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 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.

Other considerations: Reference the Mathematics COVID-19 Gap Implementation Tool Grade 7

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

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 A2, B1; II. Algebraic Reasoning D1, D2; V. Statistical Reasoning A1, C2; VII. Problem Solving and Reasoning A1, A2, A3, A4, A5, B1, C1, D1, D2; VIII. Communication and Representation A1, A2, A3, B1, B2, C1, C2, C3; IX. Connections A1, A2, B1, B2, B3.

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. (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
• 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
• 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 Center 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

TAUGHT DIRECTLY TEKS

TEKS intended to be explicitly taught in this unit.

TEKS/SE 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.

Specificity 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.
TEKS# SE# TEKS SPECIFICITY
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:
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.1. Interpret results of the mathematical problem in terms of the original real-world situation.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
• IX.B.2. Understand and use appropriate mathematical models in the natural, physical, and social sciences.
• IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.
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:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.A. Statistical Reasoning – Design a study
• V.A.1. Formulate a statistical question, plan an investigation, and collect data.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VII.A.2. Formulate a plan or strategy.
• VII.A.3. Determine a solution.
• VII.A.4. Justify the solution.
• VII.A.5. Evaluate the problem-solving process.
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.2. Evaluate the problem-solving process.
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:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
• V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
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:
• II.D. Algebraic Reasoning – Representing relationships
• II.D.1. Interpret multiple representations of equations, inequalities, and relationships.
• II.D.2. Convert among multiple representations of equations, inequalities, and relationships.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
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:
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
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:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
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:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.4. Justify the solution.
• VII.B. Problem Solving and Reasoning – Proportional reasoning
• VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
• VII.C. Problem Solving and Reasoning – Logical reasoning
• VII.C.1. Develop and evaluate convincing arguments.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII. A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII. C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
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 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
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

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 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.A. Numeric Reasoning – Number representations and operations
• I.A.2. Perform computations with rational and irrational numbers.
7.3B Apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers.

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
• 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 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.A. Numeric Reasoning – Number representations and operations
• I.A.2. Perform computations with rational and irrational numbers.
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 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.A. Numeric Reasoning – Number representations and operations
• I.A.2. Perform computations with rational and irrational numbers.
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.1. Interpret results of the mathematical problem in terms of the original real-world situation.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.2. Connect mathematics to the study of other disciplines.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
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 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:
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.1. Interpret results of the mathematical problem in terms of the original real-world situation.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.2. Connect mathematics to the study of other disciplines.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations. 