Intent

In this POW, students practice clear record keeping as an essential part of problem solving.

Mathematics

The most important mathematics addressed in this POW is the problem-solving process itself. First, students will have to try some initial guesses to get a sense of the structure of the problem situation. In a subsequent activity, they will consider a simpler version of the problem, thereby making explicit a powerful problem-solving strategy.

Progression

To help students simplify this large problem, a simpler version will be posed early in the next set of activities, in A Mini-POW About Mini-Camel.

Approximate Time

15 minutes for introduction

1 to 3 hours for activity (at home)

10 minutes to gauge progress

20 minutes for presentations

Classroom Organization

Individuals, followed by whole-class discussion and presentations

Doing the Activity

After students have read the activity aloud, model a specific case of Corey moving bananas. Mention that there are a variety of creative problem-solving strategies that might help students analyze Corey’s situation.

Note that the POW refers to a simpler version of the situation, A Mini-POW About Mini-Camel, a class activity that will help students solve the larger Corey Camel dilemma.

Discussing and Debriefing the Activity

Have at least three students present their work on the POW. Then ask whether anyone was able to get more bananas to market than any of the presenters; if so, discuss their solutions. (If fractional bananas and miles are allowed, the best Corey can do is to get 5331353313 size 12{"533" { { size 8{1} } over { size 8{3} } } } {} bananas to market. If fractions are not permitted, Corey can get 533 bananas to market.) If no one has come up with the maximum possible number, mention that there is a better answer without revealing what that answer is or how to get it.

Ask the class, How would you know when you have found the maximum possible number of bananas?

Finally, discuss the role that the mini-POW played in their work on the POW itself. Here are some questions that might help to focus the discussion.

Was the mini-POW helpful? If so, how?

Why was the mini-POW easier to solve than the POW itself (if it was)?

What is special about the numbers in both versions of the camel problem?

Could you make up another version (Super Camel?) that you could solve automatically from what you already know?

Use students’ comments to bring out the idea that insight into a hard problem might come by first looking at a simplified version of that problem.

Key Questions

Was anyone able to get more bananas to market?

How would you know when you have found the maximum possible number of bananas?

How did the mini-POW help with the POW?