June 11, 2009

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In this lesson, students will identify key questions that they will need answers to in order to have the necessary information to plan their business. They will design an appropriate survey and administer this survey to other students at the school. Finally, they will compile the results into data sets in order to analyze them.

- Educational Technology > General
- Educational Technology > Integrating Technology into the Classroom
- Mathematics > General
- Mathematics > Problem Solving
- Mathematics > Statistics

- Grade 6
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This lesson will certainly take 3, if not more, 45-minute class periods. You can save time by requiring the students to administer the survey for homework, instead of using a class period for it.

**Group Size:** Small groups

**Learning Objectives:**

1. Students will identify the key elements of good survey questions.

2. Students will identify the essential aspects of statistics (gathering, analyzing, and presenting data).

3. Students will design and administer an appropriate survey to collect data pertaining to their business idea.

4. Students will analyze the data and gather it into meaningful sets to be used in linear regression analysis.

**Materials:**

Paper/pencil

Clipboards

Microsoft Excel on a classroom computer (if possible) or TI-82 or TI-83+ calculators (if available)

Graph paper

Handout of survey results (halfway through lesson)

**Procedures:**

At this point, students should have analyzed the costs associated with various potential products that they can offer for sale. You should lead a brief discussion in which the students debate the pros and cons of various products and select **one** to produce and sell for their business.

Once the class has selected their product, explain that they need more information in order to clarify their business plan. Have students brainstorm some of the information they will need in order to have a successful business. Such questions might include preferences (i.e. do you like flavored hot chocolate? marshmallows? etc.). They will also need to gain some idea of the demand curve for the product. If they do not arrive at this conclusion themselves, lead them to it. Essentially, the idea is that in order to set a price which will earn them the maximum amount of revenue, they need to know how many units of the product they can expect to sell at a given price. The easiest way to design a survey to test for this is to create a series of questions such as the following (using cookies as an example):

*1. How many cookies per week would you buy if they cost $0.25 per cookie?*

*2. How many cookies per week would you buy if they cost $0.50 per cookie?*

*3. How many cookies per week would you buy if they cost $0.75 per cookie?*

*4. How many cookies per week would you buy if they cost $1.00 per cookie?*

*5. How many cookies per week would you buy if they cost $1.25 per cookie?*

While this will not provide ideal data, if the respondents are honest enough, this should produce a relatively uniform linear curve with a negative slope. (That is, the number of cookies per week that they are willing to buy should go down as the price goes up.)

Come up with the "official list" of questions as a class and have students break up into student groups to write their survey questions. If time permits, have students proceed to survey other students in the school -- each group should get approximately 10 - 15 responses.

Once students have executed the survey, the class will need to compile the data together. The easiest way to do this is to have a pre-printed copy of the survey questions ready to distribute to the students before the discussion. Each group can compile their own results for each question, and then you can have each group report in their results on each question to the class. Compiling all the groups' results together for every question should give a good amount of data for the anaylsis.

*Extension Idea:* *It is possible to do a digression into statistics at this point, having students work with various questions and decide what form of graph, table, or report would best represent the data. *

*Collaboration Idea: I teach both Algebra I and Math 7 at my school. In the past, I have actually had the Math 7 class design and administer the survey and write a "consultant's report" for the Algebra class, because the statistical representations (bar graphs, pie graphs, etc.) fall squarely into the Math 7 curriculum and take time away from the Algebraic portion of the project. If possible, you could collaborate with other teachers to "outsource" this portion of the project.*

The most important data collected in the survey, as relates to the Algebra I curriculum and this project, is the regression data (see above). For this data, students should record responses as ordered pairs. The cost of the cookie should be the x- (or independent)- variable, and the number of cookies bought should be the y- (or dependent)- variable. Thus, each respondent's answer for each question generates a new ordered pair. For instance, on one survey, perhaps the responses went:

*1. 10 cookies at $0.25/cookie*

*2. 8 cookies at $0.50/cookie*

*3. 5 cookies at $0.75/ cookie*

*4. 3 cookies at $1/cookie*

*5. 0 cookies at $1.25/cookie*

*Then the associated ordered pairs would be (0.25, 10), (0.5, 8), (0.75, 5), (1, 3), (1.25, 0)*

The class will then generate a very large quantity of ordered pairs. This data can be entered into a simple Excel spreadsheet with one column being the price of the cookie and the other column being the number bought. There will be lots of duplicates, that does not affect the analysis.

If there are enough computers to allow for this, walk the class through the process of setting up this spreadsheet. You can also demonstrate the scatter-plot functionalities of the Excel program, showing how it will generate a scatter-plot automatically from the set of data. If computers are unavailable, the TI-82 and TI-83+ calculators also have a functionality that will generate scatter-plots. Use one or the other (if available) to help students see the general negative relationship of the two variables.

Finally, have students use their group's data (not the entire class's data) to create their own scatterplot on pencil and paper (they will use this tomorrow for their linear regression analysis). Have them pay particular attention to scale. When they are finished, have them check their work with their partners and with you and place the scatter-plot in their portfolio. If they have also generated a scatter plot with either the calculator or the Excel spreadsheet, have them save this information so that they can work with it during the next lesson.

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