Gold Seal Lesson:
College Funds

Copernicus Education Gateway

Subject:

Mathematics

Grade:

9-12

ICLE Standards:

Mathematics as Problem Solving: Apply the process of mathematical modeling to real-world problem situations.

Mathematical Connections: Explore problems and describe results using graphic, numerical, physical, algebraic, and verbal mathematical models or representations.

Algebra: Apply the concept of quadratic relations to a real-world situations.

Functions: Model real-world phenomena with a variety of functions.

Use of Technology: Use technology to perform calculations.

Performance Task:

This task requires you to work as a member of a cooperative group. You will complete a project using quadratic relations in a real-world situation. Your group is to research colleges and select one that you would like to attend. You can choose one college as a group or each member of your group may select a college of his/her own. Determine the amount of money that should be deposited today in order to accumulate in 1 to 4 years the amount of money that you will need to attend the college you select. You can determine the amount for 1 year, 2 years, or 4 years, depending of what type of college you choose. You may decide to use as your amount the amount needed for tuition alone; the amount needed for tuition, room, and board; or the total amount that you will need for all expenses. Most college catalogs will give you these figures. Assume that you will invest your money so as to receive a 5% return on your investment, compounded quarterly. In your math journal, discuss your findings and the implications of your results.

Notes to the teacher:

1. You may wish to change the parameters here. For example, you may have the students invest their money in stocks and estimate an 8% return or you may have the money invested so as to compound the interest daily (especially if students are using the proper technology).
2. Students should use the formula P = A[1 + (r/m)]n , where P is the principal amount deposited, A is the amount desired to accumulate, r is the rate of interest, m is the number compounding periods a year, and n is the total number of compounding periods: n = m times the number of years. The students should be familiar with this formula, but if they haven't memorized it, perhaps you will need to give it to them.

Knowledge / Skills:

Understand the use of variables in expressions such as 4x, x+2, and 2x-1, solve for the variable, and know how to represent expressions such as "twice the number" or "four more than the number" using variables. (m7)

Apply the zero property of multiplication to find the solution of quadratic equations. (m53)

Understand the concepts recurrence relations and how they are applicable to such things as compound interest and annuity. (m61)

Gather information from a variety of sources, including electronic sources, and summarize, analyze, and evaluate its use for a report. (ela3)

Use writing as a tool for learning in formats such as learning logs, laboratory reports, note-taking, and journals. (ela40)

Rubric:

4 Points = The student fully accomplishes the task. He/she demonstrates complete understanding of the function used in the solution of the problem and can make application of it to a real-world situation. The student clearly communicates his/her findings in written and symbolic form.

3 Points = The student substantially accomplishes the task, but he/she needs some assistance in doing so. The student demonstrates only a partial understanding of the function used in the problem. He/she has some difficulty solving the problem. He/she attempts, but does not clearly communicate his/her findings in both written and symbolic form.

2 Points = The student is only able to accomplish the task by having sustained support from others. He/she shows a lack of understanding of how to use the function in the solution of the problem. The student’s work is disorganized and contains mathematical errors. He/she lacks good communication skills; the written and symbolic form is difficult to follow.

1 Point = Even with sustained help from others, the student is unable to accomplish the task. He/she demonstrates little understanding of functions and how to use them in the solution of problems. The student’s work is incomplete and poorly organized. There is little comprehension to his/her communication attempt.

Keywords:

ALGEBRA
ALGEBRAIC OPERATIONS
LINEAR PATTERNS
PROBLEM SOLVING
QUADRATICS
MATH IN DAILY LIFE

Grades:

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [] - 6 [] - 7 [] - 8 [] - 9 [x] - 10 [x] - 11 [x] - 12 [x]

ICLE Application:

D

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