Illuminations: Amazing Profit

# Amazing Profit

 Students use equations to determine eBay profit on new technology. EBay is an online auction agency. For a limited time after a “new” product’s street release date, it is possible to track the profit that sellers make for auctioning them on eBay. Students use previous data of selling prices to derive a linear equation for the “closing bid price” on a product.

### Learning Objectives

 Students will: Determine a linear equation for selling price of and profit from “new” technology on eBay Interpret a graph of the constructed equations Analyze relationships and trends from multiple representations of data

### Materials

 Markers or colored pencils Rulers Amazing Profit Overhead Amazing Profit Activity Sheet

### Questions for Students

 Can you think of a situation where there might be a positive slope for profit on items selling on eBay? What other kinds of items might sell for high prices in the future? How fast do you think the lines of profit for other items would come down? Do you think the profit and closing bids will always have an approximately linear relationship?

### Assessment Options

1. Other products have faced similar phenomena on eBay. Complete the activity sheet with these data points:
 Day Mean Closing Bid on eBay Profit on a \$400 Xbox 360 0 \$2,000 4 \$1,600 7 \$1,300 12 \$800

 Day Mean Closing Bid on eBay Profit on a \$250 Wii 0 \$1,000 3 \$850 6 \$600 10 \$400

### Extensions

1. Use the data table below to draw a line of best fit. The students will find that the data does not precisely lie upon a single line, but there is a line that passes very closely to each of the data points. Discuss line of best fit and other types of regression.
 Day Mean Closing Bid on eBay Profit on a \$200 iPhone 0 \$1,280 2 \$1,160 5 \$1,100 9 \$900

### Teacher Reflection

 What do you see as the next steps for strengthening your students’ mastery with interpreting graphs? Were there any questions a majority of your students struggled with overall? in a certain class? Was students’ level of enthusiasm/involvement high or low? What types of products do you think could be used to spark greater enthusiasm in the future? Did you challenge the achievers? How? Was your lesson appropriately adapted for the diverse learner? Was your lesson developmentally appropriate? If not, what was inappropriate? What would you do to change it? How did your lesson address auditory learning styles? What were some of the ways that the students illustrated that they were actively engaged in the learning process? What worked with classroom behavior management? What didn't work? How would you change what didn’t work?

### NCTM Standards and Expectations

 Algebra 6-8Use graphs to analyze the nature of changes in quantities in linear relationships. Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules. Data Analysis & Probability 6-8Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit. Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.
 This lesson was prepared by Allan Sherwood as part of the Illuminations Summer Institute.

1 period

### Lessons

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