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 Instructional Focus DocumentMathematical Models with Applications
 TITLE : Unit 06: Management of Personal Finances SUGGESTED DURATION : 14 days

#### Unit Overview

Introduction
This unit bundles student expectations that address personal finance and budgeting, including earnings, banking services and accounts, taxes, and credit options. Concepts are incorporated into both mathematical and real-world problem situations. According to the Texas Education Agency, mathematical process standards including application, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

Prior to this Unit
In Grade 6, students compared the features and costs of a checking account and a debit card offered by different local financial institutions. They distinguished between debit cards and credit cards and explained the importance of a positive credit history. In Grade 7, students were introduced to the components of a personal budget, including income; planned savings, taxes, and expenses. Students also calculated and compared simple interest and compound interest. In Grade 8, students analyzed situations to determine if they represented financially responsible decisions and identified the benefits of financial responsibility and the costs of financial irresponsibility. Students calculated the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest over different periods of time. Students also contrasted proportional y = kx and non-proportional y = mx + b linear relationships. In Algebra I, students studied linear functions and were introduced to exponential functions.

During this Unit
Students use linear equations and functions to describe proportional and non-proportional linear relationships and apply them to represent real-world problems involving earnings and budgeting. Students explore methods employees are compensated (e.g., hourly pay, base salary plus commissions, straight commission, salary, etc.) and compare the methods of compensations using various representations. Students use IRS Tax tables to determine personal income taxes and amounts to be deducted from regular pay checks. Students calculate payroll deductions including taxes, pensions, and additional employee benefits, to determine net pay. Students analyze their personal budget based on their net earnings. Students explore types of bank services, including checking and savings options, overdraft protection policies, fees and charges, online banking options, and ATM and card availability and policies, etc. Students analyze banking options based on budgetary and banking needs. Students explore and study models of credit options in retail purchasing and compare relative advantages and disadvantages of each option. Students explain option choices based on income and spending scenarios. Throughout the unit, students develop an economic way of thinking, encouraging financial responsibility for both short-term and long-term goals.

Other considerations: Reference the Mathematics COVID-19 Gap Implementation Tool HS MMA

After this Unit
Students will connect the financial literacy concepts to analyze various loan amortizations, investments for future planning, and insurance options, including life insurance, homeowner’s insurance, and auto insurance.

This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning B1; II. Algebraic Reasoning D1, D2; V. Statistical Reasoning A1, B4, C2; VII. Problem Solving and Reasoning A1, A2, A3, A4, A5, B1, C1, C2, 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 Connections Standard for Grades 9-12 from the National Council of Teachers of Mathematics (NCTM), “Instructional programs from pre-kindergarten through grade 12 should enable students to:

• recognize and use connections among mathematical ideas;
• understand how mathematical ideas interconnect and build on one another to produce a coherent whole; and
• recognize and apply mathematics in contexts outside of mathematics.

When students can see the connections across different mathematical content areas, they develop a view of mathematics as an integrated whole. As they build on their previous mathematical understandings while learning new concepts, students become increasingly aware of the connections among various mathematical topics. As students' knowledge of mathematics, their ability to use a wide range of mathematical representations, and their access to sophisticated technology and software increase, the connections they make with other academic disciplines, especially the sciences and social sciences, give them greater mathematical power” (NCTM, 2000, p. 354).

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics: Connections standard for grades 9-12. Reston, VA: National Council of Teachers of Mathematics, Inc.
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

 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? 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)
• Linear function models can be used to compare methods of compensation, including deductions, to make predictions and budgetary judgments.
• How can linear functions be used to represent and describe proportional and non-proportional relationships in methods of compensation?
• What are the differences in methods of compensation, and how are these differences illustrated in representative function models?
• How do net earnings and gross earnings compare?
• What type of deductions can be taken from an individual’s gross pay?
• How are deductions represented in linear functions used to model net earnings?
• Why must a budget be built around personal earnings?
• Mathematical Modeling
• Personal Finance
• Finance and budgeting
• Taxes
• Insurance
• 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)
• In order to maintain financial stability, consumers must be knowledgeable of the assessment and collection processes used by the various taxing entities for property taxes and personal income taxes to make predictions and budgetary judgments.
• What types of data help make decisions about personal taxes?
• How are the tax amounts determined and collected for personal property?
• How are …
• gross income
• taxable income
… determined, and why is knowing it important?
• What are …
• personal exemptions
• deductions
… and how do they affect the taxes owed?
• How does an employer determine the amount to withhold for income taxes?
• How do “Refund” and “Amount Due” compare on an IRS filing?
• How does understanding assessment and collection processes used by the various taxing entities for property taxes and personal income taxes promote a more secured financial future?
• Mathematical Modeling
• Personal Finance
• Finance and budgeting
• Taxes
• 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)
• In order to maintain financial stability, consumers must analyze bank services according to personal needs to make predictions and budgetary judgments.
• What types of data help make decisions about retail banking?
• How are decisions about banking accounts, services, fees, and protection justified?
• What factors about bank accounts and personal finances must be considered when making decisions about personal banking?
• How are the factors prioritized to realize the maximum benefits and minimum costs related to banking services?
• How does understanding of bank services according to personal needs promote a more secured financial future?
• Mathematical Modeling
• Personal Finance
• Finance and budgeting
• Banking
• 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)
• In order to maintain financial stability, consumers must analyze bank credit card services according to personal needs and compare advantages and disadvantages to make predictions and budgetary judgments.
• What types of data help make decisions about retail credit options?
• How are decisions about retail credit justified?
• What factors about credit cards and personal finances must be considered when making decisions about personal banking?
• How are the factors prioritized to realize the maximum benefits and minimum costs related to credit cards?
• How is the average daily balance calculated?
• How is monthly interest calculated using the average daily balance?
• How does understanding the advantages and disadvantages of bank credit card services according to personal needs promote a more secured financial future?
• Mathematical Modeling
• Personal Finance
• Finance and budgeting
• Banking
• Credit options
• 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 if a relationship is linear, it is always proportional rather than that all proportional relationships are linear, but not all linear relationships are proportional.

Underdeveloped Concepts:

• Some students may have weaknesses in performing calculations involving percentages and operations with decimals within algebraic expressions and equations used in solving problems.

#### Unit Vocabulary

• Annual interest rate (APR) – annual percentage rate (APR) applied to the balance on a loan compounded for a set time frame
• Appraised value – stated value of a property as set by a qualified appraiser or person who works for the local tax assessing office
• Automatic Teller Machine (ATM) – a computer terminal that provides 24/7 access for basic banking services (e.g., cash withdrawals and deposits to various checking and savings accounts) from remote locations
• Budget – a monthly or yearly spending and savings plan for an individual, family, business, or organization
• Commission plus base pay – amount of money paid that includes a base amount plus a percentage of goods sold during a pay period, pay = set percentage • amount of goods sold + base pay
• Compensation – payment for goods or services (e.g., wages, salaries, tips, fees, commissions, etc.)
• Constant rate of change – a ratio when the dependent, y-value, changes at a constant rate for each independent, x-value. All linear relationships have a constant rate of change
• Checking account – a bank account that allows customers access to their money through withdrawals and deposits (e.g., writing a check (or using a debit card) to a payee or to obtain cash from the account, making a deposit to the account, etc.)
• Credit card – a card that can be used to borrow money from financial institutions, stores, or other businesses in order to buy products and services on credit
• Debit card – a bankcard issued by a financial institution that is electronically linked to an individual’s checking account for the purpose of making banking transactions, making payments for services, and/or making purchases
• Debit card/ATM fees – fees charged by a bank for a customer's use of an ATM owned by another bank or credit union
• Deductions – the amount(s) subtracted from gross income for expense(s) allowed by the government that reduces the taxpayers’ taxable income
• Deffered payments – a loan, that may or may not change interest, in which the borrower is allowed to start making payments at some specified date in the future
• Gross pay – the total amount of personal income prior to taxes and deductions
• Hourly rate – amount of money paid per hour worked, pay = hourly rate • hours worked
• Itemized deductions – amounts deducted from gross income based on specified allowable expenses
• Layaway plans – retail sales promotion under which a customer deposits a down payment or a fraction of the cost of the merchandise and the merchandise is held on or before a specified date when the customer completes the payment and picks up the merchandise
• Net pay – the income that remains after taxes and other deductions are taken from an individual’s gross income
• Online banking – a banking system that allows an individual to perform banking services using the internet (e.g., monitor accounts, pay their bills, etc.)
• Overdraft protection – a line of credit a banking institution offers to their customers to cover overdrafts, withdrawals from an account that is greater than the balance within the account
• Payday loan – a high-interest, short term loan that is repaid when the borrower receives their next paycheck
• Payroll deductions – a percentage of money that a company withholds from its employees for the federal and state governments as required by law (e. g., income tax, social security contributions, health insurance, unemployment and disability insurances, supplemental retirement, etc.). Some deductions are determined by formulas set by the government, whereas other deductions are voluntary by the employee.
• Processing fees – fees charged by the bank to the customers for processing account activities (e.g., deposits, checks, transfers, loan payments, bill payments, etc.).
• Personal income tax – a tax based on an individual’s income for federal and/or state governments as required by law. The amount of the tax is usually determined by varying rates on different levels of taxable income which are published annually in tax tables by the federal Internal Revenue Service.
• Personal property taxes – annual state imposed tax on different types of personal properties (e.g., vehicle, farming equipment, boat, etc.) paid by a property owner to local government in which the property is located
• Property taxes – annual tax (county, city, school, etc.) based on an appraised value (land, improvements to land, buildings, etc.) paid by a land owner to local government
• Salary – a fixed annual sum that may or may not be dependent on the number of hours worked and usually paid in regular increments, such as monthly
• Slope of a line – the steepness of a line; rate of change in y (vertical) compared to the rate of change in x (horizontal), or , or , denoted as m in y = mx + b.
• Standard deduction – a flat rate amount based on income and number of exemptions the government allows in place of itemizing expenses for deduction
• Straight commission – amount of money paid based on a percentage of the goods sold, pay = set percentage • amount of goods sold

Related Vocabulary:

 Credit limits Bank balance Dental insurance Employees benefits Interest Health insurance Linear function Non-proportional linear relationship Proportional linear relationship Retirement savings Social Security payments
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 – 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 Mathematical Models with Applications 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.
• 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.
TEKS# SE# TEKS SPECIFICITY
M.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
M.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

Apply

MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE
Including, but not limited to:

• Mathematical problem situations within and between disciplines
• Everyday life
• Society
• Workplace

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• 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.
M.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

Use

A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:

• Problem-solving model
• Analyze given information
• Formulate a plan or strategy
• Determine a solution
• Justify the solution
• Evaluate the problem-solving process and the reasonableness of the solution

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• 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.
M.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

Select

TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, ESTIMATION, AND NUMBER SENSE AS APPROPRIATE, TO SOLVE PROBLEMS
Including, but not limited to:

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

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• 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.
M.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Communicate

MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, GRAPHS, AND LANGUAGE AS APPROPRIATE
Including, but not limited to:

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

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• 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.
M.1E Create and use representations to organize, record, and communicate mathematical ideas.

Create, Use

REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:

• Representations of mathematical ideas
• Organize
• Record
• Communicate
• Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
• Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• 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.
M.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:

• Mathematical relationships
• Connect and communicate mathematical ideas
• Conjectures and generalizations from sets of examples and non-examples, patterns, etc.
• Current knowledge to new learning

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• 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.
M.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Display, Explain, Justify

MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION
Including, but not limited to:

• Mathematical ideas and arguments
• Validation of conclusions
• Displays to make work visible to others
• Diagrams, visual aids, written work, etc.
• Explanations and justifications
• Precise mathematical language in written or oral communication

Note(s):

• The mathematical process standards may be applied to all content standards as appropriate.
• TxCCRS:
• 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.
M.2 Mathematical modeling in personal finance. The student uses mathematical processes with graphical and numerical techniques to study patterns and analyze data related to personal finance. The student is expected to:
M.2A Use rates and linear functions to solve problems involving personal finance and budgeting, including compensations and deductions.

Use

RATES AND LINEAR FUNCTIONS INVOLVING PERSONAL FINANCE AND BUDGETING

Including, but not limited to:

• Rates of change
• Slope of a line – the steepness of a line; rate of change in y (vertical) compared to change in x (horizontal), or or , denoted as m in y = mx + b
• Constant rate of change – a ratio when the dependent, y-value, changes at a constant rate for each independent, x-value. All linear relationships have a constant rate of change.
• Linear functions
• Linear proportional relationship (direct variation)
• Linear
• Represented by y = kx
• Constant rate of change, k
• Passes through the origin
• Linear non-proportional relationship
• Linear
• Represented by y = mx + b
• Constant slope, m
• y-intercept, b, where b ≠ 0

To Solve

PROBLEMS INVOLVING PERSONAL FINANCE AND BUDGETING, INCLUDING COMPENSATIONS AND DEDUCTIONS

Including, but not limited to:

• Compensations – payment for goods or services (e.g., wages, salaries, tips, fees, commissions, etc.)
• Hourly rate – amount of money paid per hour worked, pay = hourly rate • hours worked
• Proportional relationship (direct variation)
• Linear
• Represented by y = kx
• Constant rate of change, k, is the hourly rate.
• Passes through the origin, zero hours worked is zero pay.
• Commission
• Straight commission – amount of money paid based on a percentage of the goods sold, pay = set percentage • amount of goods sold
• Proportional relationship (direct variation)
• Linear
• Represented by y = kx
• Constant rate of change, k, is the set percentage
• Passes through the origin, zero goods sold is zero pay
• Commission plus base pay – amount of money paid that includes a base amount plus a percentage of goods sold during a pay period, pay = set percentage • amount of goods sold + base pay
• Non-proportional linear relationship
• Represented by slope-intercept form, y = mx + b
• Base pay is the y-intercept, b
• Set percentage is the slope, m
• Salary – a fixed annual sum that may or may not be dependent on the number of hours worked and usually paid in regular increments, such as monthly
• Deductions – the amount(s) subtracted from gross income for expense(s) allowed by the government that reduces the taxpayers’ taxable income
• Gross pay – the total amount of personal income prior to taxes and deductions
• Net pay – the income that remains after taxes and other deductions are taken from an individual’s gross income
• Payroll deductions – a percentage of money that a company withholds from its employees for the federal and state governments as required by law (e. g., income tax, social security contributions, health insurance, unemployment and disability insurances, supplemental retirement, etc.). Some deductions are determined by formulas set by the government, whereas other deductions are voluntary by the employee.
• Income tax withholdings are taxes withheld from an employee’s wages that are paid directly to the government.
• Social security and medical payments are percentages withheld from an employee’s pay that is matched by the employer and deposited into the federal retirement system for that employee’s social security retirement benefits.
• Retirement savings are optional savings plans or accounts requested by the employee to which the employer can make direct deposits from the employee's pay.
• Employee-paid benefits are optional benefits provided through the employer such as individual and/or family health insurance, dental insurance, and life insurance.
• Budget – a monthly or yearly spending and savings plan for an individual, family, business, or organization
• Basics of creating a budget
• Determine amount of money available for spending
• Factors to consider in budgeting spending
• Housing (mortgage, rent, insurance, taxes, maintenance)
• Transportation (auto payment, insurance, maintenance, fuel)
• Clothing and personal needs (clothes, personal hygiene and appearance, health needs)
• Food (groceries and restaurants)
• Savings
• Other (charitable giving, gifts, leisure and entertainment, including travel, etc.)

Note(s):

• Grade 7 identified the components of a personal budget, including income; planned savings for college, retirement, and emergencies; taxes; and fixed and variable expenses, and calculate what percentage each category comprises of the total budget.
• Grade 8 compared and contrasted proportional y = kx and non-proportional y = mx + b linear relationships.
• Algebra I introduced the concept of a function in terms of the linear relationship.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxCCRS
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.3. Determine a solution.
• 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.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.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.
• 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.3. Know and understand the use of mathematics in a variety of careers and professions.
M.2B Solve problems involving personal taxes.

Solve

PROBLEMS INVOLVING PERSONAL TAXES

Including, but not limited to:

• Property taxes – annual tax (county, city, school, etc.) based on an appraised value (land, improvements to land, buildings, etc.) paid by a land owner to local government
• Appraised value – stated value of a property as set by a qualified appraiser or person who works for the local tax assessing office
• Personal property taxes – annual state imposed tax on different types of personal properties (e.g., vehicle, farming equipment, boat, etc.) paid by a property owner to local government in which the property is located
• Personal income tax – a tax based on an individual's income for federal and/or state governments as required by law. The amount of the tax is usually determined by varying rates on different levels of taxable income which are published annually in tax tables by the federal Internal Revenue Service.
• Deductions – the amount(s) subtracted from gross income for expense(s) allowed by the government that reduces the taxpayers’ taxable income
• Standard deduction – a flat rate amount based on income and number of exemptions the government allows in place of itemizing expenses for deduction
• Itemized deductions – amounts deducted from gross income based on specified allowable expenses

Note(s):

• Mathematical Models with Applications examines personal taxes and how taxes are calculated.
• Various mathematical process standards will be applied to this student expectation as appropriate
• TxCCRS
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.3. Determine a solution.
• 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.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.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.
• 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.3. Know and understand the use of mathematics in a variety of careers and professions.
M.2C Analyze data to make decisions about banking, including options for online banking, checking accounts, overdraft protection, processing fees, and debit card/ATM fees.

Analyze

DATA TO MAKE DECISIONS ABOUT BANKING, INCLUDING OPTIONS FOR ONLINE BANKING, CHECKING ACCOUNTS, OVERDRAFT PROTECTION, PROCESSING FEES, AND DEBIT CARD/ATM FEES

Including, but not limited to:

• Decisions about banking options
• Online banking – a banking system that allows an individual to perform banking services using the internet (e.g., monitor accounts, pay their bills, etc.)
• Checking account – a bank account that allows customers access to their money through withdrawals and deposits (e.g., writing a check (or using a debit card) to a payee or to obtain cash from the account, making a deposit to the account, etc.)
• Automatic Teller Machine (ATM) – a computer terminal that provides 24/7 access for basic banking services (e.g., cash withdrawals and deposits to various checking and saving accounts) from remote locations
• Overdraft protection – a line of credit a banking institution offers to their customers to cover overdrafts, withdrawals from an account that is greater than the balance within the account
• Processing fees – fees charged by the bank to the customers for processing account activities (e.g., deposits, checks, transfers, loan payments, bill payments, etc.).
• Debit card – a bankcard issued by a financial institution that is electronically linked to an individual’s checking account for the purpose of making banking transactions, making payments for services, and/or making purchases
• Debit card/ATM fees – fees charged by a bank for a customer's use of an ATM owned by another bank or credit union

Note(s):

• Grade 6 compared features and costs of a checking account and a debit card offered by different local financial institutions.
• Grade 6 distinguished between debit cards and credit cards.
• Grade 6 balanced a check register that includes deposits, withdrawals, and transfers.
• Mathematical Models with Applications examines the analysis of bank services and accounts.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxCCRS
• V.B. Statistical Reasoning – Describe data
• V.B.4. Describe patterns and departure from patterns in the study of data.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• 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.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.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.
• 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.3. Know and understand the use of mathematics in a variety of careers and professions.
M.3 Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, graphs, and amortization modeling to solve problems involving credit. The student is expected to:
M.3B Analyze personal credit options in retail purchasing and compare relative advantages and disadvantages of each option.

Analyze

PERSONAL CREDIT OPTIONS IN RETAIL PURCHASING

Including, but not limited to:

• Credit card – a card that can be used to borrow money from financial institutions, stores, or other businesses in order to buy products and services on credit
• Bank credit cards and store specific credit cards
• An annual fee is charged by some credit cards.
• Minimum payment each month is based on the balance.
• Credit limits define the maximum amount that can be charged on an account.
• Limits are determined using various criteria such as credit history, credit score, and/or ability to pay based on income.
• Interest is usually charged on average balance throughout a month if entire balance is not paid each month.
• Rewards programs in the form of airline travel miles, points that can be exchanged for merchandise or services, donations to charities or scholarship funds
• Layaway plans – retail sales promotion under which a customer deposits a down payments or a fraction of the cost of the merchandise, and the merchandise is held until on or before a specified date when the customer completes the payment and picks up the merchandise
• Deferred payments – a loan, that may or may not charge interest, in which the borrower is allowed to start making payments at some specified date in the future
• Payday loan – a high-interest, short term loan that is repaid when the borrower receives their next paycheck

Compare

RELATIVE ADVANTAGES AND DISADVANTAGES OF EACH CREDIT OPTION

Including, but not limited to:

• Interest rates
• Credit card interest can vary according to credit history, balance, and other factors.
• Layaway plans charge a small fee and set the time to pay but do not charge interest.
• Deferred payment interest can vary according to the loan agreement and may or may not apply during the deferment period. The borrow can purchase large items and make payments at a later time when they feel they are more capable of meeting the monthly payment.
• Payday loans are short term, but annual interest rates (APR) is higher than with credit cards.
• Payment options
• Credit cards require a minimum payment each month based on account balance
• Layaway requires regular payments on a schedule in order to get the full amount paid within a set time period, such as 8, 10, or 12 weeks. The longer the period, the higher the fee.
• Deferred payment plans require a monthly payment which begins at some specified date in the future. Interest usually begins to apply when monthly payments begin, but can apply during the deferment period.
• Payday or cash advance loans require full payment by the borrower's next payday or the loan is "rolled over" and more interest at a higher rate is charged. The interest is charged in advance for a specified time.
• Accounting formulas for credit cards (monthly interest rate, annual interest rate, etc.)
• Annual interest rate – annual percentage rate (APR) applied to the balance on a loan compounded for a set time frame
• Periodic (daily) interest rate:
• Average daily balance (ADB) is interest charged on the amount owed at the end of each day
• Most credit card companies charge interest based on average daily balance, which means that the interest rate is effectively slightly higher than the stated APR.

Note(s):

• Grade 8 calculated the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator.
• Grade 8 identified and explained the advantages and disadvantages of different payment methods.
• Algebra I studied the exponential parent function f(x) = abx.
• Mathematical Models with Applications examines loans and interest charges.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxCCRS
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• 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.2. Understand attributes and relationships with inductive and deductive reasoning.
• 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.
• 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.
• IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.