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Instructional Focus Document
Mathematical Models with Applications
TITLE : Unit 03: Shape and Size in Architecture and Engineering SUGGESTED DURATION : 13 days

Unit Overview

This unit bundles student expectations that address geometric transformations, symmetry, perspective drawings, similarity, and proportional and non-proportional change as applied to fields of architecture and engineering. 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 Grade 6, students used scale factors involving ratios and rates to solve problems. In Grade 7, students studied similarity in relation to proportional change. In Grade 8, students studied similarity in angle relationships and applied scale factors proportionally to two-dimensional figures. In Geometry, students studied similarity, symmetry, transformations, and applied scale factors to two-dimensional and three-dimensional figures to demonstrate proportional and non-proportional change.

During this unit, students use rigid transformations that maintain congruence (translation, reflection, rotation) and non-rigid, similarity transformations (dilations) to describe mathematical patterns and structure in architecture. Students analyze reflectional and rotational symmetry as demonstrated in architecture to imply balance within structures. Students use perspective drawings to represent three-dimensional relationships in two-dimensional representations using one- and two-point perspectives. Students use a two-dimensional net and its attributes and properties to analyze the surface area and volume of a three-dimensional figure. Students use scale factor(s) applied to one or two dimensions of a three-dimensional figure to demonstrate non-proportional change in surface area and volume. Students use a scale factor applied to all three dimensions of a three-dimensional figure to demonstrate proportional change in surface area and volume. Students generate scale models or drawings, using proportional and non-proportional change, for products in the fields of engineering and architecture.

After this unit, in Unit 04, students will use similarity, symmetry, and transformations as they apply to design, measurement, and size in art and photography. In Unit 04 and Unit 05, the concepts of proportional and non-proportional change using scale factors will be applied to the fields of art and music. Throughout Mathematical Models with Applications, students will be required to take given information or collected data and determine tools and methods needed to solve the problem situation. The concepts in this unit will be applied in subsequent mathematics courses.

This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning B1; II. Algebraic Reasoning B1; VII. Functions A2; VIII. Problem Solving and Reasoning; IX. Communication and Representation; X. Connections.

According to the Connections Standard for Grades 9-12 from the National Council of Teachers of Mathematics (NCTM), “Instructional programs from pre-kindergarten through grade 12 should enable students to:

  • recognize and use connections among mathematical ideas;
  • understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
  • recognize and apply mathematics in contexts outside of mathematics.

When students can see the connections across different mathematical content areas, they develop a view of mathematics as an integrated whole. As they build on their previous mathematical understandings while learning new concepts, students become increasingly aware of the connections among various mathematical topics. As students' knowledge of mathematics, their ability to use a wide range of mathematical representations, and their access to sophisticated technology and software increase, the connections they make with other academic disciplines, especially the sciences and social sciences, give them greater mathematical power” (NCTM, 2000, p. 354).

 

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics: Connections standard for 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/collegereadiness/crs.pdf

OVERARCHING UNDERSTANDINGS and QUESTIONS

Algebraic and geometric relationships can be used to describe mathematical and real-world patterns.

  • Why is it important to describe the algebraic relationships found in numeric patterns?
  • Why is it important to describe the geometric relationships found in spatial patterns?
  • What algebraic relationships can be found in patterns?
  • What geometric relationships can be found in patterns?

Attributes and properties of two- and three-dimensional geometric shapes are foundational to developing geometric and measurement reasoning.

  • Why is it important to compare and contrast attributes and properties of two- and three-dimensional geometric shapes?
  • How does analyzing the attributes and properties of two- and three-dimensional geometric shapes develop geometric and measurement reasoning?

Application of attributes and measures of figures can be generalized to describe geometric relationships which can be used to solve problem situations.

  • Why are attributes and measures of figures used to generalize geometric relationships?
  • How can numeric patterns be used to formulate geometric relationships?
  • Why is it important to distinguish measureable attributes?
  • How do geometric relationships relate to other geometric relationships?
  • Why is it essential to develop generalizations for geometric relationships?
  • How are geometric relationships applied to solve problem situations?
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

  • Patterns/Rules

Relations

  • Proportional Relationships

Geometric Reasoning

  • Congruence
  • Geometric Attributes/Properties
  • Geometric Relationships
  • Perspective Drawings
  • Scale Factors
  • Similar Figures
  • Symmetry
  • Transformations

Associated Mathematical Processes

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

Mathematical patterns can be analyzed to develop models of algebraic and geometric relationships.

  • How are algebraic relationships in a problem situation represented, and what are the connections between the representations?
  • How are mathematical patterns observed and described in similarity, transformations, symmetry, and perspective used to model geometric relationships?

Geometric relationships such as similarity, transformations, symmetry, and perspective can be used to model, describe, and solve problems in architecture and engineering.

  • Which geometric transformations maintain congruence, and how are congruent transformations applied in architecture and engineering?
  • Which geometric transformations demonstrate similarity, and how is similarity applied in architecture and engineering?
  • What is the purpose of symmetry, and how is it illustrated in architecture and engineering?
  • What are the different types of perspective, and how are they illustrated and applied in architecture and engineering?
  • How are similarity, transformations, symmetry, and perspective used to model problems in architecture and engineering?
  • How are similarity, transformations, symmetry, and perspective used to describe problems in architecture and engineering?
  • How are similarity, transformations, symmetry, and perspective used to solve problems in architecture and engineering?
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

  • Ratios

Relations

  • Proportional Relationships

Geometric Reasoning

  • Geometric Attributes/Properties
  • Two-Dimensional Figures
  • Three-Dimensional Figures

Measurement Reasoning

  • Dimensional Change
  • Length
  • Surface Area
  • Volume

Associated Mathematical Processes

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

A two-dimensional net and its attributes and properties can be used to determine surface area and volume of a three-dimensional figure.  

  • Why can a three-dimensional figure be represented by a two-dimensional net?
  • How are the attributes and properties of two-dimensional figures used to determine surface area and volume of a three-dimensional figure?

Using scale factor(s) on one or two dimensions of a three-dimensional figure results in a non-proportional change in surface area and volume, whereas using a scale factor to all three dimensions of a three-dimensional figure results in a proportional change in surface area and volume.

  • How are similar figures generated?
  • When is dimensional change in three-dimensional figures proportional?
  • When is dimensional change in three-dimensional figures non-proportional?
  • What are some of the possible effects on the surface area and volume of an object when a scale factor is applied to just one of the dimensions?  Scale factor(s) on two dimensions?  Scale factor(s) three dimensions?
  • How can the resulting effects on the measurements of the scaled object be predicted?
  • How do architects and engineers use scale factors to create proportional and non-proportional three-dimensional designs?

MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

  • Some student may think that when a scale factor is applied to only one or two dimensions of a three-dimensional figure that the figure will change proportionally rather than changing non-proportionally.
  • Some students may think that when a scale factor is applied to all dimensions in a figure, the surface and volume are changed by the same scale factor rather than the surface area and volume changing by the square and cube of the scale factor, respectively.
  • Some students may think any repeated use of a shape arranged in a plane produces a tessellation rather than understanding that a tessellation must be the complete pattern that covers the entire plane leaving no spaces.

Unit Vocabulary

  • Dilation – non-rigid, similarity transformation in which a figure is enlarged or reduced using a scale factor and a center of dilation
  • One-point perspective (vanishing point) – a linear perspective that occurs when all parallel lines drawn away from the viewer appear to converge in a single vanishing point on the horizon line
  • Perspective drawing – a type of drawing using lines and points that can represent a three-dimensional view on a two-dimensional surface
  • Reflection – rigid transformation in which each point in a geometric figure is at an equal distance on the opposite side of a given line (line of symmetry)
  • Rotation – rigid transformation where each point on the figure is rotated about a given point
  • Similar figures – shapes whose angles are congruent and side lengths are proportional (equal scale factor)
  • Symmetry – refers to geometric figures or graphs consisting of two parts on either side of a point, line, or plane that are identical or congruent to each other
  • Transformation  – one to one mapping of points in a plane such that each point in the pre-image has a unique image and each point in the image has a pre-image
  • Tessellation – the covering of an infinite plane with repetitions of one or more shapes or tiling units with no gaps or overlapping. Tessellations undergo isometric transformations in such a way as to form a pattern that fills a plane in a symmetrical way.
  • Translation – rigid transformation moving all points in a geometric figure the same distance and the same direction
  • Two-point perspective – a linear perspective that occurs when all parallel lines drawn away from the viewer appear to converge in two different points on the horizon line that create a 90° angle from the point of projection or common vertex

Related Vocabulary:

  • Net
  • Non-proportional change
  • Proportional change
  • Scale factor
  • Similarity
  • Surface area
  • Tessellation
  • Three-dimensional figure
  • Two-dimensional figure
  • Vanishing point
  • Volume
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

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)
M.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
M.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
M.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
M.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
M.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
M.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
M.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
M.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
M.6 Mathematical modeling in science and engineering. The student applies mathematical processes with algebra and geometry to study patterns and analyze data as it applies to architecture and engineering. The student is expected to:
M.6A Use similarity, geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in architecture.

Use

SIMILARITY, GEOMETRIC TRANSFORMATIONS, SYMMETRY, AND PERSPECTIVE DRAWINGS

Including, but not limited to:

  • Similar figures – shapes whose angles are congruent and side lengths are proportional (equal scale factor)
  • Geometric transformations
    • Translation – rigid transformation moving all points in a geometric figure the same distance and the same direction
    • Reflection – rigid transformation in which each point in a geometric figure is at an equal distance on the opposite side of a given line (line of symmetry)
    • Rotation – rigid transformation where each point on the figure is rotated about a given point
    • Dilation – non-rigid, similarity transformation in which a figure is enlarged or reduced using a scale factor and a center of dilation
  • Symmetry – refers to geometric figures or graphs consisting of two parts on either side of a point, line, or plane that are identical or congruent to each other
  • Perspective drawing – a type of drawing using lines and points that can represent a three-dimensional view on a two-dimensional surface
    • One-point perspective (vanishing point) – a linear perspective that occurs when all parallel lines drawn away from the viewer appear to converge in a single vanishing point on the horizon line
    • Two-point perspective – a linear perspective that occurs when all parallel lines drawn away from the viewer appear to converge in two different points on the horizon line that create a 90° angle from the point of projection or common vertex
  • Property of congruence
    • Congruence is preserved when a two-dimensional figure is transformed and the image is identical in shape and size.
    • Congruence is not preserved when a two-dimensional figure is transformed and the image is not identical in shape and/or identical in size.
  • Property of orientation of the vertices
    • Orientation of the vertices of an image is determined by naming the vertices in the same order as the corresponding vertices of its pre-image and not determined by a figure’s direction or a figure’s size.
    • Orientation of the vertices is preserved in translation, rotations, and dilations.
    • Orientation of the vertices is not preserved in reflections.
  • Tessellation – the covering of an infinite plane with repetitions of one or more shapes or tiling units with no gaps or overlapping. Tessellations undergo isometric transformations in such a way as to form a pattern that fills a plane in a symmetrical way.
    • One or more different figures may be used to create a tessellated pattern.
    • The sum of all the interior angles that meet at any vertex must be 360o.

To Describe

MATHEMATICAL PATTERNS AND STRUCTURE IN ARCHITECTURE  (AS APPLIED TO SCIENCE AND ENGINEERING)

Including, but not limited to:

  • Tiling with tessellations
  • Symmetry is also evident in art and architecture. Symmetry implies a balance.
    • Two types of symmetry can be seen in many drawings and pictures.
      • Reflection symmetry reflects across an axis of symmetry.
      • Rotational symmetry occurs if a figure can be rotated less than 360° around a central point and still look the same as the original.
  • Perspective drawings
  • Similar figures

Note(s):

  • Grade Level(s)
    • Grade 7 studied similarity in relation to proportional change.
    • Grade 8 studied similarity in angle relationships.
    • Geometry studied similarity, symmetry, and all transformations as applied to figures and proofs.
    • Mathematical Models with Applications introduces perspective drawing.
    • 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
      • B1 – Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions.
    • VII. Functions
      • A2 – Recognize and distinguish between different types of functions.
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
M.6B Use scale factors with two-dimensional and three-dimensional objects to demonstrate proportional and non-proportional changes in surface area and volume as applied to fields.

Use

SCALE FACTORS WITH TWO-DIMENSIONAL AND THREE-DIMENSIONAL OBJECTS

Including, but not limited to:

  • Proportional change by a scale factor of two-dimensional figures creates similar figures
  • Proportional change by a scale factor of three dimensional figures creates similar figures
  • Non-proportional change by a scale factor of two dimensional figures creates non-similar figures
  • Non-proportional change by a scale factor of three-dimensional figures creates non-similar figures

To Demonstrate

PROPORTIONAL AND NON-PROPORTIONAL CHANGES IN SURFACE AREA AND VOLUME AS APPLIED TO FIELDS

Including, but not limited to:

  • Proportional and non-proportional changes in surface area and volume in building and architectural planning
  • Proportional and non-proportional changes in surface area and volume in engineering commercial packaging

Note(s):

  • Grade Level(s)
    • Grade 6 used scale factors involving ratios and rates to solve problems.
    • Grade 8 applied scale factors to two-dimensional figures.
    • Algebra I studied the linear parent function f(x) = x.
    • Geometry studied the use of scale factors on two-dimensional and three-dimensional figures to effect proportional and non-proportional change.
    • 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
      • B1 – Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions.
    • VII. Functions
      • A2 – Recognize and distinguish between different types of 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 09/01/2016
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