 ## Iditarod: Statistics and Rates

Mathematics

### Objective

Students analyze statistical data and work with rates.

### Directions

Introduce the Exploration
Ask the students if they have ever heard of the Iditarod. Let them talk about it or tell them yourself that the Iditarod is a race of over 1,000 miles that mushers and their dogs run in Alaska. Tell them that they will learn about this race in this exploration, and they will have an opportunity to work with data from the race.
Activity 1: Prize Money
Have students use the website listed below to answer the following questions. How much more does the first place winner make than the last place winner? Express your answer in dollars, and then show the increase as a percentage. You may need to review with your students how to calculate the percentage increase.
Activity 2: The Red Lantern Musher
Have students find the most recent race that has data on the finishing time of the winner and the finishing time of the last place finisher, also known as the Red Lantern Musher. They should calculate their rates of travel in miles per day to the nearest hundredth. What is the difference in their rate of travel? You may need to review with students how to calculate a rate.
Activity 3: Winning Rates
Have students complete the following activities. You may need to review with your students how to calculate a rate. The equation should be in the form t = d / r (where t = time, d = distance, and r = rate).
Find the times of the winner in 1973 and the most recent winner. Calculate their rates of travel in miles per day to the nearest hundredth. What is the difference in their rate of travel?
Imagine that the most recent winner can always run his or her dogs at the same rates no matter what the distance. Write an equation that shows how to calculate the time to run a given distance.
Imagine that the most recent winner ran his or her dogs for a distance of 1,300 miles at the rate you calculated in Part A. Use the equation you wrote in Part B to calculate how much time it would take to go 1,300 miles.
Activity 4: A Sample of Mushers
Have students complete the following activities. You may need to review the topic of probability with your students. Help them understand that if their sample size was 10 and five out of the 10 mushers were between the ages of 40 and 49, then the probability of a musher being 40 to 49 in age is 5/10 or 1/2. Discuss the results with your students. If they came fairly close in the predictions they should feel successful in their ability to predict based on looking at a sample.
Look at the page that names the mushers. You are going to try to predict the age of a musher. First, you will look at the ages of many mushers. How many mushers and their ages do you think you should look at in order to make an accurate prediction? Once you decide how many mushers you need age information on (sample size), click on that number of mushers to collect the age data. Use the chart on the work sheet to assign probabilities various age categories.
Make a prediction on the ages of a randomly selected group of 10 mushers. Use the probabilities you created in Part A.
Select 10 mushers that you did not select in Part A. Collect the data on their ages. How accurate was the prediction you made in Part B?

### Resources

• copies of the activity sheet (see the link below)
• computer access