Standards - Mathematics

2019 - Mathematics Course of Study Document
Mathematics (2019) Grade(s): 09-12 - Mathematical Modeling

MA19.MM.2

Use elements of the Mathematical Modeling Cycle to solve real-world problems involving finances.

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Knowledge

Students know:
  • how to approach and solve real-world financial problems using mathematical models.

Skills

Students are able to:
  • Read a real-world financial problem and distinguish between relevant and non-relevant information.
  • Create and apply a mathematical model to solve a real-world financial problem.
  • Analyze their work and their findings.
  • note restrictions or limits that arise when using a mathematical model.
  • Share their findings with others.
  • Apply their work to similar situations.

Understanding

Students understand that:
  • Real-world financial problems can be solved using a mathematical model.
  • There is a defined process to follow to create a mathematical model for financial problem solving.
  • Mathematical models sometimes have limitations or need to be restricted in order to produce valid answers.

Vocabulary

  • Mathematical Modeling Cycle
  • Mathematical Model
Mathematics (2019) Grade(s): 09-12 - Mathematical Modeling

MA19.MM.3

Organize and display financial information using arithmetic sequences to represent simple interest and straight-line depreciation.

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Knowledge

Students know:
  • how to select information from a real-world financial problem, such as the initial amount of the investment and its periodic rate of change, and use it to model simple interest and straight line depreciation.

Skills

Students are able to:
  • Identify the first term and the common difference in an arithmetic sequence.
  • Recognize that the first term of an arithmetic sequence is the initial value of a loan or investment.
  • Recognize that the common difference in an arithmetic sequence is the rate of change in the loan or investment.
  • Use an arithmetic sequence to model simple interest or straight-line depreciation.
  • Display data found by using an arithmetic sequence to model simple interest or straight-line depreciation.

Understanding

Students understand that:
  • The initial amount of an investment and its periodic rate of change correlate to the first term and the common difference in an arithmetic sequence.
  • Arithmetic sequences can be used to model simple interest and straight-line depreciation.

Vocabulary

  • Simple Interest
  • Straight Line Depreciation
  • Arithmetic Sequence
Mathematics (2019) Grade(s): 09-12 - Mathematical Modeling

MA19.MM.4

Organize and display financial information using geometric sequences to represent compound interest and proportional depreciation, including periodic (yearly, monthly, weekly) and continuous compounding.

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Knowledge

Students know:
  • how to select information from a real-world financial problem, such as the initial amount of the investment and its periodic rate of change, and use it along with a geometric sequence to model compound interest and proportional depreciation.

Skills

Students are able to:
  • Identify the first term and common ratio in a geometric sequence.
  • Recognize that the first term of a geometric sequence is the initial value of the loan or investment.
  • Recognize that the common ratio is either (1+rate of growth) or (1-Rate of decay).
  • Use a geometric sequence to model compound interest or proportional depreciation.
  • Display data found using a geometric sequence to model compound interest or proportional depreciation. Relate APR to APY using compound interest formulas.

Understanding

Students understand that:
  • the initial amount of an investment or a loan and its periodic rate of change correlate to the first term and the common difference in a geometric sequence.
  • Geometric sequences can be used to model compound interest and proportional depreciation.
  • The annual percentage rate is the yearly rate of interest while the annual percentage yield is the rate you actually pay when compound interest is included.

Vocabulary

  • Compound Interest
  • Geometric Sequence
  • Proportional Depreciation
  • Periodic
  • Annual Percentage Rate
  • Annual Percentage Yield

Aligned Learning Resources

Exponential Growth and Decay
Mathematics (2019) Grade(s): 09-12 - Mathematical Modeling

MA19.MM.5

Explain the relationship between annual percentage yield (APY) and annual percentage rate (APR) as values for $r$ in the formulas $A=P(1+r)^t$ and $A=Pe^{rt}$.

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Knowledge

Students know:
  • how to calculate both simple interest and compound interest and straight line depreciation and proportional depreciation.

Skills

Students are able to:
  • Create tables that compare interest paid/owed on accounts using simple interest and compound interest.
  • Create tables that compare depreciation on items using straight line depreciation and proportional depreciation.

Understanding

Students understand that:
  • interest can be calculated in different ways and there are advantages and disadvantages to each method. (earning interest vs. paying interest).
  • Depreciation can be calculated in different ways and there are advantages and disadvantages to each method.

Vocabulary

  • Simple Interest
  • Compound Interest
  • Straight Line Depreciation
  • Proportional Depreciation
Mathematics (2019) Grade(s): 09-12 - Mathematical Modeling

MA19.MM.6

Investigate growth and reduction of credit card debt using spreadsheets, including variables such as beginning balance, payment structures, credits, interest rates, new purchases, finance charges, and fees.

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Knowledge

Students know:
  • how to calculate the balance on a credit card.

Skills

Students are able to:
  • Calculate the growth of credit card debt or the reduction of credit card debt.
  • Recognize that payments or new purchases affect the balance on a credit card.
  • Recognize that annual fees and interest rates affect the balance on a credit card.
  • Recognize that making a minimum payment does not significantly reduce the balance on a credit card.
  • Use a spreadsheet to perform repetitive calculations.

Understanding

Students understand that:
  • Credit card balances can grow due to high interest rates, finance charges, fees and new purchases.
  • Care should be taken to insure that credit card balances are monitored and controlled.

Vocabulary

  • Beginning Balance
  • Payment Structure
  • Investment Rate
  • Finance Charge
  • Fee
Mathematics (2019) Grade(s): 09-12 - Mathematical Modeling

MA19.MM.7

Compare and contrast housing finance options including renting, leasing to purchase, purchasing with a mortgage, and purchasing with cash.

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Knowledge

Students know:
  • how to calculate the cost of renting a house for a period of time.
  • how to calculate the cost of purchasing a house with a mortgage.
  • how to organize data on housing costs.
  • how to compare and contrast housing cost data.

Skills

Students are able to:
  • Calculate the cost of renting a house.
  • Calculate the cost of renting to own a house.
  • Calculate the cost of a house through a mortgage purchase.
  • Calculate the cost of a house through a cash purchase.
  • Compare and contrast the cost of purchasing a home using different methods.

Understanding

Students understand that:
  • there are many ways to pay for housing. Each method has advantages and disadvantages for individuals.

Vocabulary

  • Rent
  • Lease to Purchase
  • Mortgage
  • Interest Rate
  • Down Payment
Mathematics (2019) Grade(s): 09-12 - Mathematical Modeling

MA19.MM.8

Investigate the advantages and disadvantages of various means of paying for an automobile, including leasing, purchasing by cash, and purchasing by loan.

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Knowledge

Students know:
  • how to calculate the cost of leasing a car.
  • how to calculate the cost of an automobile loan.
  • how to organize data on car purchases.
  • how to compare and contrast the car purchase data.

Skills

Students are able to:
  • Use the compound interest formula to calculate the cost of purchasing a car through a loan.
  • Calculate the cost of a car when leased.
  • organize car purchase data.
  • Compare and contrast data to make an informed decision.

Understanding

Students understand that:
  • there are different methods for purchasing a car. Each method has advantages and disadvantages for individuals.

Vocabulary

  • Lease
  • Principal
  • Interest Rate
  • Compounding Periods

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