Students will translate a linear situation into a rule and examine the graph and table of that rule. The linear rule is attendance at an event as a function of cost of a ticket. When this rule is multiplied by the cost, a quadratic revenue function is obtained. Students will then generate a table and a graph for this function and use that representation to answer questions about the situation. A consensus for expenses can be reached (both fixed and variable) and a rule for profit (also quadratic) will be obtained and can be explored.

Recognize, use and learn about mathematics in contexts outside mathematics By applying their own knowledge outside the classroom and combining it with mathematics skills to analyze a real situation. Understand various types of patterns and functional relationships. By working with a situation involving many variables and observing that some relate in a linear pattern and others in a quadratic pattern.

Students should be able to use the distributive property to view the revenue and profit rules in several forms. Students should be able to look at tabled information and plot points on a coordinate system if technology is not used for the tables and graphs.

It is recommended that technology be encouraged during this activity so that students can concentrate on observations about the tables and graphs, and so they can concentrate and contribute to the development of the rules for attendance, revenue and profit. The order of activities might be: Large group discussion of the situation and development of the attendance rule. Individual exploration of the questions. Large group discussion of revenue and development of the rule. A discussion of why a quadratic rule makes sense in this situation should be conducted either before or after the students explore the questions. Individual exploration of the questions. Large group discussion which generates a consensus expense expression. Maybe something like $2000 fixed with maybe a clean-up fee of $.50 per person, generating a rule: c(3000-300c)-2000-.50c = -300c2-3000c-.50c-2000.

Completion of the activity, participation in discussion. Classroom observation and informal probes.

Situation and questions available on Web page

A technology that will graph and table a function rule is highly recommended for this activity. At least scientific calculators should be available to aid in generation of tables.