Information+for+Teacher


 * Summary**

Students will spend 3 class periods or 6 hours (not including time outside of the classroom) investigating a real real world problem. Specifically students will design a t-shirt logo, financial document and advertisement for a small business team (3 students).


 * Overarching Enduring Understandings for this Unit:**
 * Model real world situations using mathematics
 * Use problem solving skills to solve a real world problem


 * Topical Enduring Understandings for this Unit:**
 * Create equations to represent a real world problem
 * Use spreadsheets or tables to organize financial data
 * Perform computations with real numbers
 * Justify and support financial decisions using mathematics


 * Overarching Essential Questions for this Unit:**

How can mathematics be applied to a real world situation?


 * Topical Essential Questions for this Unit:**

How can equations be used to simplify mathematical operations needed in a real world situation?


 * NCTM Standards**

Represent and analyze mathematical situations and structures using algebraic symbols Compute fluently and make reasonable estimates Representations Problem Solving Reasoning and Proofs Communication Connections
 * use symbolic algebra to represent and explain mathematical relationships
 * judge the reasonableness of numerical computations and their results.
 * create and use representations to organize, record, and communicate mathematical ideas;
 * select, apply, and translate among mathematical representations to solve problems;
 * use representations to model and interpret physical, social, and mathematical phenomena.
 * build new mathematical knowledge through problem solving;
 * solve problems that arise in mathematics and in other contexts;
 * apply and adapt a variety of appropriate strategies to solve problems;
 * monitor and reflect on the process of mathematical problem solving.
 * make and investigate mathematical conjectures;
 * develop and evaluate mathematical arguments and proofs;
 * select and use various types of reasoning and methods of proof.
 * organize and consolidate their mathematical thinking through communication;
 * communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
 * analyze and evaluate the mathematical thinking and strategies of others;
 * use the language of mathematics to express mathematical ideas precisely.
 * recognize and apply mathematics in contexts outside of mathematics.

Materials
Poster boards colored pencils, markers plain paper rulers, protractors, compasses (available for students to request) Computers (optional) Spreadsheet software, such as Microsoft Excel (optional) Advertising software, such as Microsoft Publisher (optional) Stencils (optional) calculators Sample presentation(s)

Modified Support Materials
For struggling students, providing them with blank tables to organize the data. Ask them to look up the following terms: revenue, expenses, profit and loss. Provide a Star graphic organizer for the brainstorming activities. Provide a Splash graphic organizer so that they can think about multiple representations of the data and how they connect to each other. This can help students build the bridge between the real and symbolic. Provide a list of explicit questions for each part that they can answer and then use to synthesis their results. Partner them with one or more students who are at a higher cognitive level. For deeply struggling students suggest they act out the scenario with a partner using monopoly or other paper money to complete the financial transactions. Have them discuss what happens when customers pay $10, $15 and $20 for their shirts using the paper money. Then have them discuss what happens when customers purchase 50, 100, 150, 200, 250 and 300 shirts. How is the amount of money customers pay related to the number of customers who purchase shirts?

For advanced students encourage them to complete as many of the optional activities as time allows. Specifically ask them to model their results graphically and compare the results to the other companies. According to the graph, under which circumstances is the company they chose the most profitable for their team? How many shirts do they need to sell if they want to sell them for only $10 each? For calculations, have them organize their math arguments as an algebraic proof. If they need practice, have them redo this for each of the ideal prices they would like to sell the shirts at. Alternatively have them look at the other representations and determine another method that could be used to select the circumstances under which the ideal price could be offered.

It is highly recommended that the teacher complete the activity before assigning it to the students to see what other areas their students might needs support in.