Intent

This last POW of the unit is a more complicated version of POW 11: Eight Bags of Gold.

Mathematics

In this variation of Eight Bags of Gold, not only are there more bags, but we do not know whether the counterfeit bag is lighter or heavier than the rest. Students will be able to find the counterfeit bag without too much difficulty if they are not limited to three weighings. When the weighings are limited, the problem becomes much more difficult. Very few students have been able to solve it with three weighings. Many teachers have been unable to do so as well.

Progression

Students will begin work on the POW now, with presentations scheduled for late in the unit.

Approximate Time

30 minutes for introduction

1 to 3 hours for activity (at home)

20 minutes for presentations

Classroom Organization

Individuals

Doing the Activity

Tell students that this is an extension of POW 11: Eight Bags of Gold but much more difficult. Have students read over the activity and then ask, How are Twelve Bags of Gold and Eight Bags of Gold similar? How are they different?

Then give students class time to begin exploring this significantly difficult problem.

Discussing and Debriefing the Activity

After the POW presentations, ask whether other students had different ways of approaching the problem or arrived at a different solution, and have them share their ideas.

If no one was able to solve the problem with only three weighings, acknowledge the difficulty of the problem and perhaps suggest that students keep working on it.

Ask, How was your work on POW 11: Eight Bags of Gold helpful (or might be helpful in the future, if you haven’t yet solved the problem)?