Crossing The River With Dogs

So Tedd Herr and Ken Johnson's Crossing The River with Dogs from Key Curriculum Press is definitely one of my favorite math text books ever. I first learned about the book when I was still a student at Keene State where one of my methods classmates was using in a ninth grade class she was in. The book is designed for a problem solving course and I was lucky enough to be able to adopt it for use at John Stark. We don't (yet) have a problem solving course at ASB, but I still use the book whenever possible. The text has an enormous selection of well written problems adaptable for any math class. We have been studying mathematical induction in my Math HL class and so I decided to use the milk lovers problem from the text and extend it into an induction problem for my students.

Tree, Polly, Manas, and Sahil loved milk. They convinced their older brother, Ankit, who did all the shopping, to buy them each their own gallon of milk because they each liked it so much. They all put their names on their full gallons. It happened that on this day they were all really thirsty and each took ten drinks according to a different system. Tree started by drinking half of the milk in her container. Then she drank one-third of what was left. Then she drank one-fourth of what was left, then one-fifth, and so on. Polly started by drinking one-eleventh of her milk, then one-tenth of what was left, and so on. Manas started by drinking one-half of his milk, then two-thirds of what was left, then three fourths of what was left, then four-fifths, and so on. Sahil started by drinking one-half of his milk, then one-half of what was left, then one half of what was left, and so on.
To do: After each had taken ten drinks, how much milk remained in each container? Write a formula for the amount of milk left in each container after n drinks if they had continued drinking in the patterns originally indicated. Prove these formulas using induction or other methods. In what order do the 4 finish their milk? Discuss.

Here is the pages document this problem I created for my students. They are going to use it for a "practice" IA. 

Download Milk Lovers Pages '09 Files