of two functions.
    • Precalculus extends these skills to convert between parametric and rectangular equations.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxCCRS:
    • II. Algebraic Reasoning
      • D2 – Translate among multiple representations of equations and relationships.
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
P.3C Use parametric equations to model and solve mathematical and real-world problems.

Use

PARAMETRIC EQUATIONS

Model, Solve

MATHEMATICAL AND REAL-WORLD PROBLEMS USING PARAMETRIC EQUATIONS

Including, but not limited to:

  • Linear motion
    • General form: 
    • Variables
      • t (time)
      • (xy) (location at time t)
      • (x0y0) (starting point)
      • a (rate of change in the horizontal direction)
      • b (rate of change in the vertical direction)
      •  (slope)
  • Vector equations
    • General form: 
    • Variables and constants
      • t (time in seconds)
      • (xy) (location at time t)
      • (x0y0) (starting point)
      • v (constant velocity)
      • θ (direction, measured as a rotation angle in standard position)
  • Applications
  • Projectile motion
    • General form: 
    • Variables and constants
      • t (time in seconds)
      • (xy) (location at time t)
      • v (initial velocity)
      • θ (angle at which the projectile is launched or released, measured from the horizontal)
      • h0 (initial height)
      • g (acceleration due to gravity, 32 ft/s2 or 9.8 m/s2)
    • Applications
  • Curve sketching
    • General form: 
      • Parametric curve is determined by the points (x, y) = (f(t), g(t)) as t varies
      • Applications

Note(s):

  • Grade Level(s):
    • Geometry applied the trigonometric ratios (sine, cosine) to determine side lengths and angle measures in triangles.
    • Algebra I analyzed the features of linear and quadratic functions.
    • Precalculus combines these skills to develop parametric equations that model real-world situations such as linear and projectile motion.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxCCRS:
    • II. Algebraic Reasoning
      • D2 – Translate among multiple representations of equations and relationships.
    • 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 08/24/2016
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