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 TITLE : Unit 02: One-Variable Equations and Inequalities SUGGESTED DURATION : 16 days

#### Unit Overview

Introduction
This unit bundles student expectations that address one-variable, two-step equations and inequalities and personal financial literacy standards regarding a family budget estimator, simple interest and compound interest earnings, and monetary incentives. 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 wrote, modeled, and solved one-variable, one-step equations and inequalities and wrote corresponding real-world problems given one-variable, one-step equations or inequalities. They determined if given values made one-variable, one-step equations or inequalities true and represented solutions for one-variable, one-step equations and inequalities on number lines. Additionally, students extended previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle. Grade 3 students identified the costs and benefits of planned and unplanned spending decisions, while Grade 4 students compared the advantages and disadvantages of various savings options.

During this Unit
Students extend their previous work with one-variable, one-step equations and inequalities to one-variable, two-step equations and inequalities. Students model and solve one-variable, two-step equations and inequalities with concrete and pictorial models and algebraic representations. Solutions to equations and inequalities are represented on number lines and given values are used to determine if they make an equation or inequality true. Students are expected to write an equation or inequality to represent conditions or constraints within a problem and then, conversely, when given an equation or inequality out of context, students are expected to write a corresponding real-world problem to represent the equation or inequality. Additionally, students write and solve equations using geometric concepts, including the sum of the angles in a triangle, complementary angles, supplementary angles, straight angles, adjacent angles, and vertical angles. Equations and inequalities are extended to include problem situations involving monetary incentives such as sales, rebates, or coupons. Financial literacy aspects such as calculating and comparing simple and compound interest as well as utilizing a family budget estimator to determine the minimum household budget needed for a family to meet its basic needs is also explored. Although the formula for compound interest utilizes an exponent, student experiences for writing, modeling, solving, and evaluating equations and inequalities should focus primarily on linear relationships.

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

After this Unit
In Units 03 – 08, students will continue to apply their understanding of writing and solving equations and inequalities, as applicable. In Grade 8, students will use rational number coefficients and constants to write one-variable equations or inequalities with variables on both sides, as well as write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign. Students will model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants. Additionally, students will identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations. Students will use informal arguments to establish facts about the sum of angles and measures of exterior angles of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. Grade 8 students will explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time and also calculate and compare simple interest and compound interest earnings

In Grade 7, modeling and solving one-variable, two-step equations and inequalities is STAAR Readiness Standard 7.11A. Writing one-variable, two-step equations and inequalities, representing their solutions on a number line, and  determining if a given value(s) makes the equation or inequality true are identified as STAAR Supporting Standards 7.10A, 7.10B, and 7.11B. Writing real-world problems given a one-variable, two-step equation or inequality is STAAR Supporting Standard 7.10C. These standards are subsumed under the Grade 7 STAAR Reporting Category 2: Computations and Algebraic Relationships. Writing and solving equations using geometry concepts is identified as STAAR Supporting Standard 7.11C and is listed under the Grade 7 STAAR Reporting Category 3: Geometry and Measurement. All of these standards are a foundational block of the Grade 7 Texas Response to Curriculum Focal Points (TxRCFP): Using expressions and equations to describe relationships in a variety of contexts, including geometric problems. Using a family budget estimator is identified as STAAR Supporting Standard 7.13D, calculating and comparing simple interest and compound interest earnings is identified as STAAR Supporting Standard 7.13E, and analyzing and comparing monetary incentives is identified as STAAR Supporting Standard 7.13F. These three 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 C1, C2, D1, D2; III. Geometric and Spatial Reasoning C1; 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, in Principles and Standards for School Mathematics (2000), “Fluency with algebraic symbolism helps students to represent and solve problems in many areas of the curriculum…Students should be able to operate fluently on algebraic expressions, combining them and reexpressing them in alternative forms. These skills underlie the ability to find exact solutions for equations, a goal that has always been at the heart of the algebra curriculum” (p. 300 – 301). Algebraic expressions are the foundation for all equations and inequalities, therefore, “Students need an understanding of how to apply mathematical properties and how to reserve equivalence as [expressions] simplify” (Van de Walle, Karp, & Bay-Williams, 2010, p. 263). Developing concepts of equations and inequalities can intuitively take a financial approach. Allowing students to experience problem situations which require “personal finance management will remedy the problems of financial illiteracy and, thus, financial insecurity by preventing them from occurring in the first place. Coupled with skill-building exercises, good quality instruction can prepare individuals and families to make decisions in a variety of financial situations” (Gentry, 2012, p.14).

Gentry, D. B. (2012). Financial fitness... It’s priceless: Public policy deliberation guide. Alexandria, VA: American Association of Family Consumer Sciences.
National Council of Teachers of Mathematics. (2000). Principles and standards for school 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
Van de Walle, J., Karp, K., & Bay-Williams, J. (2010). Elementary and middle school mathematics: Teaching developmentally. Boston, MA: Pearson Education, Inc.

 Quantitative relationships model problem situations efficiently and can be used to make generalizations, predictions, and critical judgements in everyday life. What patterns exist within different types of quantitative relationships and where are they found in everyday life? Why is the ability to model quantitative relationships in a variety of ways essential to solving problems in everyday life?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Equations and inequalities can be modeled, written, and solved using various methods to gain insight into the context of the situation and make critical judgments about algebraic relationships and flexible strategies.
• What is the process for writing a real-world problem to represent constraints or conditions within an …
• equation?
• inequality?
• How can a(n) …
• concrete model
• pictorial model
• algebraic representation
… be used to model and solve an …
• equation
• inequality?
• What models effectively and efficiently represent how to solve equations and inequalities?
• What is the process for solving an …
• equation
• inequality
…, and how can the process be …
• described verbally?
• represented algebraically?
• When considering equations and inequalities, …
• why is the variable isolated in order to solve?
• how are negative values represented in concrete and pictorial models?
• how does a negative coefficient affect the equality or inequality symbol when solving?
• how are the solution processes alike and different?
• how are the solutions alike and different?
• why must the solution be justified in terms of the problem situation?
• why does equivalence play an important role in the solving process?
• Why is it important to understand when and how to use standard algorithms?
• If the equality symbol of an equation is changed to an inequality symbol that includes equal to, why is the solution to the equation always included in the solution to the inequality?
• How does knowing more than one solution strategy build mathematical flexibility?
• How can a solution to an …
• equation
• inequality
… be represented on a number line?
• What is the process for evaluating an …
• equation
• inequality
… for a given value?
• Expressions, Equations, and Relationships
• Numeric and Algebraic Representations
• Expressions
• Equations
• Inequalities
• Equivalence
• Operations
• Properties of operations
• Order of operations
• Representations
• 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.

 Quantitative relationships model problem situations efficiently and can be used to make generalizations, predictions, and critical judgements in everyday life. What patterns exist within different types of quantitative relationships and where are they found in everyday life? Why is the ability to model quantitative relationships in a variety of ways essential to solving problems in everyday life?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Equations and inequalities can be modeled, written, and solved using various methods to gain insight into the context of the situation and make critical judgments about algebraic relationships and efficient strategies.
• Why are expressions considered foundational to equations and inequalities?
• How are constraints or conditions within a problem situation represented in an …
• equation?
• inequality?
• How does the context of a problem situation, relationships within and between operations, and properties of operations aid in writing an equation and/or inequality to represent the problem situation?
• How can a(n) …
• concrete model
• pictorial model
• algebraic representation
… be used to model and solve an …
• equation?
• inequality?
• What models effectively and efficiently represent how to solve equations and inequalities?
• What is the process for solving an …
• equation
• inequality
…, and how can the process be …
• described verbally?
• represented algebraically?
• When considering equations and inequalities, …
• why is the variable isolated in order to solve?
• how are negative values represented in concrete and pictorial models?
• how does a negative coefficient affect the equality or inequality symbol when solving?
• how are the solution processes alike and different?
• how are the solutions alike and different?
• why must the solution be justified in terms of the problem situation?
• why does equivalence play an important role in the solving process?
• Why is it important to understand when and how to use standard algorithms?
• If the equality symbol of an equation is changed to an inequality symbol that includes equal to, why is the solution to the equation always included in the solution to the inequality?
• How does knowing more than one solution strategy build mathematical flexibility?
• What is the process for evaluating an …
• equation
• inequality
… for a given value?
• Illustrating and analyzing geometric relationships in models and diagrams aid in representing attributes of geometric figures with quantifiable measures and equations in order to generalize geometric relationships and solve problems.
• How can problem situations involving …
• complementary angles
• supplementary angles
• the sum of the angles in a triangle
• the Triangle Inequality Theorem
… be represented and solved using an equation or inequality?
• When angles are complementary, why does the sum always equal 90°?
• When angles are supplementary, why does the sum always equal 180°?
• When finding the sum of the angles in a triangle, why does the sum always equal 180°?
• What relationship exists among vertical angles?
• What relationship exists among supplementary angles and straight angles?
• Why is the sum of two side lengths of a triangle always greater than the third side length?
• What model(s) can be used to represent …
• vertical angles
• complementary angles
• supplementary angles
• straight angles
• the sum of the angles in a triangle
• the Triangle Inequality Theorem
…, and how can the model lead to a generalization that can be represented with an equation and/or inequality?
• Expressions, Equations, and Relationships
• Composition and Decomposition of Figures and Angles
• Geometric Representations
• One-dimensional representations
• Two-dimensional figures
• Geometric Relationships
• Measure relationships
• Geometric properties
• Numeric and Algebraic Representations
• Expressions
• Equations
• Inequalities
• Equivalence
• Operations
• Properties of operations
• Order of operations
• Representations
• 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.

 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)
• Understanding interest, monetary incentives, and a family budget estimator helps one make informed financial management decisions, which promotes a more secured financial future.
• What factors contribute to the amount of money a family needs to meet its basic needs?
• How does the amount of money needed by a family to meet its basic needs vary from family to family?
• What is the process to determine the minimum household budget a family needs to meet its basic needs, and how can an equation be used to represent the household budget?
• What is the process to determine the hourly wage a family needs to meet its basic needs, and how can an equation and/or inequality be used to represent the hourly wage needed?
• How does understanding the necessary income to meet family needs help promote a more secured financial future?
• What is the difference between simple interest and compound interest?
• How are the equations for simple interest and compound interest different?
• What is the process for determining the amount of simple or compound interest earned on an investment or added to a loan?
• How are interest rates applied to money that is invested or borrowed?
• How does understanding simple and compound interest help promote a more secured financial future?
• What are monetary incentives and how do they benefit a consumer?
• What is the process for determining the value of a monetary incentive, and how can an equation be used to represent the value of the monetary incentive?
• What is the difference between a sale, rebate, and coupon?
• When would one monetary incentive be more valuable than another monetary incentive?
• How does understanding monetary incentives help promote a more secured financial future?
• Personal Financial Literacy
• Family Budget Estimator
• Interest
• Simple
• Compound
• Monetary Incentives
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

#### MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

• Some students may think that operations involving negatives when solving inequalities always require the inequality symbol to be reversed instead of applying the rule of reversing the inequality symbol when dividing or multiplying both sides of an inequality by a negative value.
• Some students may think that a constant term can be combined with a variable term (e.g., 2x + 5 = 7x).
• Some students may think that answers to both equations and inequalities are exact answers instead of correctly identifying the solutions to equations as exact answers and the solutions to inequalities as range of answers.

Underdeveloped Concepts:

• Some students may think variables are letters representing an object as opposed to representing a number or quantity of objects.
• Some students may think that a variable is only a placeholder as it is in an equation.
• Some students may think the equal sign means, “solve this” or “the answer is” rather than understanding that equal sign represents a quantitative and balanced relationship.

#### Unit Vocabulary

• Adjacent angles – two non-overlapping angles that share a common vertex and exactly one ray
• Basic needs – minimum necessities
• Budget – a monthly or yearly spending and savings plan for an individual, family, business, or organization
• Coefficient – a number that is multiplied by a variable(s)
• Complementary angles – two angles whose degree measures have a sum of 90°
• Compound interest for an investment – interest that is calculated on the latest balance, including all compounded interest that has been added to the original principal investment
• Congruent angles – angles whose angle measurements are equal
• Constant – a fixed value that does not appear with a variable(s)
• Coupon – an amount deducted from the total cost of an item
• Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
• Family budget estimator – determines the monthly or annual base income that is needed for a family
• Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
• Order of operations – the rules of which calculations are performed first when simplifying an expression
• Positive rational numbers – the set of numbers that can be expressed as a fraction , where a and b are counting (natural) numbers
• Principal of an investment – the original amount invested
• Rebate – an amount returned or refunded for purchasing an item or items
• Sale – a reduced amount or price of an item
• Simple interest for an investment – interest paid on the original principal in an account, disregarding any previously earned interest
• Solution set – a set of all values of the variable(s) that satisfy the equation or inequality
• Straight angle – an angle with rays extending in opposite directions and whose degree measure is 180°
• Supplementary angles – two angles whose degree measures have a sum of 180°
• Variable – a letter or symbol that represents a number
• Vertical angles – a pair of non-adjacent, non-overlapping angles formed by two intersecting lines creating angles that are opposite and congruent to each other
• Wage – the amount usually earned per hour or over a given period of time

Related Vocabulary:

 Angle measure Borrow Condition Constraint Decimal Deposit Earning Equivalent Equality Equal to Evaluate Exponent Expression Fraction Greater than Greater than or equal to Hourly wage Household Improper fraction Integer Interest Less than Less than or equal to Manufacturer Mixed number Not equal to Number line Parentheses/brackets Retailer Savings Simplify Solution Solve Tax Triangle Whole number Workweek
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 REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, ESTIMATION, AND NUMBER SENSE AS APPROPRIATE, TO SOLVE PROBLEMS

Including, but not limited to:

• Appropriate selection of tool(s) and techniques to apply in order to solve problems
• Tools
• Real objects
• Manipulatives
• Paper and pencil
• Technology
• Techniques
• Mental math
• Estimation
• Number sense

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxRCFP:
• 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.
7.10 Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations and inequalities to represent situations. The student is expected to:
7.10A Write one-variable, two-step equations and inequalities to represent constraints or conditions within problems.
Supporting Standard

Write

ONE-VARIABLE, TWO-STEP EQUATIONS AND INEQUALITIES TO REPRESENT CONSTRAINTS OR CONDITIONS WITHIN PROBLEMS

Including, but not limited to:

• Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
• Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
• Variable – a letter or symbol that represents a number
• One variable on one side of the equation or inequality
• Coefficient – a number that is multiplied by a variable(s)
• Integers
• Decimals
• Fractions
• Constant – a fixed value that does not appear with a variable(s)
• Integers
• Decimals
• Fractions
• Two-step equations and inequalities
• A “step” only refers to an action involving both sides of the equation or inequality (combining like terms on a single side of the equation or inequality does not constitute a step).
• Solution set – a set of all values of the variable(s) that satisfy the equation or inequality
• Constraints or conditions
• Distinguishing between equations and inequalities
• Characteristics of equations
• Equates two expressions
• Equality of the variable
• One solution
• Characteristics of inequalities
• Shows the relationship between two expressions in terms of >, <, ≥, ≤, or ≠
• Inequality of the variable
• One or more solutions
• Equality and inequality words and symbols
• Equal to, =
• Greater than, >
• Greater than or equal to, ≥
• Less than, <
• Less than or equal to, ≤
• Not equal to, ≠
• Relationship of order of operations within an equation or inequality
• Order of operations – the rules of which calculations are performed first when simplifying an expression
• Parentheses/brackets: simplify expressions inside parentheses or brackets in order from left to right
• Exponents: rewrite in standard numerical form and simplify from left to right
• Limited to positive whole numer exponents
• Multiplication/division: simplify expressions involving multiplication and/or division in order from left to right
• Addition/subtraction: simplify expressions involving addition and/or subtraction in order from left to right
• One-variable, two-step equations from a problem
• One-variable, two-step inequalities from a problem

Note(s):

• Grade 6 wrote one-variable, one-step equations and inequalities to represent constraints or conditions within problems.
• Grade 7 represents writing one-variable, two-step equations and inequalities to represent constraints or conditions within problems.
• Grade 8 will write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
• TxCCRS:
• 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.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.
7.10B Represent solutions for one-variable, two-step equations and inequalities on number lines.
Supporting Standard

Represent

SOLUTIONS FOR ONE-VARIABLE, TWO-STEP EQUATIONS AND INEQUALITIES ON NUMBER LINES

Including, but not limited to:

• Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
• Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
• Variable – a letter or symbol that represents a number
• One variable on one side of the equation or inequality
• Coefficient – a number that is multiplied by a variable(s)
• Integers
• Decimals
• Fractions
• Constant – a fixed value that does not appear with a variable(s)
• Integers
• Decimals
• Fractions
• Two-step equations and inequalities
• A “step” only refers to an action involving both sides of the equation or inequality (combining like terms on a single side of the equation or inequality does not constitute a step).
• Solution set – a set of all values of the variable(s) that satisfy the equation or inequality
• Constraints or conditions
• Distinguishing between equations and inequalities
• Characteristics of equations
• Equates two expressions
• Equality of the variable
• One solution
• Characteristics of inequalities
• Shows the relationship between two expressions in terms of >, <, ≥, ≤, or ≠
• Inequality of the variable
• One or more solutions
• Equality and inequality words and symbols
• Equal to, =
• Greater than, >
• Greater than or equal to, ≥
• Less than, <
• Less than or equal to, ≤
• Not equal to, ≠
• Representations of solutions to equations and inequalities on a number line
• Closed circle
• Equal to, =
• Greater than or equal to, ≥
• Less than or equal to, ≤
• Open circle
• Greater than, >
• Less than, <
• Not equal to, ≠

Note(s):

• Grade 6 represented solutions for one-variable, one-step equations and inequalities on number lines.
• Grade 7 represents solutions for one-variable, two-step equations and inequalities on number lines.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
• TxCCRS:
• II.C. Algebraic Reasoning – Solving equations, inequalities, and systems of equations and inequalities
• II.C.1. Describe and interpret solution sets of equalities and inequalities.
• 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.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.
7.10C Write a corresponding real-world problem given a one-variable, two-step equation or inequality.
Supporting Standard

Write

A CORRESPONDING REAL-WORLD PROBLEM GIVEN A ONE-VARIABLE, TWO-STEP EQUATION OR INEQUALITY

Including, but not limited to:

• Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
• Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
• Variable – a letter or symbol that represents a number
• One variable on one side of the equation or inequality
• Coefficient – a number that is multiplied by a variable(s)
• Integers
• Decimals
• Fractions
• Constant – a fixed value that does not appear with a variable(s)
• Integers
• Decimals
• Fractions
• Two-step equations and inequalities
• A “step” only refers to an action involving both sides of the equation or inequality (combining like terms on a single side of the equation or inequality does not constitute a step).
• Solution set – a set of all values of the variable(s) that satisfy the equation or inequality
• Constraints or conditions
• Distinguishing between equations and inequalities
• Characteristics of equations
• Equates two expressions
• Equality of the variable
• One solution
• Characteristics of inequalities
• Shows the relationship between two expressions in terms of >, <, ≥, ≤, or ≠
• Inequality of the variable
• One or more solutions
• Equality and inequality words and symbols
• Equal to, =
• Greater than, >
• Greater than or equal to, ≥
• Less than, <
• Less than or equal to, ≤
• Not equal to, ≠
• Relationship of order of operations within an equation or inequality
• Order of operations – the rules of which calculations are performed first when simplifying an expression
• Parentheses/brackets: simplify expressions inside parentheses or brackets in order from left to right
• Exponents: rewrite in standard numerical form and simplify from left to right
• Limited to positive whole numer exponents
• Multiplication/division: simplify expressions involving multiplication and/or division in order from left to right
• Addition/subtraction: simplify expressions involving addition and/or subtraction in order from left to right
• Corresponding real-world problem from a one-variable, two-step equation
• Corresponding real-world problem from a one-variable, two-step inequality

Note(s):

• Grade 6 wrote corresponding real-world problems given one-variable, one-step equations or inequalities.
• Grade 7 writes corresponding real-world problems given one-variable, two-step equations or inequalities.
• Grade 8 will write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
• 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.
• 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.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.
• 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.
7.11 Expressions, equations, and relationships. The student applies mathematical process standards to solve one-variable equations and inequalities. The student is expected to:
7.11A Model and solve one-variable, two-step equations and inequalities.

Model, Solve

ONE-VARIABLE, TWO-STEP EQUATIONS AND INEQUALITIES

Including, but not limited to:

• Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
• Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
• Variable – a letter or symbol that represents a number
• One variable on one side of the equation or inequality
• Coefficient – a number that is multiplied by a variable(s)
• Integers
• Decimals
• Fractions
• Constant – a fixed value that does not appear with a variable(s)
• Integers
• Decimals
• Fractions
• Two-step equations and inequalities
• A “step” only refers to an action involving both sides of the equation or inequality (combining like terms on a single side of the equation or inequality does not constitute a step).
• Solution set – a set of all values of the variable(s) that satisfy the equation or inequality
• Constraints or conditions
• Distinguishing between equations and inequalities
• Characteristics of equations
• Equates two expressions
• Equality of the variable
• One solution
• Characteristics of inequalities
• Shows the relationship between two expressions in terms of >, <, ≥, ≤, or ≠
• Inequality of the variable
• One or more solutions
• Equality and inequality words and symbols
• Equal to, =
• Greater than, >
• Greater than or equal to, ≥
• Less than, <
• Less than or equal to, ≤
• Not equal to, ≠
• Relationship of order of operations within an equation or inequality
• Order of operations – the rules of which calculations are performed first when simplifying an expression
• Parentheses/brackets: simplify expressions inside parentheses or brackets in order from left to right
• Exponents: rewrite in standard numerical form and simplify from left to right
• Limited to positive whole numer exponents
• Multiplication/division: simplify expressions involving multiplication and/or division in order from left to right
• Addition/subtraction: simplify expressions involving addition and/or subtraction in order from left to right
• Model and solve one-variable, two-step equations (concrete, pictorial, algebraic)
• Model and solve one-variable, two-step inequalities (concrete, pictorial, algebraic)
• Solutions to one-variable, two-step equations from a problem situation
• Solutions to one-variable, two-step inequalities from a problem situation

Note(s):

• Grade 6 modeled and solved one-variable, one-step equations and inequalities that represented problems, including geometric concepts.
• Grade 8 will model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
• TxCCRS:
• I.A. Numeric Reasoning – Number representations and operations
• I.A.2. Perform computations with rational and irrational numbers.
• II.C. Algebraic Reasoning – Solving equations, inequalities, and systems of equations and inequalities
• II.C.2. Explain the difference between the solution set of an equation and the solution set of an inequality.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.3. Determine a solution.
• 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.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
7.11B Determine if the given value(s) make(s) one-variable, two-step equations and inequalities true.
Supporting Standard

Determine

IF THE GIVEN VALUE(S) MAKE(S) ONE-VARIABLE, TWO-STEP EQUATIONS AND INEQUALITIES TRUE

Including, but not limited to:

• Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
• Inequality – a mathematical statement composed of algebraic and/or numeric expressions set apart by an inequality symbol
• Variable – a letter or symbol that represents a number
• One variable on one side of the equation or inequality
• Coefficient – a number that is multiplied by a variable(s)
• Integers
• Decimals
• Fractions
• Constant – a fixed value that does not appear with a variable(s)
• Integers
• Decimals
• Fractions
• Two-step equations and inequalities
• A “step” only refers to an action involving both sides of the equation or inequality (combining like terms on a single side of the equation or inequality does not constitute a step).
• Solution set – a set of all values of the variable(s) that satisfy the equation or inequality
• Constraints or conditions
• Distinguishing between equations and inequalities
• Characteristics of equations
• Equates two expressions
• Equality of the variable
• One solution
• Characteristics of inequalities
• Shows the relationship between two expressions in terms of >, <, ≥, ≤, or ≠
• Inequality of the variable
• One or more solutions
• Equality and inequality words and symbols
• Equal to, =
• Greater than, >
• Greater than or equal to, ≥
• Less than, <
• Less than or equal to, ≤
• Not equal to, ≠
• Relationship of order of operations within an equation or inequality
•  Order of operations – the rules of which calculations are performed first when simplifying an expression
• Parentheses/brackets: simplify expressions inside parentheses or brackets in order from left to right
• Exponents: rewrite in standard numerical form and simplify from left to right
• Limited to positive whole numer exponents
• Multiplication/division: simplify expressions involving multiplication and/or division in order from left to right
• Addition/subtraction: simplify expressions involving addition and/or subtraction in order from left to right
• Evaluation of a given value(s) as a possible solution to one-variable, two-step equations
• Evaluation of a given value(s) as a possible solution to one-variable, two-step inequalities

Note(s):

• Grade 6 determined if the given value(s) make(s) one-variable, one-step equations or inequalities true.
• Grade 8 will identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
• TxCCRS:
• I.A. Numeric Reasoning – Number representations and operations
• I.A.2. Perform computations with rational and irrational numbers.
• II.C. Algebraic Reasoning – Solving equations, inequalities, and systems of equations and inequalities
• II.C.1. Describe and interpret solution sets of equalities and inequalities.
7.11C Write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships.
Supporting Standard

Write, Solve

EQUATIONS USING GEOMETRY CONCEPTS, INCLUDING THE SUM OF THE ANGLES IN A TRIANGLE, AND ANGLE RELATIONSHIPS

Including, but not limited to:

• Equation – a mathematical statement composed of algebraic and/or numeric expressions set equal to each other
• Variable – a letter or symbol that represents a number
• One variable on one side of the equation
• Coefficient – a number that is multiplied by a variable(s)
• Integers
• Decimals
• Fractions
• Constant – a fixed value that does not appear with a variable(s)
• Integers
• Decimals
• Fractions
• Solution set – a set of all values of the variable(s) that satisfy the equation
• Equations from geometry concepts
• Angle measures as numeric and/or algebraic expressions
• Sum of the angles in a triangle
• Other angle relationships
• Adjacent angles – two non-overlapping angles that share a common vertex and exactly one ray
• Complementary angles – two angles whose degree measures have a sum of 90°
• Supplementary angles – two angles whose degree measures have a sum of 180°
• Straight angle – an angle with rays extending in opposite directions and whose degree measure is 180°
• Congruent angles – angles whose angle measurements are equal
• Arc(s) on angles are usually used to indicate congruency (one set of congruent angles would have 1 arc, another set of congruent angles would have 2 arcs, etc.).
• Arcs and tick marks on angles can be used to indicate congruency (one set of congruent angles would have 1 arc with 1 tick mark, another set of congruent angles would have 1 arc with 2 tick marks, etc.)
• Vertical angles – a pair of non-adjacent, non-overlapping angles formed by two intersecting lines creating angles that are opposite and congruent to each other
• Real-life situation involving angle measures

Note(s):

• Grade 4 determined the measure of an unknown angle formed by two non-overlapping adjacent angles given one or both angle measures.
• Grade 6 extended previous knowledge of triangles and their properties to include the sum of angles of a triangle, the relationship between the lengths of sides and measures of angles in a triangle, and determining when three lengths form a triangle.
• Grade 6 modeled and solved one-variable, one-step equations and inequalities that represent problems, including geometric concepts.
• Grade 8 will use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Using expressions and equations to describe relationships in a variety of contexts, including geometric problems
• TxCCRS:
• I.A. Numeric Reasoning – Number representations and operations
• I.A.2. Perform computations with rational and irrational numbers.
• III.C. Geometric and Spatial Reasoning – Connections between geometry and other mathematical content strands
• III.C.1. Make connections between geometry and algebraic equations.
• 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.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.
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:
7.13D Use a family budget estimator to determine the minimum household budget and average hourly wage needed for a family to meet its basic needs in the student's city or another large city nearby.
Supporting Standard

Use

A FAMILY BUDGET ESTIMATOR

Including, but not limited to:

• Budget – a monthly or yearly spending and savings plan for an individual, family, business, or organization
• Family budget estimator – determines the monthly or annual base income that is needed for a family
• Components of a family budget estimator
• Location of family
• Number of parents/guardians in the household
• Number of children in the household
• Basic needs
• Housing
• Food
• Medical Insurance
• Medial out-of-pocket expenses
• Transportation
• Child care
• Other family needs
• Savings (e.g., emergencies, retirement, college, etc.)
• Federal taxes
• Payroll tax
• Income tax
• Earned income credit
• Child tax credit
• Budget components are usually rounded to the nearest whole dollar amount.
• Values of budget components vary depending on location within a country, state, city, or county.
• Data from multiple sources is used to create a family budget estimator.

To Determine

THE MINIMUM HOUSEHOLD BUDGET AND AVERAGE HOURLY WAGE NEEDED FOR A FAMILY TO MEET ITS BASIC NEEDS IN THE STUDENT'S CITY OR ANOTHER LARGE CITY NEARBY

Including, but not limited to:

• Wage – the amount usually earned per hour or over a given period of time
• Basic needs – minimum necessities
• Minimum household budget is usually a monthly budget and is determined by finding the difference between the sum of the cost of basic needs, savings, and taxes and the total household income
• Average hourly wage is calculated by dividing the minimum household budget by the number of hours worked each month by each working adult in the household
• A typical workweek is considered 40 hours or 8 hours per day.
• The number of hours worked per month varies depending on the number of working days in the month but can usually be considered as 20 working days per month.
• Average hourly wage needed in the student’s city
• Average hourly wage needed in nearby larger city
• Career opportunities to meet family budget needs

Note(s):

• Grade 5 balanced a simple budget.
• Grade 7 introduces using a family budget estimator to determine the minimum household budget and average hourly wage needed for a family to meet its basic needs in the student's city or another large city nearby.
• 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.
• 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.
7.13E Calculate and compare simple interest and compound interest earnings.
Supporting Standard

Calculate, Compare

SIMPLE INTEREST AND COMPOUND INTEREST EARNINGS

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
• Principal of an investment – the original amount invested
• Simple interest for an investment – interest paid on the original principal in an account, disregarding any previously earned interest
• Compound interest for an investment – interest that is calculated on the latest balance, including all compounded interest that has been added to the original principal investment
• Formulas for interest from STAAR Grade 7 Mathematics Reference Materials
• Simple interest
• I = Prt, where I represents the interest, P represents the principal amount deposited, r represents the interest rate in decimal form, and t represents the number of years the amount is deposited
• Compound interest
• A = P(1+r)t, where A represents the total accumulated amount, including the principal and earned compounded interested, P represents the principal amount, r represents the interest rate in decimal form, and t represents the number of years the principal amount is deposited
• Comparing simple and compound interest earnings

Note(s):

• Grade 8 will calculate and compare simple interest and compound interest earnings.
• Algebra I will refer to 1 + r in the compound interest formula, A = P(1 + r)t, as the factor and will be given the variable b.
• 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.
• 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.
7.13F Analyze and compare monetary incentives, including sales, rebates, and coupons.
Supporting Standard

Analyze, Compare

MONETARY INCENTIVES, INCLUDING SALES, REBATES, AND COUPONS

Including, but not limited to:

• Monetary incentives
• Sale – a reduced amount or price of an item
• May be offered by a store or manufacturer depending on the location of the purchase
• Rebate – an amount returned or refunded for purchasing an item or items
• May be offered by the store or manufacturer
• May be instant or require a rebate form with proof of purchase to be mailed in
• Coupon – an amount deducted from the total cost of an item
• May be offered by manufacturers or by retailers
• Some retailers may allow coupons to be stacked by accepting both a store coupon and a manufacturer’s coupon.

Note(s):