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Instructional Focus Document
Mathematical Models with Applications
TITLE : Unit 09: Probability SUGGESTED DURATION : 13 days

Unit Overview

This unit bundles student expectations that address the application of algebraic expressions and equations associated with linear and exponential relationships to describe mathematical patterns in probability. 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 7, students made predictions and determined theoretical and experimental probabilities in problem situations, including the introduction of the Fundamental Counting Principle. In Geometry, students studied combinations and permutations in contextual problems.

During this unit, students determine the number of ways an event may occur using combinations, permutations, and the Fundamental Counting Principle. Students perform experiements, demonstrating empirical probability, to predict the likelihood of an event occurring from the outcomes of the experiment. Students use the same events, calculating theoretical probability, to predict the likelihood of an event occurring using formulas and mathematical calculations without conducting an experiment. Students then compare the experimental outcomes to the calculated theoretical probability. After conducting multiple experiments, students realize as the number of trials in the experiment increases, the experimental probability of an event approaches the theoretical probability of the same event, known as the Law of Large Numbers. Students define binomial distribution and use the formula, with and without technology, to generate probabilities of various events. They perform various experiments using binomial distribution and compare the theoretical model to the experimental results to determine the reasonableness of the theoretical model. Students define geometric distribution and use the formula, with and without technology, to generate probabilities of various events. Students use the results of experiments and theoretical models to make general comparisons of theoretical to empirical probability.

After this unit, students will create a data collection and research project in which they will formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions. Students will present their methods used, analyses conducted, and conclusions drawn through the use of one or more of the following: a written report, a visual display, an oral report, or a multi-media presentation.

This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning B1; II. Algebraic Reasoning B1; V. Probabilistic Reasoning A1, B1, B2; 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).

Education Policy Improvement Center (2009), Texas College and Career Standards, Austin, TX, University of Texas Printing.
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.

OVERARCHING UNDERSTANDINGS and QUESTIONS

The probability or chance of an event occurring can be determined by various methods, interpreted for reliability, and used to make predictions and inferences in problem situations.

  • Why is it important to understand and use probability?
  • How do theoretical and empirical probability compare?
  • Why is it important to understand and determine total possible outcomes?
  • What methods can be used to determine probability?
  • How can probability be represented?
  • How is the probability of an event(s) used to make predictions and inferences in 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.

Probabilistic Reasoning

  • Conclusions/Predictions
  • Events
  • Permutations/Combinations
  • Sample Spaces

 

Associated Mathematical Processes

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

The number of ways an event may occur can be determined using combinations, permutations, and the Fundamental Counting Principle.

  • How can combinations be used to determine the number of ways an event may occur?
  • How can permutations be used to determine the number of ways an event may occur?
  • How can it be determined whether to use combinations or permutations?
  • When can the Fundamental Counting Principle be applied?
  • How can the Fundamental Counting Principle be used to determine the number of ways an event may occur?
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

 

Probabilistic Reasoning

  • Conclusions/Predictions
  • Events
  • Probability of an Event
  • Simulations
  • Theoretical/Empirical Probability

 

Associated Mathematical Processes

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

Probability is the likelihood of an event occurring from the total possible outcomes, and probability can be applied to solve mathematical and real-world problem situations.

  • How can total possible outcomes or sample space be determined?
  • How is probability of an event determined?
  • How is probability of an event represented?
  • How can probability based on area be used to solve contextual problems?
  • How do with replacement or without replacement factor into determining if two events are independent or dependent?
  • How is the probability of independent and dependent events applied in contextual problems?

 

Theoretical probability of an event occurring is calculated using formulas and empirical probability of an event occurring is determined by analyzing data collected experimentally.

  • What is the purpose of determining the probability of the occurrence of an event?
  • How do theoretical probability and empirical probability compare?
  • What conditions might necessitate the use of theoretical probability?
  • What conditions might necessitate the use of empirical probability?
  • Why might the theoretical probability and empirical probability of a particular event differ?
  • How does the number of trials in an experiment affect the validity of the empirical probability?
  • How can a theoretical probability be determined from an area model?
  • How can an empirical probability be simulated using an area model?

 

Experiments and simulations can be used to test the reasonableness of theoretical probability models.

  • What types of theoretical probability models can be tested using experiments and simulations?
  • How are experiments used to test the reasonableness of theoretical probability models?
  • How are simulations used to test the reasonableness of theoretical probability models?
  • What is meant by a binomial probability theoretical model?
  • How is an experiment designed to determine the reasonableness of a binomial theoretical model for a particular situation?
  • What is meant by a geometric area probability model?
  • How is an experiment designed to determine the reasonableness of a geometric theoretical model for a particular situation?

MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

  • Some students may think they are to use the same ratio of events rather than changing the ratio when one is drawn or taken out and not replaced.

 

Underdeveloped Concepts:

  • Some students may misunderstand the multiplication of ratios and want to add instead.

Unit Vocabulary

  • Binomial probability – probability that an experiment with n trials results in exactly r successes, when the probability of success of each trial is p.
  • Binomial probability formula: nCr  pr  q(nr), where n is the number of trials in the experiment, r is the number of successes, p is the probability of success on a trial, and q is the probability of failure on a trial.
  • Combinations – number of different ways a set of objects can be selected without regard to a specific order
  • Empirical (experimental) probability – probability of an event occurring predicted by the results of an experiment
  • Formula for combinations: nCr = , where n is the total number of objects in the set and r is the number to be chosen.
  • Formula for permutations: nPr, where n is the total number of objects in the set and r  is the number to be chosen.
  • Geometric probability – probability that involves the comparison of geometric measures such as length or area.
  • Geometric probability formula, which is the same as for finding the simple probability of an event. However, the outcomes will be geometric measurements.
  • Law of large numbers – as the number of trials in an experiment increases, the experimental probability of an event approaches the theoretical probability of the same event, meaning the difference between the experimental and theoretical probability will be closer to zero
  • Permutations – number of different ways a set of objects can be selected with regard to a specific order
  • Theoretical probability – the likelihood of an event occurring predicted by using formulas and mathematical calculations without conducting an experiment

 

Related Vocabulary:

  • Binomial model
  • Combination
  • Empirical
  • Event
  • Geometric model
  • Outcome
  • Permutation
  • Probability
  •  Success
  • Theoretical
  • Trial
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.8 Mathematical modeling in social sciences. The student applies mathematical processes to determine the number of elements in a finite sample space and compute the probability of an event. The student is expected to:
M.8A Determine the number of ways an event may occur using combinations, permutations, and the Fundamental Counting Principle.

Determine

THE NUMBER OF WAYS AN EVENT MAY OCCUR USING COMBINATIONS, PERMUTATIONS, AND THE FUNDAMENTAL COUNTING PRINCIPLE

Including, but not limited to:

  • Event – a probable situation or condition
  • Combinations – number of different ways a set of objects can be selected without regard to a specific order
    • Formula for combinations: nCr, where n is the total number of objects in the set and r is the number to be chosen.
    • Graphing calculator technology to determine combinations
  • Permutations – number of different ways a set of objects can be selected with regard to a specific order
    • Formula for permutations: nPr = , where n is the total number of objects in the set and r  is the number to be chosen.
    • Graphing calculator technology to determine permutations
  • Fundamental Counting Principle – if one event has a possible outcomes and a second independent event has b possible outcomes, then there are a b total possible outcomes for the two events together

Note(s):

  • Grade Level(s)
    • Grade 7 introduced the Fundamental Counting Principle.
    • Geometry studied combinations and permutations in contextual problems.
    • 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.
    • V. Probabilistic Reasoning
      • A1 – Determine the nature and the number of elements in a finite sample space
      • B1 – Compute and interpret the probability of an event and its complement
      • B2 – Compute and interpret the probability of conditional and compound events
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
M.8B Compare theoretical to empirical probability.

Compare

THEORETICAL TO EMPIRICAL PROBABILITY

Including, but not limited to:

  • Empirical (experimental) probability – the likelihood of an event occurring from the outcomes of an experiment
  • Theoretical probability – the likelihood of an event occurring predicted by using formulas and mathematical calculations without conducting an experiment

Note(s):

  • Grade Level(s)
    • Grade 7 made predictions and determined theoretical and experimental probabilities in 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
      • B1 – Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions.
    • V. Probabilistic Reasoning
      • A1 – Determine the nature and the number of elements in a finite sample space
      • B1 – Compute and interpret the probability of an event and its complement
      • B2 – Compute and interpret the probability of conditional and compound events
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
M.8C Use experiments to determine the reasonableness of a theoretical model such as binomial or geometric.

Use

EXPERIMENTS OF A THEORETICAL MODEL SUCHAS AS BINOMIAL OR GEOMETRIC

Including, but not limited to:

  • Binomial probability – probability that an experiment with n trials results in exactly r successes, when the probability of success of each trial is p
    • Binomial probability formula: nCr • pr q(n-r), where n is the number of trials in the experiment, r is the number of successes, p is the probability of success on a trial, and q is the probability of failure on a trial.
  • Geometric probability – probability that involves the comparison of geometric measures such as length or area
    • Geometric probability formula: , which is the same as for finding the simple probability of an event. However, the outcomes will be geometric measurements.

To Determine

THE REASONABLENESS OF A THEORETICAL MODEL SUCH AS BINOMIAL OR GEOMETRIC

Including, but not limited to:

  • Application of formulas
  • Law of large numbers – as the number of trials in an experiment increases, the experimental probability of an event approaches the theoretical probability of the same event, meaning the difference between the experimental and theoretical probability will be closer to zero

Note(s):

  • Grade Level(s)
    • Grade 7 made predictions and determined theoretical and experimental probabilities in 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
      • B1 – Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions.
    • V. Probabilistic Reasoning
      • A1 – Determine the nature and the number of elements in a finite sample space
      • B1 – Compute and interpret the probability of an event and its complement
      • B2 – Compute and interpret the probability of conditional and compound events
    • 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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