INTRODUCTION TO THE PROBLEM TO BE INVESTIGATED
A fast food chain is offering a free hockey card with every order of fries (alone, or as part of a combo).
When you purchase fries, you will receive a card for a player on the hockey team. Of course, you will want to “Collect the whole set!” as the restaurant's commercials encourage you to do. We will investigate, with the use of a mathematical model, how many purchases it would take to “Collect the whole set!”
I absolutely love using this investigation/project with students, in large part because there is obviously no one correct answer to the question, "How many purchases are required to collect the whole set?"
I think it's very enriching for students to analyze the world in a "probabilistic" sense and not in terms of right or wrong. It encourages students to make *reasonable* conclusions, not simply find a correct answer.
This guided project is step-by-step, and likely needs very little intervention on the part of the teacher/homeschooling parent, but it's engaging for all ages and you might want to do it too! (Well, if you're like me and you love running simulations a bunch of times.)
After completing this investigation, students should really understand the concept of a mathematical model and running a simulation Furthermore, each time you run a simulation, you might get a different result, so simulations are best done multiple times and the different outcomes can be analyzed using measures of central tendency (mean, median, mode) to arrive at a "reasonable" prediction. So much of our modern information is based on such simulations that I think it's a very worthwhile activity for students, at any age.
This is a 6 page investigation, and includes the same 6 pages again with answers filled in.