1. Mathematical Modeling Joanne Rossi Becker Dept. of Mathematics San José State University joanne.rossibecker@sjsu.edu

2. Mathematical Modeling in the CCSS-M

3. What does modeling mean? Read the handout from the CCSS-M Highlight 3 key short phrases or words that you think most convey the meaning of mathematical modeling Be prepared to share your choices with the whole group

4. What math modeling is not It is not modeling in the sense of, “I do; now you do.” It is not modeling in the sense of using manipulatives to represent mathematical concepts It is not modeling in the sense of a “model” being just a graph, equation, or function. Modeling is a process. It is not just starting with a real-world situation and solving a math problem; it is returning to the real-world situation and using the mathematics to inform our understanding of the world. It is not beginning with the mathematics and then moving to the real world; it is starting with the real world (concrete) and representing it with mathematics.

5. Two uses of Math Modeling Modeling as vehicle: an alternative setting in which students can learn mathematics Modeling as content: modeling itself is the content

6. A modeling example: Chain Letter Max has received this email: Dear Friend, do you want to get rich quickly? Just follow the instructions below carefully and you may never have to work again. 1. At the bottom of this email there are 8 names and addresses. 2. Send $5 to the name at the top of this list. 3. Delete that name and add your own name and address at the bottom of the list. 4. Send this email to 5 new friends.

7. Questions In groups consider the following questions. If the process goes as promised, how much money would Max receive? Discuss what might go wrong with the process. Suppose that 3 out of every 5 people throw away any chain letters they receive but the other 2 people participate. Then how much money would be sent to Max? How could you modify the chain letter to maximize the amount of money Max would receive? Develop a mathematical model (a formula) that shows how to calculate the money Max receives based on: The amount sent to the top name on the list The number of people on the list The number of people projected to respond positively to the email

8. Discussion Share results Discuss any assumptions made How did you use the mathematical modeling diagram in your work?