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ConnectionsSession 06 Overviewtab aTab btab ctab dtab eReference
Part B

Exploring Connections
  Introduction | Calculating Interest | A More Efficient Method | Interest Calculator | Reviewing Connections | Your Journal

 
 

What connections did you include on your list? Remember that we were looking for connections within the activity, to other mathematical areas, and to contexts outside mathematics.


Here are some connections you might have noted:

Show Answer
Sample Answer:
Connections among mathematical ideas within this activity:
  • Understanding of how compound interest relates to computational and algebraic procedures
  • Number sense and problem solving when modifying and comparing situations
  • Computations and notation of percentages, including fractional percentages
  • Fractional exponents
  • The limit concept

Connections to other mathematical areas:

  • The basic meaning and use of exponents in equations
  • Iterative versus closed mathematical rules
  • Other representations ("What if?" scenarios in table form or graphs)
  • The derivation and other uses of e

Connections to contexts outside mathematics:

  • Consumer decisions regarding interest-bearing accounts
  • The concept of "yield" on a fixed-return investment
  • The use of quantitative data to support financial decision-making
  • How the technique of calculating compound interest relates to other financial issues
  • How exponential growth might relate to other real-world phenomena
 

If you would like to supplement your list of connections, please do so now.


After you've had a chance to review your connections worksheet, please answer the following questions:


Question: How might the methods used to develop the interest formulas help people understand and interpret these formulas? What connections might one make while developing the formulas?

Show Answer
Sample Answer:
Starting by creating the table helps build an understanding of compound interest, but it also prompts a need for a more efficient approach. Connections within mathematics are made to algebra, to the idea of a limit, and to the concept of finding generalized mathematical techniques for solving specific problems. More broadly, the presentation and use of quantitative data to make an investment decision is a key connection –– in particular, creating and evaluating "What if?" scenarios with different values and variables.
 

Question: What might you explain with particular care as you discuss the investment options with a friend?

Show Answer
Sample Answer:
Helping someone understand how each option can be represented mathematically poses an initial challenge. But equally important is to be sure that your friend understands how this information could connect to a real-life context –– for instance, how to consider quantitative data accurately and responsibly as part of a decision that will have additional non-mathematical factors, for instance, making choices between leasing or buying a car.
 

Question: How is the consideration of different time periods, such as 4 versus 10 years, connected to other work with exponential functions?

Show Answer
Sample Answer:
Considering different time periods relates to functions where the variable x is part of the exponent. Although we might be tempted to think that 1.03 is so close to 1 that rounding down won't make a big difference, a graph of such a function would show that the factor determined by x1.03 increases significantly.
 

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