The students had just completed unit 25 in the Applied Mathematics series published by CORD which emphasizes conic sections. Each student took photographs of conic sections and geometric figures and used them to create posters. Students used the data to solve problems and to write about two different situations where more than one logical conclusion could be drawn.

Grade Level: 9-12    Math Concepts and skills used: Decimals, Geometry, Measurement, Patterns, Percent, Whole Number Operations

The lesson incorporated several of them at the secondary and lower levels.

Maine Learning Results, secondary level:
B1: Use various techniques to approximate solutions, determine the reasonableness of answer, and justify the results.
F2: Derive and use formulas for area, surface area, and volume of many types of geometric figures.
G1: Create a graph to represent a real-life situation and draw inferences from it.
G2: Translate and solve a real-life problem using symbolic language.
G3: Model phenomena using a variety of functions.
H3. Formulate and solve equations and inequalities.
J1: Analyze situations where more than one logical conclusion can be drawn from data presented.

The Assignment:

APPLIED MATH
ORONO MATH TRAIL
ANALYSIS OF COLLECTED DATA

You will use the information that you collected on the Orono math trail in the following ways:

I. To write entries for the business directory
II. To complete a poster and make an oral presentation in class
III. To formulate solutions to the questions on the worksheet outside of class
IV. To solve problems in class during the time set aside for the final exam.

I. BUSINESS DIRECTORY:

1. After you have interviewed your business owner, make sure that the information on your questionnaire is correct. Look at the outline posted in the classroom and determine in which category your business would appear on the list. Prepare copy in the following format to enter into the computer:

Name of business
Address
Services offered that apply to students and parents
Business hours
Phone number
Other important information

2. Type your information on the computer in room 85 and save it under your name in the folder entitled business directory.

II. POSTER:

1. You are to create a poster displaying some of the geometric shapes and conic sections that you observed on the Orono math trail. You should include the pictures that you took. You may also include other drawings or pictures. The information should tell the viewer the name of the figure, where the figure was located, and any other information that would help the viewer learn more about the figures. Your poster should be attractive and get the viewer's attention.
2. There should be written information to accompany your pictures. You may want to type up the information and attach it to your poster.
3. In class you will make an oral presentation describing your poster and the information on it.

III. WORKSHEET:

1. While you were on the Orono math trail, you made not of a vacant business property in the downtown area. In one or more paragraphs, describe a business or service that you feel should be housed in that property. In your description include the reason why you feel this business or service would make downtown Orono a better place for students and adults.

While you were at The Store, you decided to invite some of your friends there for an end of the school year gathering and treat them to refreshments. You have some limitations.

a. The number of friends that you invite is equal to the total number of letters in your first and last names.
b. You may only treat them to cookies and / or carrot cake.
Use the information from your data sheets and your own plan to answer the following questions.

2. How many people are you inviting to The Store? Include this number in your paragraph below.

3. Write a paragraph to explain what you are going to treat the people whom you invite. Include the names of the items and the amounts of each that you plan to buy for your guests. Do not forget to treat yourself. These items are taxable. You can assume that you are charging this to your math credit card.

4. Show the mathematics required to determine the total cost of all of the items purchased in #3 and circle the final answer.

5. Write an equation that relates the number of guests (g) to the total cost (c) of the items purchased.

6. On a sheet of graph paper, draw a graph to illustrate the relation between the number of guests and the total cost. On your graph, let the domain = (whole numbers less than or equal to 17). Attach your graph paper to your written work.

7. On your graph paper, write the name of the type of function your graph is.

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