10-12 > Mathematics
 Grade level: 10-12 Subject: Mathematics Duration: 3 class periods
 Objectives | Materials | Procedures | Evaluation | Vocabulary | Academic Standards | Credit

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Objectives
Students will
• Research the history of money and share presentations.
• Solve problems of proportions using the Rule of Three and the Inverse Rule of Three.
• Convert American and foreign currencies.
• Calculate problems of limiting value using the formula S = Penas it pertains to annual percentage rate.
Materials
• Concepts in Business Mathematics: Economics and Financeprogram
• Computer with Internet access
• Print resources about the history of money
Procedures
1. Have students research the history of money using print and Web resources. The following Web sites are a good starting point:
2. When students have completed their research, ask them to summarize their findings in a one-page report.
3. Have each student choose a partner. Ask students to share their reports with their partners and answer any questions. Then have students summarize their partners? reports for the class, including at least three interesting facts.
4. Show students examples of proportions and solve them using the Rule of Three. Ask students how the terms in the proportion correspond to the terms in the statement of the Rule of Three. Allow students time to practice.
5. Show students examples of proportions and solve them using the Inverse Rule of Three. Ask students how the terms in the proportion correspond to the terms in the statement of the Inverse Rule of Three. Allow students time to practice.
6. Have students look up current exchange rates. Good resources include these:Have students choose an amount of American dollars and convert it to three different currencies. Also have them explain how to find the exchange rate from dollars to pesos if they are given the exchange rate from pesos to dollars.
7. Using a fixed yearly interest rate, provide students with several examples of total interest and annual percentage rate when varying the number of compounding intervals. Allow students time to practice.
8. Show students an example of a limiting value, for example of the series 1,1 + 1/2, 1 + 1/2 + 1/4, and so on. (The series has a limiting value of 2 because each number in the series is halfway between the previous number and 2.) Explain that similarly,eis a limiting value that arises in the calculation of annual percentage rate. Allow students time to practice with the formula S = Pen.
Evaluation
Use the following three-point rubric to evaluate students' work during this lesson.
• Three points: Students thoroughly researched the history of money and shared an accurate presentation; correctly solved all problems of proportions; accurately converted currencies; and correctly solved all problems of limiting value.
• Two points: Students adequately researched the history of money and shared a mostly accurate presentation; correctly solved most of the problems of proportions; accurately converted most currencies; and correctly solved most problems of limiting value.
• One point: Students poorly researched the history of money and shared a mostly inaccurate presentation; incorrectly solved all or most problems of proportions; inaccurately converted most or all currencies; and incorrectly solved all or most problems of limiting value.
Vocabulary
barter
Definition:A mercantile system by which goods and services are directly traded for each other and no formal currency is present
Context:Developing societies often improve their economic efficiency by introducing currency over a barter system.

compound interest
Definition:Interest that accumulates on both the initial amount of the loan (the principal) and the interest already accumulated
Context:Most banks use compound interest instead of simple interest.

cost
Definition:Expenses incurred, as by a business
Context:If a business makes \$1,000 and spends \$750 for a difference of \$250, its costs total \$750.

exchange rate
Definition:The factor by which the amount of one currency is multiplied to yield an equivalent amount of another currency
Context:If, at a given time, 100 U.S dollars are worth as much as 110 Canadian dollars, 1.1 Canadian dollars to U.S. dollars is the exchange rate.

interest
Definition:Money generated by principal over time, as in a loan or savings account
Context:If you borrow \$500 and agree to pay it back with 5% of the \$500 added in a year, the extra 5% is the interest and 5% is said to be the interest rate.

principal
Definition:The initial amount of the loan, before interest is added or paid
Context:If you take out a loan in the amount of \$250 that you will pay back with interest, the \$250 is the principal.

National Council of Teachers of Mathematics (NCTM)
The National Council of Teachers of Mathematicsprovides guidelines for teaching mathematics in grades K?12 to promote mathematical literacy. To view the standards,click here.
This lesson plan addresses the following national standards:
• Solve problems that arise in mathematics and other contexts
• Understand how mathematical ideas interconnect and build on one another to produce a coherent whole
• Recognize and apply mathematics in contexts outside of mathematics

Mid-continent Research for Education and Learning (McREL)
McREL?s Content Knowledge: A Compendium of Standards and Benchmarks for K­?12 Education addresses 14 content areas. To view the standards and benchmarks,click here.
This lesson plan addresses the following national standards:

• Mathematics: Understands and applies basic and advanced properties of the concepts of numbers; understands and applies basic and advanced properties of functions and algebra; understands the general nature and uses of mathematics
• Economics: Understands savings, investment, and interest rates
• History: United States History: Understands how political, religious, and social institutions emerged in the English colonies