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Instructional Focus Document
Grade 7 Mathematics
TITLE : Unit 01: Number and Operations SUGGESTED DURATION : 9 days

Unit Overview

Introduction
This unit bundles student expectations that address sets and subsets of rational numbers, operations with rational numbers, and personal financial literacy standards regarding sales tax, income tax, financial assets and liabilities records, and net worth statements. 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 6, students classified whole numbers, integers, and rational numbers using a visual representation, such as a Venn diagram, to describe relationships between sets of numbers. Students performed all four operations with integers as well as multiplied and divided positive rational numbers fluently. This included whole numbers, decimals, fractions, and percents converted to equivalent decimals or fractions for multiplying or dividing. Grade 5 students defined income tax, payroll tax, sales tax, and property tax.

During this Unit
Students use a visual representation to organize and display the relationship of the sets and subsets of rational numbers, which include counting (natural) numbers, whole numbers, integers, and rational numbers. Students also apply and extend operations with rational numbers to include negative fractions and decimals. Grade 7 students are expected to fluently add, subtract, multiply, and divide various forms of positive and negative rational numbers that include integers, decimals, fractions, and percents converted to equivalent decimals or fractions. Exposure to solving mathematical and real-world situations assists students in generalizing operations with positive and negative rational numbers, which builds fluency and reasonableness of solutions. Students also create and organize a financial assets and liabilities record, construct a net worth statement, calculate sales tax for a given purchase, and calculate income tax for earned wages.

After this Unit
In Units 2 – 12, students will continuously apply rational number operations to solve problems with equations and inequalities, ratios and rates, similarity, probability, geometry, measurement, and statistical representations. In Grade 8, students will extend their knowledge of sets and subsets of numbers to describe relationships between sets of real numbers as well as solve problem situations involving real numbers

Additional Notes
In Grade 7, describing relationships between sets of rational number is identified as STAAR Supporting Standard 7.2 and is subsumed under the Grade 7 STAAR Reporting Category 1: Probability and Numerical Representations. Using addition, subtraction, multiplication, and division to solve problems involving rational numbers is identified as STAAR Readiness Standard 7.3B while adding, subtracting, multiplying, and dividing rational numbers fluently is identified as STAAR Supporting Standard 7.3A. The two standards are included in the Grade 7 STAAR Reporting Category 2: Computations and Algebraic Relationships. All of these standards are a foundational block of the Grade 7 Texas Response to Curriculum Focal Points (TxRCFP): Developing fluency with rational numbers and operations to solve problems in a variety of contexts. Calculating sales tax and income tax, as well a financial assets and liabilities record and constructing a net worth statement are identified as STAAR Supporting Standards 7.13A and 7.13C. These two standards are included within the Grade 7 STAAR Reporting Category 4: Data Analysis and Personal Financial Literacy and the Grade 7 Focal Point: Financial Literacy (TxRCFP). This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning, VIII. Problem Solving and Reasoning, IX. Communication and Representation, and X. Connections.

Research
According to the National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics (2000), “In the middle grades, students should continue to refine their understandings of addition, subtraction, multiplication, and division as they use these operations with fractions, decimals, percents, and integers” (p. 218). Developing an understanding of operations of all rational numbers helps in solving linear equations. Students reference the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. (NCTM, 2006, p. 19) Based on findings from a report prepared for the U.S. Department of the Treasury, “In addition to knowledge and banking behavior, financial education also has the potential to influence student’s attitudes about savings and financial institutions” (Wiedrich, Collins, Rosen, & Rademacher, 2014, p. 25). Additionally, “Financial education in schools, even small amounts, does appear to increase financial knowledge and capability…[as well as] improved student attitudes towards savings and the usefulness of financial institutions” (p. 32).

 

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.
National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through grade 8 mathematics. Reston, VA: National Council of Teachers of Mathematics, Inc.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9
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
Wiedrich, K., Collins, J., Rosen, L., & Rademacher, I. (2014). Financial education and account access among elementary students: findings from the assessing the financial capabilities outcomes youth pilot. Retrieved from http://opportunitytexas.org/images/stories/AFCO%20Youth%20Full%20Report%20Final.pdf


  • Numeracy requires the ability to work flexibly with quantities in order to recognize, reason, and solve situations of varying contexts in everyday life, society, and the work place.
    • How is numeracy like literacy?
    • What are some examples of numeracy in everyday life, society, and the work place?
    • How does context influence understanding of a quantity?
    • Why is the ability to work flexibly with quantities essential to developing the foundations of numeracy?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
  • Rational numbers create a more sophisticated number system where new relationships exist within and between sets and subsets of numbers (counting numbers; whole numbers; integers; rational numbers).
    • What representations can be used to visually demonstrate relationships between sets and subsets of numbers?
    • How does organizing numbers in sets and subsets aid in understanding the relationships between rational numbers?
    • What relationships exist between sets and subsets of numbers?
    • How are the elements in counting (natural) numbers, whole numbers, integers, and rational numbers related?
    • How can a number belong to the same set of numbers but not necessarily the same subset of numbers?
    • What relationship exists between rational numbers and the other number sets?
  • Number and Operations
    • Number
      • Counting (natural) numbers
      • Whole numbers
      • Integers
      • Rational numbers
    • Number Representations
      • Sets and subsets
    • Relationships and Generalizations
      • Numerical
      • Equivalence
    • Representations
  • Associated Mathematical Processes
    • 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.

  • Understanding and generalizing operational relationships leads to more sophisticated representations and solution strategies in order to investigate or solve problem situations in everyday life.
    • What relationships exist within and between mathematical operations?
    • How does generalizing operational relationships lead to developing more flexible, efficient representations and/or solution strategies?
    • Why is understanding the problem solving process an essential part of learning and working mathematically?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
  • Estimation strategies can be used to mentally approximate solutions and determine reasonableness of solutions (rational numbers).
    • What strategies can be used to estimate solutions to problems?
    • When might an estimated answer be preferable to an exact answer?
    • How can an estimation aid in determining the reasonableness of an actual solution?
    • When might one estimation strategy be more beneficial than another?
  • Recognizing and understanding operational relationships in a variety of problem situations leads to efficient, accurate, and flexible representations and solution strategies (rational numbers).
    • How does the context of a problem situation affect the representation, operation(s), and/or solution strategy that could be used to solve the problem?
    • How does understanding …
      • relationships within and between operations
      • properties of operations
      • relationships between fractions and decimals
      … aid in determining an efficient strategy or representation to investigate and solve problem situations?
    • Why is it important to understand when and how to use standard algorithms?
  • Operational understandings lead to generalizations that aid in determining the reasonableness of solutions (rational numbers).
    • When adding two non-zero positive rational numbers, why is the sum always greater than each of the addends?
    • When two non-zero rational numbers have the same sign, why does the sum always have the same sign as both addends?
    • When two non-zero rational numbers have different signs, why does the sum always have the sign of the addend with the greatest absolute value?
    • When subtracting two non-zero positive rational numbers with the minuend greater than the subtrahend, why is the difference always less than the minuend?
    • When subtracting two non-zero positive rational numbers with the subtrahend greater than the minuend, why is the difference always less than the minuend and negative?
    • When subtracting a negative integer in an expression, why is the expression usually rewritten as addition?
    • When multiplying two non-zero positive rational numbers greater than one, why is the product always greater than each of the factors?
    • When multiplying two non-zero positive rational numbers with one of the factors greater than one, why is the product always greater than the smallest factor?
    • When multiplying two non-zero positive rational numbers with both factors less than one, why is the product less than the smallest factor?
    • When multiplying or dividing two rational numbers with the same sign, why is the product or quotient positive?
    • When multiplying or dividing two rational numbers with different signs, why is the product or quotient negative?
    • When dividing two non-zero positive rational numbers with the dividend less than the divisor, why is the quotient always greater than zero and less than one?
    • When dividing two non-zero positive rational numbers with the dividend greater than the divisor, why is the quotient always greater than one?
    • Why is dividing by a non-zero rational number equivalent to multiplying by its reciprocal?
    • When multiplying or dividing two or more rational numbers with no negative signs or an even number of negative signs, why is the product or quotient positive?
    • When multiplying or dividing two or more rational numbers with one negative sign or an odd number of negative signs, why is the product or quotient negative?
  • Number and Operations
    • Number
      • Rational numbers
    • Operations
      • Addition
      • Subtraction
      • Multiplication
      • Division
    • Relationships and Generalizations
      • Numerical
      • Operational
    • Solution Strategies and Algorithms
  • Associated Mathematical Processes
    • Tools and Techniques
    • Communication
    • 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.

  • Understanding and generalizing operational relationships leads to more sophisticated representations and solution strategies in order to investigate or solve problem situations in everyday life.
    • What relationships exist within and between mathematical operations?
    • How does generalizing operational relationships lead to developing more flexible, efficient representations and/or solution strategies?
    • Why is understanding the problem solving process an essential part of learning and working mathematically?
  • Financial and economic knowledge leads to informed and rational decisions allowing for effective management of financial resources when planning for a lifetime of financial security.
    • Why is financial stability important in everyday life?
    • What economic and financial knowledge is critical for planning for a lifetime of financial security?
    • How can mapping one’s financial future lead to significant short and long-term benefits?
    • How can current financial and economic factors in everyday life impact daily decisions and future opportunities?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
  • Estimation strategies can be used to mentally approximate solutions and determine reasonableness of solutions (rational numbers).
    • What strategies can be used to estimate solutions to problems?
    • When might an estimated answer be preferable to an exact answer?
    • How can an estimation aid in determining the reasonableness of an actual solution?
    • When might one estimation strategy be more beneficial than another?
  • Recognizing and understanding operational relationships in a variety of problem situations leads to efficient, accurate, and flexible representations and solution strategies (rational numbers).
    • How does the context of a problem situation affect the representation, operation(s), and/or solution strategy that could be used to solve the problem?
    • How does understanding …
      • relationships within and between operations
      • properties of operations
      • relationships between fractions, decimals, and percents
      … aid in determining an efficient strategy or representation to investigate and solve problem situations?
    • Why is it important to understand when and how to use standard algorithms?
    • Why is it important to be able to perform operations with rational numbers fluently?
  • Understanding taxes and net worth helps one make informed financial management decisions, which promotes a more secured financial future.
    • How does the understanding operations with rational numbers aid in calculating …
      • sales tax for a given purchase?
      • income tax for earned wages?
    • What is the process for calculating …
      • sales tax for a given purchase?
      • income tax for earned wages?
    • How does understanding sales tax and income tax help promote a more secured financial future?
    • What are examples of financial …
      • assets?
      • liabilities?
    • What is the process of …
      • creating and organizing a financial assets and liabilities record?
      • constructing a net worth statement?
    • What factors affect the amount of income tax paid to the federal government?
    • What are some examples of a financial …
      • asset?
      • liability?
    • What is the relationship between an individual’s financial assets and liabilities when they have a negative or positive net worth?
    • How does understanding assets, liabilities, and net worth help promote a more secured financial future?
  • Number and Operations
    • Number
      • Rational numbers
    • Operations
      • Addition
      • Subtraction
      • Multiplication
      • Division
    • Relationship and Generalizations
      • Numerical
      • Operational
      • Equivalence
    • Solution Strategies and Algorithms
  • Personal Financial Literacy
    • Financial Records
      • Assets
      • Liabilities
    • Net Worth
    • Taxes
      • Sales tax
      • Income tax on earned wages
  • 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 the sum of any two rational numbers is always greater than each of the two addends.
  • Some students may think the difference of any two rational numbers is always less than the minuend.
  • Some students may think the product of any two rational numbers is always greater than each of the factors.
  • Some students may think the quotient of any two rational numbers is always less than the dividend.
  • Some students may think the value of a property or home is a liability, rather than an asset, if there is an outstanding mortgage on the property or home.
  • Some students may think the sales tax is the total cost rather than the amount added to the price to determine the total cost.

Underdeveloped Concepts:

  • Some students may think that a number can only belong to one set (counting [natural] numbers, whole numbers, integers, or rational numbers) rather than understanding that some sets of numbers are nested within another set as a subset.
  • 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.
  • Some students may attempt to perform computations with percents without converting them to equivalent decimals or fractions before multiplying or dividing.
  • 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

  • Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
  • Earned wages – the amount an individual earns over given period of time
  • Financial asset – an object or item of value that one owns
  • Financial liability – an unpaid or outstanding debt
  • Fluency – efficient application of procedures with accuracy
  • Income tax – a percentage of money paid on the earned wages of an individual or business for the federal and/or state governments as required by law
  • Integers – the set of counting (natural numbers), their opposites, and zero {–n, …, –3, –2, –1, 0, 1, 2, 3, ..., n}. The set of integers is denoted by the symbol Z.
  • Net worth – the total assets of an individual after their liabilities have been settled
  • Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
  • Rational numbers – the set of numbers that can be expressed as a fraction , where a and b are integers and b ≠ 0. The set of rational numbers is denoted by the symbol Q.
  • Sales tax – a percentage of money collected by a store (retailer), in addition to a good or service that was purchased, for the local government as required by law
  • Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}

Related Vocabulary:

  • Addend
  • Consumer
  • Decimal
  • Difference
  • Dividend
  • Divisor
  • Factor
  • Federal government
  • Filing status (income tax)
  • Fraction
  • Head of household filer
  • Improper fraction
  • Income
  • Investor
  • Local government
  • Married joint filers
  • Minuend
  • Mixed number
  • Percent
  • Product
  • Quotient
  • Reciprocal
  • Repeating decimal
  • Set of numbers
  • Single filer
  • Subset of numbers
  • Subtrahend
  • Sum
  • Tax rate
  • Taxable income bracket
  • Terminating decimal
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 7 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.
7.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
7.1A 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:
    • Developing fluency with rational numbers and operations to solve problems in a variety of contexts
    • Representing and applying proportional relationships
    • Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
    • Comparing sets of data
  • TxCCRS:
    • X. Connections
7.1B 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:
    • Developing fluency with rational numbers and operations to solve problems in a variety of contexts
    • Representing and applying proportional relationships
    • Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
    • Comparing sets of data
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
7.1C

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 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
      • 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:
    • Developing fluency with rational numbers and operations to solve problems in a variety of contexts
    • Representing and applying proportional relationships
    • Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
    • Comparing sets of data
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
7.1D

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:
    • Developing fluency with rational numbers and operations to solve problems in a variety of contexts
    • Representing and applying proportional relationships
    • Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
    • Comparing sets of data
  • TxCCRS:
    • IX. Communication and Representation
7.1E 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:
    • Developing fluency with rational numbers and operations to solve problems in a variety of contexts
    • Representing and applying proportional relationships
    • Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
    • Comparing sets of data
  • TxCCRS:
    • IX. Communication and Representation
7.1F 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:
    • Developing fluency with rational numbers and operations to solve problems in a variety of contexts
    • Representing and applying proportional relationships
    • Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
    • Comparing sets of data
  • TxCCRS:
    • X. Connections
7.1G 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:
    • Developing fluency with rational numbers and operations to solve problems in a variety of contexts
    • Representing and applying proportional relationships
    • Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
    • Comparing sets of data
  • TxCCRS:
    • IX. Communication and Representation
7.2 Number and operations. The student applies mathematical process standards to represent and use rational numbers in a variety of forms. The student is expected to:
7.2A Extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of rational numbers.
Supporting Standard

Extend

PREVIOUS KNOWLEDGE OF SETS AND SUBSETS USING A VISUAL REPRESENTATION TO DESCRIBE RELATIONSHIPS BETWEEN SETS OF RATIONAL NUMBERS

Including, but not limited to:

  • Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
  • Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
  • Integers – the set of counting (natural numbers), their opposites, and zero {–n, …, –3, –2, –1, 0, 1, 2, 3, ..., n}. The set of integers is denoted by the symbol Z.
  • Rational numbers – the set of numbers that can be expressed as a fraction , where a and b are integers and b ≠ 0. The set of rational numbers is denoted by the symbol Q.
  • Visual representations of the relationships between sets and subsets of rational numbers

To Describe

RELATIONSHIPS BETWEEN SETS OF NUMBERS

Including, but not limited to:

  • All counting (natural) numbers are a subset of whole numbers, integers, and rational numbers.
  • All whole numbers are a subset of integers and rational numbers.
  • All integers are a subset of rational numbers.
  • All counting (natural) numbers, whole numbers, and integers are a subset of rational numbers.
  • Not all rational numbers are an integer, whole number, or counting (natural) number.
  • Terminating and repeating decimals are rational numbers but not integers, whole numbers, or counting (natural) numbers.

Note(s):

  • Grade Level(s):
    • Grade 6 classified whole numbers, integers, and rational numbers using a visual representation such as a Venn diagram to describe relationships between sets of numbers.
    • Grade 8 will extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Developing fluency with rational numbers and operations to solve problems in a variety of contexts
  • TxCCRS:
    • I. Numeric Reasoning
    • IX. Communication and Representation
7.3 Number and operations. The student applies mathematical process standards to add, subtract, multiply, and divide while solving problems and justifying solutions. The student is expected to:
7.3A Add, subtract, multiply, and divide rational numbers fluently.
Supporting Standard

Add, Subtract, Multiply, and Divide

RATIONAL NUMBERS FLUENTLY

Including, but not limited to:

  • Rational numbers – the set of numbers that can be expressed as a fraction , where a and b are integers and b ≠ 0. The set of rational numbers is denoted by the symbol Q.
  • Fluency – efficient application of procedures with accuracy
    • One-step, one operation problems and/or situations can be used to determine fluency with each operation
  • Addition, subtraction, multiplication, and division involving various forms of positive and negative rational numbers
    • Integers
    • Decimals
    • Fractions
    • Percents converted to equivalent decimals or fractions for multiplying or dividing fluently
  • Mathematical and real-world problem situations
    • Multi-step problems
    • Multiple operations

Note(s):

  • Grade Level(s):
    • Grade 5 added and subtracted positive rational numbers fluently.
    • Grade 6 multiplied and divided positive rational numbers fluently.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Developing fluency with rational numbers and operations to solve problems in a variety of contexts
  • TxCCRS:
    • I. Numeric Reasoning
    • IX. Communication and Representation
7.3B Apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers.
Readiness Standard

Apply, Extend

PREVIOUS UNDERSTANDINGS OF OPERATIONS TO SOLVE PROBLEMS USING ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION OF RATIONAL NUMBERS

Including, but not limited to:

  • Rational numbers – the set of numbers that can be expressed as a fraction , where a and b are integers and b ≠ 0. The set of rational numbers is denoted by the symbol Q.
  • Various forms of positive and negative rational numbers
    • Integers
    • Decimals
    • Fractions
    • Percents converted to equivalent decimals or fractions for multiplying or dividing
  • Equivalent representations of a negative number
  • Generalizations of integer operations
    • Addition and subtraction
      • If a pair of addends has the same sign, then the sum will have the sign of both addends.
      • If a pair of addends has opposite signs, then the sum will have the sign of the addend with the greatest absolute value.
      • A subtraction problem may be rewritten as an addition problem by adding the opposite of the integer following the subtraction symbol, and then applying the rules for addition.
    • Multiplication and division
      • If two rational numbers have the same sign, then the product or quotient is positive.
      • If two rational numbers have opposite signs, then the product or quotient is negative.
      • When multiplying or dividing two or more rational numbers, the product or quotient is positive if there are no negative signs or an even number of negative signs.
      • When multiplying or dividing two or more rational numbers, the product or quotient is negative if there is one negative sign or an odd number of negative signs.
  • Connections between generalizations for integer operations to rational number operations for addition and subtraction
  • Recognize that dividing by a rational number and multiplying by its reciprocal result in equivalent values.
  • Connections between generalizations for integer operations to rational number operations for multiplication and division
  • Mathematical and real-world problem situations
    • Multi-step problems
    • Multiple operations

Note(s):

  • Grade Level(s):
    • Grade 6 multiplied and divided positive rational numbers fluently.
    • Grade 6 determined, with and without computation, whether a quantity is increased or decreased when multiplied by a fraction, including values greater than or less than one.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Developing fluency with rational numbers and operations to solve problems in a variety of contexts
  • TxCCRS:
    • I. Numeric Reasoning
    • IX. Communication and Representation
7.13 Personal financial literacy. The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one's life as a knowledgeable consumer and investor. The student is expected to:
7.13A Calculate the sales tax for a given purchase and calculate income tax for earned wages.
Supporting Standard

Calculate

THE SALES TAX FOR A GIVEN PURCHASE AND CALCULATE INCOME TAX FOR EARNED WAGES

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
    • Percents converted to equivalent decimals or fractions for multiplying or dividing
  • Sales tax – a percentage of money collected by a store (retailer), in addition to a good or service that was purchased, for the local government as required by law
    • Sales tax is set by the local government (city, county, and state) and the money stays within those local systems
  • Earned wages – the amount an individual earns over a given period of time
  • Income tax – a percentage of money paid on the earned wages of an individual or business for the federal and/or state governments as required by law
    • Fixed tax rate
      • Determined by a single rate regardless of taxable income or filing status
    • Multiple tax rates
      • Determined by a fixed rate on different brackets (levels) of taxable income and an individual’s income tax filing status of single, married joint, or head of household
        • Income tax filing status
          • Single can be claimed by any individual filing an income tax return.
          • Married-joint can be claimed by married couples or individuals who have been widowed within the last two years.
          • Head of household can be claimed individuals who pay for more than half of the household expenses and have at least one dependent (usually a child) that lives with them.
        • Income tax brackets and rates are published by the state and/or federal government annually
        • Income tax goes directly to federal government; the state of Texas does not collect income tax.
        • Income tax rates fluctuate from year to year due to inflation and other federal and/or state government budgets.
        • Earned income is rounded to the nearest whole dollar for purposes of tax brackets.
        • Income tax is rounded to the nearest whole dollar.

Note(s):

  • Grade Level(s):
    • Grade 5 defined income tax, payroll tax, sales tax, and property tax.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Financial Literacy
  • TxCCRS:
    • I. Numeric Reasoning
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
7.13C Create and organize a financial assets and liabilities record and construct a net worth statement.
Supporting Standard

Create, Organize

A FINANCIAL ASSETS AND LIABILITIES RECORD

Including, but not limited to:

  • Financial asset – an object or item of value that one owns
    • Assets represent a positive value in relation to net worth.
  • Financial liability – an unpaid or outstanding debt
    • Liabilities represent a negative value in relation to net worth; values may or may not be indicated by a negative sign.
  • Financial assets and liabilities records may fluctuate each month depending on payments made towards liabilities, whether additional liabilities are taken on, or if the value of an asset changes due to appreciation or depreciation.

Construct

A NET WORTH STATEMENT

Including, but not limited to:

  • Net worth – the total assets of an individual after their liabilities have been settled
  • An individual’s net worth may be positive or negative depending on the amount of their assets and liabilities.
  • Process of constructing a net worth statement
    • Calculate the value of an individual’s assets.
    • Calculate the value on an individual’s liabilities.
    • Calculate the net worth, the difference between an individual’s assets and liabilities.
  • Determine the missing value of an asset or liability when given net worth and remaining values.

Note(s):

  • Grade Level(s):
    • Grade 6 balanced a check register that included deposits, withdrawals, and transfers.
    • Grade 7 introduces creating and organizing a financial assets and liabilities record and constructing a net worth statement.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Financial Literacy
  • TxCCRS:
    • I. Numeric Reasoning
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
The English Language Proficiency Standards (ELPS), as required by 19 Texas Administrative Code, Chapter 74, Subchapter A, §74.4, outline English language proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement ELPS as an integral part of each subject in the required curriculum.

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


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

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


Choose appropriate ELPS to support instruction.

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