Overview and Background

Overview & Background:
Students will get practice problem solving.

Objectives:
Students will use their problem solving skills. According to Susanna Epp, (author of Discrete Mathematics with Applications) solving these types of puzzles will help develop a sense for the flow of deductive reasoning students will use later in mathematical proofs of all types.

Epp, S. (1990). Discrete Mathematics with Applications. Belmont, California: Wadsworth Publishing Company. (1995) Discrete Mathematics with Applications, Second Edition. Boston, Massachusetts: PWS Publishing.

Skills Learned (Standards):
CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.

Audiences:
There is no math background required for this activity, so it can be used at any time, probably starting in middle school and up. One suggestion is to use this as a first day of school activity to get students back to thinking about math, but in a fun way.

Lesson Plan and Activity

Step 1

Explain the riddle. It says that a farmer goes to market and buys a fox, a goose, and a bag of beans. To get home the farmer has to cross a river in a boat that can only hold himself plus one other item. Left alone the fox would eat the goose and the goose would eat the bag of beans. The goal is to figure out how the farmer can get everything across safely.

Step 2

In groups of four ask students to solve this riddle. Students should be given the models to act out the situation as they try to solve the riddle. One solution is for the farmer to first take the goose to the other side. Next, he returns and brings the fox over. On the next return he brings the goose with him. Then he takes the bag of beans to the other side and returns. Finally he brings the goose back over.

Step 3

Once a group has a solution, ask them if there are other solutions. One variation is to switch the roles of the fox and the bag of beans.

Step 4

Have groups share their solution. Ask them why it is necessary for the goose to be brought over first. Essentially it works out this way because the goose can’t be left alone with either the fox or the beans.

Step 5

Show students this clip from The Simpsons where Homer goes to the store to get rat poison to deal with a rat infestation. He is driving Maggie and their dog, Santa’s Little Helper, home. Homer gets distracted, which causes the car to go off a bridge. Homer needs to cross a river. There is a boat but it can only carry two items at a time. Maggie can’t be left alone with the poison because she may swallow it. Santa’s Little Helper can’t be left alone with Maggie because he may bite her. Homer has to figure out how to get everyone safely across. The clip can be seen here https://www.youtube.com/watch?v=lX4T7KxmAwU. There is also a discussion of the problem in this video or you can just show the clip from the show.

Step 6

Have students figure out how this is equivalent to the previous riddle. To solve Homer’s riddle he first takes Maggie over to the other side. Then he returns and brings the poison over. He brings Maggie back to the other side and brings Santa’s Little Helper across. Finally, he returns and brings Maggie back over. In this version Maggie is equivalent to the goose, the poison is equivalent to the fox, and Santa’s Little Helper is equivalent to the bag of beans.

Duration of Lesson

This activity will take around 25 minutes.

Preparation

Students don’t need any background knowledge to do this activity.

Rubric and Assessment

This activity can be done without an assessment or can count for a participation grade.
Question (points)
Participation in solving the riddle (7)
Participation in presenting solution (3)
Total 10

A Fox, a Goose, and a Bag of Beans Logic Riddle