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 – Realworld problem solving
 VII.D.1. Interpret results of the mathematical problem in terms of the original realworld 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld 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 problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.

Use
A PROBLEMSOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEMSOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION Including, but not limited to:
 Problemsolving model
 Analyze given information
 Formulate a plan or strategy
 Determine a solution
 Justify the solution
 Evaluate the problemsolving 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 problemsolving process.
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.2. Evaluate the problemsolving 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld 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 nonexamples, 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, yvalue, changes at a constant rate for each independent, xvalue. 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 nonproportional relationship
 Linear
 Represented by y = mx + b
 Constant slope, m
 yintercept, 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
 Nonproportional linear relationship
 Represented by slopeintercept form, y = mx + b
 Base pay is the yintercept, 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.
 Employeepaid 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 nonproportional 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 – Realworld problem solving
 VII.D.1. Interpret results of the mathematical problem in terms of the original realworld 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld 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):
 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
 VII.A. Problem Solving and Reasoning – Mathematical problem solving
 VII.A.3. Determine a solution.
 VII.D. Problem Solving and Reasoning – Realworld problem solving
 VII.D.1. Interpret results of the mathematical problem in terms of the original realworld 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld 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 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
 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 – Realworld problem solving
 VII.D.1. Interpret results of the mathematical problem in terms of the original realworld 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld 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 highinterest, 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) = ab^{x}.
 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, realworld situations, and everyday life
 IX.B.1. Use multiple representations to demonstrate links between mathematical and realworld situations.
 IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.
