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

Unit Overview

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. 

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 B1; VII. Functions A2; VIII. Problem Solving and Reasoning; IX. Communication and Representation; X. Connections.

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/collegereadiness/crs.pdf

OVERARCHING UNDERSTANDINGS and QUESTIONS

Function models for problem situations can be determined by collecting and analyzing data using a variety of representations and applied to make predictions and critical judgments in terms of the problem situation.

  • Why is it important to determine and apply function models for problem situations?
  • What representations can be used to analyze collected data and how are the representations interrelated?
  • Why is it important to analyze various representations of data when determining appropriate function models for problem situations?
  • How does technology aid in the analysis and application of modeling and solving problem situations?

Knowledgeable consumers and investors develop an economic way of thinking and problem solving.

  • How does financial literacy affect financial responsibility and long-term goals?
Performance Assessment(s) Overarching Concepts
Unit Concepts
Unit Understandings
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.

Algebraic Reasoning

  • Equations
  • Patterns/Rules
  • Ratios/Rates
  • Solve

Functions

  • Constant of Proportionality
  • Linear Functions

Personal Financial Literacy

  • Budget
  • Expenses
  • Income
  • Jobs
  • Taxes

Associated Mathematical Processes

  • Application
  • Tools and Techniques
  • Problem Solving Model
  • Communication
  • Representations
  • Relationships 
  • Justification

Linear functions can be used to represent and solve real-world problem situations.

  • How can linear functions be used to describe personal earnings?
  • What type of earnings are modeled by a proportional linear relationship?
  • What type of earnings are modeled by a non-proportional linear relationship?
  • How are rates of linear functions related to personal earnings?
  • How are compensations and deductions represented in linear function modeling earnings?
  • What is difference in net earnings and gross earnings?
  • How are earnings and a budget related?
  • Why must a budget be built around personal earnings?
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.

Algebraic Reasoning

  • Equations
  • Patterns/Rules
  • Rates
  • Solve

Personal Financial Literacy

  • Taxes

Associated Mathematical Processes

  • Application
  • Tools and Techniques
  • Problem Solving Model
  • Communication
  • Representations
  • Relationships 
  • Justification

Analysis of financial options involves interpretation of data from various sources.

  • What types of data help make decisions about personal taxes?
  • How are decisions about personal taxes justified?

Property taxes are based on a tax rate applied to the appraised value of the property.

  • What are the entities that tax personal property?
  • How are the tax amounts determined for a particular property?

Income tax is paid to the government based on income, exemptions, and deductions.

  • How is gross income determined?
  • How is taxable income determined?
  • What are personal exemptions and how do they affect the taxes owed?
  • What are deductions and how do they affect the taxes owed?
  • How does an employer determine the amount to withhold for income taxes?

 

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.

Algebraic Reasoning

  • Equations
  • Patterns/Rules
  • Rates
  • Solve

Functions

  • Linear Functions
  • Non-Linear Functions

Personal Financial Literacy

  • Borrowing/Lending/Credit
  • Deposits/Withdrawals/Transfers
  • Financial Institutions
  • Financial Records
  • Interest
  • Investments/Savings

Associated Mathematical Processes

  • Application
  • Tools and Techniques
  • Problem Solving Model
  • Communication
  • Representations
  • Relationships 
  • Justification

Analysis of financial options involves interpretation of data from various sources.

  • What types of data help make decisions about retail banking?
  • How are decisions about banking accounts, services, fees, and protection justified?

Making decisions about banking options requires analysis of multiple types of data.

  • What factors about bank accounts must be considered when making decisions about personal banking?
  • What factors about 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?
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.

Algebraic Reasoning

  • Equations
  • Patterns/Rules
  • Rates
  • Solve

Functions

  • Linear Functions
  • Non-Linear Functions

Personal Financial Literacy

  • Assets/Liabilities
  • Borrowing/Lending/Credit
  • Credit Reports
  • Financial Records
  • Interest

Associated Mathematical Processes

  • Application
  • Tools and Techniques
  • Problem Solving Model
  • Communication
  • Representations
  • Relationships 
  • Justification

Analysis of financial options involves interpretation of data from various sources.

  • What types of data help make decisions about retail credit options?
  • How are decisions about retail credit justified?

Choosing among retail credit options requires analysis of multiple types of information and data.

  • What factors about credit cards must be considered when making decisions about personal banking?
  • What factors about personal finances must be considered when making decisions about credit cards?
  • 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?

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 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.
  • 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 paycheck described as an annual sum that may or may not be dependent on the number of hours worked. Salaries are usually stated in annual terms, but are paid in increments on a regular time schedule, 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 Creator if your district has granted access to that tool.

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

Texas Higher Education Coordinating Board – Texas College and Career Readiness Standards (select CCRS from Standard Set dropdown menu)

Texas Instruments – Graphing Calculator Tutorials

Texas Education Agency – STAAR Mathematics Resources

Texas Education Agency – Revised Mathematics TEKS: Vertical Alignment Charts

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

Texas Education Agency – Mathematics Curriculum

Texas Education Agency – Mathematics TEKS: Supporting Information

Texas Education Agency – Interactive Mathematics Glossary

TEKS# SE# TEKS Unit Level Specificity
 
  • Bold black text in italics: Knowledge and Skills Statement (TEKS)
  • Bold black text: Student Expectation (TEKS)
  • Strike-through: Indicates portions of the Student Expectation that are not included in this unit but are taught in previous or future unit(s)
  • Blue text: Supporting information / Clarifications from TCMPC (Specificity)
  • Blue text in italics: Unit-specific clarification
  • Black text: Texas Education Agency (TEA); Texas College and Career Readiness Standards (TxCCRS)
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:
    • X. Connections
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:
    • VIII. Problem Solving and Reasoning
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:
    • VIII. Problem Solving and Reasoning
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:
    • IX. Communication and Representation
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:
    • IX. Communication and Representation
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:
    • X. Connections
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:
    • IX. Communication and Representation
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 relationships
        • 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 Level(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
    • I. Numeric Reasoning
      • B1 – Perform computations with real and complex numbers.
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
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):  

  • Grade Level(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
    • I. Numeric Reasoning
      • B1 – Perform computations with real and complex numbers.
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
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 Level(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
    • I. Numeric Reasoning
      • B1 – Perform computations with real and complex numbers.
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
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 Level(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
    • I. Numeric Reasoning
      • B1 – Perform computations with real and complex numbers.
    • II. Algebraic reasoning
      • B1 – Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions.
    • VII. Functions
      • A2 – Recognize and distinguish between different types of functions.
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
The English Language Proficiency Standards (ELPS), as required by 19 Texas Administrative Code, Chapter 74, Subchapter A, §74.4, outline English language proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement ELPS as an integral part of each subject in the required curriculum.

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


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

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


Choose appropriate ELPS to support instruction.

ELPS# Subsection C: Cross-curricular second language acquisition essential knowledge and skills.
Click here to collapse or expand this section.
ELPS.c.1 The ELL uses language learning strategies to develop an awareness of his or her own learning processes in all content areas. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.1A use prior knowledge and experiences to understand meanings in English
ELPS.c.1B monitor oral and written language production and employ self-corrective techniques or other resources
ELPS.c.1C use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary
ELPS.c.1D speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known)
ELPS.c.1E internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment
ELPS.c.1F use accessible language and learn new and essential language in the process
ELPS.c.1G demonstrate an increasing ability to distinguish between formal and informal English and an increasing knowledge of when to use each one commensurate with grade-level learning expectations
ELPS.c.1H develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for patterns in language, and analyzing sayings and expressions commensurate with grade-level learning expectations.
ELPS.c.2 The ELL listens to a variety of speakers including teachers, peers, and electronic media to gain an increasing level of comprehension of newly acquired language in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in listening. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.2A distinguish sounds and intonation patterns of English with increasing ease
ELPS.c.2B recognize elements of the English sound system in newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters
ELPS.c.2C learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions
ELPS.c.2D monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed
ELPS.c.2E use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language
ELPS.c.2F listen to and derive meaning from a variety of media such as audio tape, video, DVD, and CD ROM to build and reinforce concept and language attainment
ELPS.c.2G understand the general meaning, main points, and important details of spoken language ranging from situations in which topics, language, and contexts are familiar to unfamiliar
ELPS.c.2H understand implicit ideas and information in increasingly complex spoken language commensurate with grade-level learning expectations
ELPS.c.2I demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs.
ELPS.c.3 The ELL speaks in a variety of modes for a variety of purposes with an awareness of different language registers (formal/informal) using vocabulary with increasing fluency and accuracy in language arts and all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in speaking. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.3A practice producing sounds of newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters to pronounce English words in a manner that is increasingly comprehensible
ELPS.c.3B expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication
ELPS.c.3C speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired
ELPS.c.3D speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency
ELPS.c.3E share information in cooperative learning interactions
ELPS.c.3F ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments
ELPS.c.3G express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics
ELPS.c.3H narrate, describe, and explain with increasing specificity and detail as more English is acquired
ELPS.c.3I adapt spoken language appropriately for formal and informal purposes
ELPS.c.3J respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment.
ELPS.c.4 The ELL reads a variety of texts for a variety of purposes with an increasing level of comprehension in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in reading. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1, certain of these student expectations apply to text read aloud for students not yet at the stage of decoding written text. The student is expected to:
ELPS.c.4A learn relationships between sounds and letters of the English language and decode (sound out) words using a combination of skills such as recognizing sound-letter relationships and identifying cognates, affixes, roots, and base words
ELPS.c.4B recognize directionality of English reading such as left to right and top to bottom
ELPS.c.4C develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials
ELPS.c.4D use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to enhance comprehension of written text
ELPS.c.4E read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned
ELPS.c.4F use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language
ELPS.c.4G demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs
ELPS.c.4H read silently with increasing ease and comprehension for longer periods
ELPS.c.4I demonstrate English comprehension and expand reading skills by employing basic reading skills such as demonstrating understanding of supporting ideas and details in text and graphic sources, summarizing text, and distinguishing main ideas from details commensurate with content area needs
ELPS.c.4J demonstrate English comprehension and expand reading skills by employing inferential skills such as predicting, making connections between ideas, drawing inferences and conclusions from text and graphic sources, and finding supporting text evidence commensurate with content area needs
ELPS.c.4K demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and performing critical analyses commensurate with content area and grade-level needs.
ELPS.c.5 The ELL writes in a variety of forms with increasing accuracy to effectively address a specific purpose and audience in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in writing. In order for the ELL to meet grade-level learning expectations across foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1, certain of these student expectations do not apply until the student has reached the stage of generating original written text using a standard writing system. The student is expected to:
ELPS.c.5A learn relationships between sounds and letters of the English language to represent sounds when writing in English
ELPS.c.5B write using newly acquired basic vocabulary and content-based grade-level vocabulary
ELPS.c.5C spell familiar English words with increasing accuracy, and employ English spelling patterns and rules with increasing accuracy as more English is acquired
ELPS.c.5D edit writing for standard grammar and usage, including subject-verb agreement, pronoun agreement, and appropriate verb tenses commensurate with grade-level expectations as more English is acquired
ELPS.c.5E employ increasingly complex grammatical structures in content area writing commensurate with grade-level expectations, such as:
ELPS.c.5F write using a variety of grade-appropriate sentence lengths, patterns, and connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired
ELPS.c.5G narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired.
Last Updated 09/01/2016
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