## Thursday, December 2, 2010

### Ticket Prices

The other night, Dawson and I were doing some math together and we ran across a problem that asked to interpret a scatterplot for the average movie ticket prices for the past 10 years. We poked around online until we found this image: http://www.the-numbers.com/market/We used the information to come up with an average price and dropped it into Excel and came up with a best fit line and all. Personally, I find Excel clunky, but since we could use it to quickly calculate average price, we went with it. But it just so happens that I'm doing linear relationships with my 7th graders, so I get a two-fer with this one. Step 1: Calculate average ticket prices and created a scatter plot. This went pretty quickly, but one group mistook the raw number for the average ticket price. For example: from 2003 to 2004 the revenue went down, but so did the number of tickets sold. The raw numbers led this group to believe that the prices went down. After a quick conversation, they realized that if the number of tickets sold decreases as well, the price can actually increase. Step 2: Predict the price of a ticket in 2020 and justify answer. Most groups used the trend of the graph to predict, but one group actually calculated the average rate of change from year to year and came up with \$.24/year. They used this to extrapolate a price in 2020. Step 3: Decide what type of curve best fits the data. Two camps on this one: Those who thought it was linear and those who thought it would be like "the graph we got when we did compound interest." Nice work kids. Note: We will explore that exponential thingy but we ran out of time today. Step 4: What line would best fit the data?They were creating a group graph so they took a meter stick and just plopped it down where they thought the line should go. Step 5: Estimate the equation of that line.We played with this applet yesterday, so students had a pretty good idea how to use the graph to predict what the equation should look like. I was pleasantly surprised at the fact that all groups decided the rate of change was somewhere between \$.22 and \$.25 and all said the initial condition was \$4.34. Step 6: Let GeoGebra work her magic. Add the ordered pairs and use the "Best Fit Line" tool to calculate the regression. Step 7: How good was our guess?