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Instructional Focus Document
Grade 6 Mathematics
TITLE : Unit 01: Equivalent Forms of Fractions, Decimals, and Percents SUGGESTED DURATION : 10 days

Unit Overview

Introduction
This unit bundles student expectations that address representing and generating equivalent forms of fractions, decimals, and percents as well as solving real-world problems involving fractions, decimals, and percents. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, 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. The introduction to the grade level standards state, “While the use of all types of technology is important, the emphasis on algebra readiness skills necessitates the implementation of graphing technology."

Prior to this Unit
In Grade 4, students determined if two given fractions were equivalent using a variety of methods. Additionally, in Grade 5 students added and subtracted positive rational numbers fluently, including problems involving mixed forms of rational numbers.

During this Unit
Students extend their mathematical foundations of equivalency within rational numbers, including percents. Concrete and pictorial models, including 10 by 10 grids, strip diagrams, and number lines are used to represent multiples of benchmark fractions and percents. Additionally, percents are represented with concrete and pictorial models, fractions, and decimals. Students continue their understanding of equivalency by generating and using equivalent forms of fractions, decimals, and percents to solve real-world problems, including those involving money. Percents less than or greater than 100%, including percents with fractional or decimal values such as 8.25% or  are encompassed within this unit. Students apply their understandings of percents to solve real-world problems that involve finding the whole given a part and the percent, the part given the whole and a percent, and the percent given the part and the whole. Methods for solving real-world problem situations involving percents, such as the use of proportions or scale factors between ratios, are not included in this unit. Computations within this unit are restricted to operational capabilities from Grade 5 which include sums and differences with any positive rational numbers, products with factors limited to a whole number by a whole number, a decimal by a decimal, or a whole number by a fraction, and quotients limited to whole number dividends and divisors, a decimal dividend by a whole number divisor, or whole number and unit fraction dividends and divisors.

After this Unit
In Unit 02, students will further their understanding of equivalency by ordering whole numbers, positive and negative rational numbers, and integers. In Unit 03, students will add, subtract, multiply, and divide whole numbers, positive rational numbers, and integers. In Unit 05, students will examine percents again through the lens of proportional reasoning with ratios and rates. At that time, the proportion method and utilizing scale factors between ratios will be appropriate methods to solve real-world problem situations involving percent. In Grade 7, students will solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems.

Additional Notes
In Grade 6, generating equivalent forms of fractions, decimals, and percents is identified as STAAR Readiness Standard 6.4G. Representing percents with concrete models, fractions and decimals is STAAR Supporting Standard 6.4E. Representing benchmark fractions and percents with concrete and pictorial models and numbers, as well as using equivalent fractions, decimals, and percents to show equal parts of the same whole are identified as STAAR Supporting Standards 6.4F and 6.5C. All of these standards are subsumed under the Grade 6 STAAR Reporting Category 1:  Numerical Representations and Relationships. Solving real-world problems involving percents is identified as STAAR Readiness Standard 6.5B and part of the Grade 6 STAAR Reporting Category 2: Computations and Algebraic Relationships. All of these standards are subsumed under the Grade 6 Texas Response to Curriculum Focal Points (TxRCFP): Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning, IX. Communication and Representation, VIII. Problem Solving and Reasoning, and X. Connections.

Research
According to Van de Walle, Bay-Williams, Lovin, and Karp (2013), “Physical models provide the main link between fractions, decimal, and percents. Students should develop an understanding of the percent equivalence of familiar fractions (halves, thirds, fourths, fifths, and eighths)” (p. 162). The essential understanding of percent is built on the concept of 100. “Students who understand that percent means parts out of one hundred and have a good pictorial representation of percent are more successful in solving percent problems than those who do not” (Reyes, Lindquist, Lambdin & Smith, 2012, p. 292). Additionally, as students initially begin to solve problems involving percents instruction should include “activities that center on direct translation of experiences involving 100” (p. 293). When determining equivalent forms of fractions, decimals, and percents, Van de Walle et al. (2013) suggests that rather than, “rush[ing] to develop rules or procedures for different types of problems – encourage students to notice patterns…Require student to use manipulatives, drawings, and contexts to explain their solutions” (p. 166).

 

Reyes, R. E., Lindquist, M., Lambdin, D. V., & Smith, N. L. (2012). Helping children learn mathematics. (10th ed.). Hoboken, NJ: Wiley.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from https://www.texasgateway.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013
Van de Walle, J., Bay-Williams, J., Lovin, L., & Karp, K., (2013). Teaching student-centered mathematics: Developmentally appropriate instruction for grades 6 - 8. Boston, MA: Pearson.


  • Quantitative relationships model problem situations efficiently and can be used to make generalizations, predictions, and critical judgements in everyday life.
    • What patterns exist within different types of quantitative relationships and where are they found in everyday life?
    • Why is the ability to model quantitative relationships in a variety of ways essential to solving problems in everyday life?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
  • Understanding how two quantities vary together (covariation) and can be reasoned up and down in situations involving invariant (constant) relationships builds flexible numeric reasoning in order to make predictions and critical judgements about the relationship (fractions; decimals; percents).
    • Fractions, decimals, and percents are modeled and described to develop an understanding of proportional relationships and these relationships are applied to represent equivalence and solve problem situations.
      • How can representing percents using …
        • concrete models
        • fractions
        • decimals
        … aid in problem solving?
      • How can representing benchmark fractions and percents using …
        • 10 by 10 grid
        • strip diagrams
        • number lines
        • numbers
        … aid in problem solving?
      • How are the models for fractions and percents …
        • alike?
        • different?
      • What is the relationship between benchmark fractions, their multiples, and unit fractions?
      • How can an equivalent …
        • fraction be generated when given a decimal or percent?
        • decimal be generated when given a fraction or percent?
        • percent be generated when given a decimal or fraction?
      • What types of models and strategies can be used to generate equivalent forms of fractions, decimals, and percents?
      • Why is the ability to model numbers in a variety of ways essential to solving problems in everyday life?
      • How can benchmark fractions and percents be used to solve problems involving money?
      • How can concrete and pictorial models aid in understanding and determining the whole, part, or percent when two of the three are given?
  • Proportionality
    • Fractions and Decimals
      • Percents
    • Relationships and Generalizations
      • Equivalence
      • Benchmark fractions and percents
    • Representations
    • Solution Strategies
  • Associated Mathematical Processes
    • Application
    • Problem Solving Model
    • Tools and Techniques
    • Communication
    • Representations
    • Relationships
    • Justification
Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

  • Some students may think that a percent may not exceed 100%.
  • Some students may think that a percent may not be less than 1%.
  • Some students may divide a decimal by 100 by moving the decimal two places to the left when trying to convert it to a percent rather than multiplying by 100 and moving the decimal two places to the right.
  • Some students may think the value of 43% of 35 is the same value of 43% of 45 because the percents are the same rather than considering that the wholes of 35 and 45 are different, so 43% of each quantity will be different.

Underdeveloped Concepts:

  • Some students may not realize which operation is easier to use when converting between number forms.
  • Some students may confuse decimal place values when converting decimals to fractions.
  • Some students may have difficulty recognizing the part and the whole in problem situations.
  • Some students may believe every fraction relates to a different rational number instead of realizing equivalent fractions relate to the same relative amount.
  • Some students may try to convert a fraction to a decimal by placing the denominator in the dividend rather than the numerator.
  • Some students may think that a fraction can be converted to a decimal by simply writing the numerator and denominator as digits after a decimal (e.g.,  is equivalent to 0.78).

Unit Vocabulary

  • Percent – a part of a whole expressed in hundredths
  • Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
  • Strip diagram – a linear model used to illustrate number relationships

Related Vocabulary:

  • 10 by 10 grid
  • Area model
  • Place value
  • Benchmark fraction
  • Benchmark percent
  • Decimal
  • Decimal notation
  • Denominator
  • Equivalent
  • Fraction
  • Fraction circle
  • Fraction notation
  • Improper fraction
  • Mixed number
  • Multiple
  • Number line
  • Numerator
  • Part
  • Proper fraction
  • Whole
  • Whole number
Unit Assessment Items System Resources Other Resources

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Unit Assessment Items that have been published by your district may be accessed through Search All Components in the District Resources tab. Assessment items may also be found using the Assessment Creator if your district has granted access to that tool.

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

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

 

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

 

Texas Education Agency – Mathematics Curriculum

 

Texas Education Agency – STAAR Mathematics Resources

 

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

 

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

 

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

 

Texas Education Agency Texas Gateway – Resources Aligned to Grade 6 Mathematics TEKS

 

Texas Instruments – Graphing Calculator Tutorials


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

Legend:

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

Legend:

  • Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
  • Unit-specific clarifications are in italicized, blue text.
  • Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
  • A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.
6.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
6.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard

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.
  • TxRCFP:
    • Using operations with integers and positive rational numbers to solve problems
    • Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
    • Using expressions and equations to represent relationships in a variety of contexts
    • Understanding data representation
  • TxCCRS:
    • X. Connections
6.1B 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.
Process Standard

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.
  • TxRCFP:
    • Using operations with integers and positive rational numbers to solve problems
    • Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
    • Using expressions and equations to represent relationships in a variety of contexts
    • Understanding data representation
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
6.1C 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.
Process Standard

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.
  • TxRCFP:
    • Using operations with integers and positive rational numbers to solve problems
    • Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
    • Using expressions and equations to represent relationships in a variety of contexts
    • Understanding data representation
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
6.1D

Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.


Process Standard

Communicate

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

Including, but not limited to:

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

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Using operations with integers and positive rational numbers to solve problems
    • Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
    • Using expressions and equations to represent relationships in a variety of contexts
    • Understanding data representation
  • TxCCRS:
    • IX. Communication and Representation
6.1E Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard

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.
  • TxRCFP:
    • Using operations with integers and positive rational numbers to solve problems
    • Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
    • Using expressions and equations to represent relationships in a variety of contexts
    • Understanding data representation
  • TxCCRS:
    • IX. Communication and Representation
6.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard

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.
  • TxRCFP:
    • Using operations with integers and positive rational numbers to solve problems
    • Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
    • Using expressions and equations to represent relationships in a variety of contexts
    • Understanding data representation
  • TxCCRS:
    • X. Connections
6.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard

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.
  • TxRCFP:
    • Using operations with integers and positive rational numbers to solve problems
    • Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
    • Using expressions and equations to represent relationships in a variety of contexts
    • Understanding data representation
  • TxCCRS:
    • IX. Communication and Representation
6.4 Proportionality. The student applies mathematical process standards to develop an understanding of proportional relationships in problem situations. The student is expected to:
6.4E

Represent ratios and percents with concrete models, fractions, and decimals.


Supporting Standard

Represent

PERCENTS WITH CONCRETE MODELS, FRACTIONS, AND DECIMALS

Including, but not limited to:

  • Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
  • Various forms of positive rational numbers
    • Counting (natural) numbers
    • Decimals
    • Fractions
    • Percents
      • Percent – a part of a whole expressed in hundredths
  • Percent
    • Numeric forms
    • Concrete and pictorial models of percents
      • Objects
      • Fraction circle
      • Strip diagram – a linear model used to illustrate number relationships
      • 10 by 10 grid
      • Number line
    • Numeric representation of percents
      • Fraction notation
      • Decimal notation

Note(s):

  • Grade Level(s):
    • Grade 6 introduces representing ratios and percents with concrete models, fractions, and decimals.
    • Grade 7 will solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
  • TxCCRS:
    • IX. Communication and Representation
    • X. Connections
6.4F Represent benchmark fractions and percents such as 1%, 10%, 25%, 33 1/3%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers.
Supporting Standard

Represent

BENCHMARK FRACTIONS AND PERCENTS SUCH AS 1%, 10%, 25%, 33%, AND MULTIPLES OF THESE VALUES USING 10 BY 10 GRIDS, STRIP DIAGRAMS, NUMBER LINES, AND NUMBERS

Including, but not limited to:

  • Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
  • Various forms of positive rational numbers
    • Counting (natural) numbers
    • Decimals
    • Fractions
    • Percents
      • Percent – a part of a whole expressed in hundredths
  • Benchmark fractions ()
    • Multiples of benchmark fractions
  • Benchmark percents (1%, 10%, 25%, 33%)
    • Multiples of benchmark percents
  • Various representations of benchmark fractions and percents and their multiples
    • 10 by 10 grid
    • Strip diagram – a linear model used to illustrate number relationships
    • Number line
    • Numerically

Note(s):

  • Grade Level(s):
    • Grade 6 introduces representing benchmark fractions and percents such as 1%, 10%, 25%, 33%, and multiples of these values using 10 by 10 grids, strip diagrams, number lines, and numbers.
    • Grade 7 will solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
  • TxCCRS:
    • I. Numeric Reasoning
    • IX. Communication and Representation
6.4G Generate equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money.
Readiness Standard

Generate

EQUIVALENT FORMS OF FRACTIONS, DECIMALS, AND PERCENTS USING REAL-WORLD PROBLEMS, INCLUDING PROBLEMS THAT INVOLVE MONEY

Including, but not limited to:

  • Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
  • Various forms of positive rational numbers
    • Counting (natural) numbers
    • Decimals
    • Fractions
    • Percents
      • Percent – a part of a whole expressed in hundredths
  • Equivalent forms of positive rational numbers in real-world problem situations, including money
    • Given a fraction, generate a decimal and percent
    • Given a decimal, generate a fraction and percent
    • Given a percent, generate a fraction and decimal

Note(s):

  • Grade Level(s):
    • Grade 6 introduces generating equivalent forms of fractions, decimals, and percents using real-world problems, including problems that involve money.
    • Grade 6 introduces ordering a set of rational numbers arising from mathematical and real-world contexts.
    • Grade 7 will solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
  • TxCCRS:
    • I. Numeric Reasoning
    • IX. Communication and Representation
    • X. Connections
6.5 Proportionality. The student applies mathematical process standards to solve problems involving proportional relationships. The student is expected to:
6.5B Solve real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models.
Readiness Standard

Solve

REAL-WORLD PROBLEMS TO FIND THE WHOLE GIVEN A PART AND THE PERCENT, TO FIND THE PART GIVEN THE WHOLE AND THE PERCENT, AND TO FIND THE PERCENT GIVEN THE PART AND THE WHOLE, INCLUDING THE USE OF CONCRETE AND PICTORIAL MODELS

Including, but not limited to:

  • Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
  • Various forms of positive rational numbers
    • Counting (natural) numbers
    • Decimals
    • Fractions
    • Percents
      •  Percent – a part of a whole expressed in hundredths
  • Multiple methods for solving real-world problem situations involving percent
    • Concrete and pictorial models (e.g., objects, area model, strip diagram, 10 by 10 grid, number line, etc.)
  • Various types of real-world problem situations involving percent
    • Limited to situations in which the parts and percents are less than the whole
    • Finding the whole given a part and a percent
    • Finding the part given the whole and a percent
    • Finding the percent given the part and the whole

Note(s):

  • Grade Level(s):
    • Grade 6 introduces solving real-world problems to find the whole given a part and the percent, to find the part given the whole and the percent, and to find the percent given the part and the whole, including the use of concrete and pictorial models.
    • Grade 7 will solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
  • TxCCRS:
    • I. Numeric Reasoning
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
6.5C Use equivalent fractions, decimals, and percents to show equal parts of the same whole.
Supporting Standard

Use

EQUIVALENT FRACTIONS, DECIMALS, AND PERCENTS TO SHOW EQUAL PARTS OF THE SAME WHOLE

Including, but not limited to:

  • Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
  • Various forms of positive rational numbers
    • Counting (natural) numbers
    • Decimals
    • Fractions
    • Percents
      • Percent – a part of a whole expressed in hundredths
  • Various representations to show equal parts of the same whole
    • 10 by 10 grid
    • Strip diagram – a linear model used to illustrate number relationships
    • Number line

Note(s):

  • Grade Level(s):
    • Grade 6 introduces using equivalent fractions, decimals, and percents to show equal parts of the same whole.
    • Grade 7 will solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Understanding and applying ratios and rates and using equivalent ratios to represent proportional relationships
  • TxCCRS:
    • I. Numeric Reasoning
    • IX. Communication and Representation
The English Language Proficiency Standards (ELPS), as required by 19 Texas Administrative Code, Chapter 74, Subchapter A, §74.4, outline English language proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement ELPS as an integral part of each subject in the required curriculum.

School districts shall provide instruction in the knowledge and skills of the foundation and enrichment curriculum in a manner that is linguistically accommodated commensurate with the student’s levels of English language proficiency to ensure that the student learns the knowledge and skills in the required curriculum.


School districts shall provide content-based instruction including the cross-curricular second language acquisition essential knowledge and skills in subsection (c) of the ELPS in a manner that is linguistically accommodated to help the student acquire English language proficiency.

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


Choose appropriate ELPS to support instruction.

ELPS# Subsection C: Cross-curricular second language acquisition essential knowledge and skills.
Click here to collapse or expand this section.
ELPS.c.1 The ELL uses language learning strategies to develop an awareness of his or her own learning processes in all content areas. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.1A use prior knowledge and experiences to understand meanings in English
ELPS.c.1B monitor oral and written language production and employ self-corrective techniques or other resources
ELPS.c.1C use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary
ELPS.c.1D speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known)
ELPS.c.1E internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment
ELPS.c.1F use accessible language and learn new and essential language in the process
ELPS.c.1G demonstrate an increasing ability to distinguish between formal and informal English and an increasing knowledge of when to use each one commensurate with grade-level learning expectations
ELPS.c.1H develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for patterns in language, and analyzing sayings and expressions commensurate with grade-level learning expectations.
ELPS.c.2 The ELL listens to a variety of speakers including teachers, peers, and electronic media to gain an increasing level of comprehension of newly acquired language in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in listening. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.2A distinguish sounds and intonation patterns of English with increasing ease
ELPS.c.2B recognize elements of the English sound system in newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters
ELPS.c.2C learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions
ELPS.c.2D monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed
ELPS.c.2E use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language
ELPS.c.2F listen to and derive meaning from a variety of media such as audio tape, video, DVD, and CD ROM to build and reinforce concept and language attainment
ELPS.c.2G understand the general meaning, main points, and important details of spoken language ranging from situations in which topics, language, and contexts are familiar to unfamiliar
ELPS.c.2H understand implicit ideas and information in increasingly complex spoken language commensurate with grade-level learning expectations
ELPS.c.2I demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs.
ELPS.c.3 The ELL speaks in a variety of modes for a variety of purposes with an awareness of different language registers (formal/informal) using vocabulary with increasing fluency and accuracy in language arts and all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in speaking. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.3A practice producing sounds of newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters to pronounce English words in a manner that is increasingly comprehensible
ELPS.c.3B expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication
ELPS.c.3C speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired
ELPS.c.3D speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency
ELPS.c.3E share information in cooperative learning interactions
ELPS.c.3F ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments
ELPS.c.3G express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics
ELPS.c.3H narrate, describe, and explain with increasing specificity and detail as more English is acquired
ELPS.c.3I adapt spoken language appropriately for formal and informal purposes
ELPS.c.3J respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment.
ELPS.c.4 The ELL reads a variety of texts for a variety of purposes with an increasing level of comprehension in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in reading. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1, certain of these student expectations apply to text read aloud for students not yet at the stage of decoding written text. The student is expected to:
ELPS.c.4A learn relationships between sounds and letters of the English language and decode (sound out) words using a combination of skills such as recognizing sound-letter relationships and identifying cognates, affixes, roots, and base words
ELPS.c.4B recognize directionality of English reading such as left to right and top to bottom
ELPS.c.4C develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials
ELPS.c.4D use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to enhance comprehension of written text
ELPS.c.4E read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned
ELPS.c.4F use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language
ELPS.c.4G demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs
ELPS.c.4H read silently with increasing ease and comprehension for longer periods
ELPS.c.4I demonstrate English comprehension and expand reading skills by employing basic reading skills such as demonstrating understanding of supporting ideas and details in text and graphic sources, summarizing text, and distinguishing main ideas from details commensurate with content area needs
ELPS.c.4J demonstrate English comprehension and expand reading skills by employing inferential skills such as predicting, making connections between ideas, drawing inferences and conclusions from text and graphic sources, and finding supporting text evidence commensurate with content area needs
ELPS.c.4K demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and performing critical analyses commensurate with content area and grade-level needs.
ELPS.c.5 The ELL writes in a variety of forms with increasing accuracy to effectively address a specific purpose and audience in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in writing. In order for the ELL to meet grade-level learning expectations across foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1, certain of these student expectations do not apply until the student has reached the stage of generating original written text using a standard writing system. The student is expected to:
ELPS.c.5A learn relationships between sounds and letters of the English language to represent sounds when writing in English
ELPS.c.5B write using newly acquired basic vocabulary and content-based grade-level vocabulary
ELPS.c.5C spell familiar English words with increasing accuracy, and employ English spelling patterns and rules with increasing accuracy as more English is acquired
ELPS.c.5D edit writing for standard grammar and usage, including subject-verb agreement, pronoun agreement, and appropriate verb tenses commensurate with grade-level expectations as more English is acquired
ELPS.c.5E employ increasingly complex grammatical structures in content area writing commensurate with grade-level expectations, such as:
ELPS.c.5F write using a variety of grade-appropriate sentence lengths, patterns, and connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired
ELPS.c.5G narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired.
Last Updated 08/01/2018
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