Escape from the Tomb

• Lesson
9-12
1

Students are presented with a problem: two bowls are suspended from the ceiling by springs. One bowl is lower than the other. In one bowl, you can only place marbles; in the other bowl, you can only place bingo chips. How many items must be placed in each bowl so that the heights of the bowls are the same?

Before giving this activity to your students:

• Look through the Escape From the Tomb Activity Packet. Complete the packet in advance to familiarize yourself with the activity and questions.
• Assemble two bowls and springs, and attach them to something hanging from the ceiling in front of classroom. One bowl should be lower than the other. Measure the difference from the floor to the bottom of each bowl.
• When doing this activity with less mature students, you should assemble the bowl and spring and attach them to something hanging from the ceiling (like a light fixture) prior to the class period. That is, you may not wish to let all students assemble the bowls by themselves. Each team of three students will need two bowls.

If marbles or bingo chips are not available, these items can be substituted with any small object of uniform size and weight such as paper clips, beads, pennies, dry beans, popcorn kernels, and so forth. The only stipulation is that one item must be noticeably heavier than the other.

If your class consists of advance algebra students, only give them the first page of the activity packet, and allow them to figure out a way to solve the problem with their teams.

The class should be divided into teams of three students. Each student in the team should be assigned a job. One student is assigned the position as recorder. She will record the data from the experiments. The second student is assigned the position as measurer. He will accurately measure the distance from the bottom of the bowl to the floor (in centimeters). The third student is responsible for placing items gently into the bowl.

If bowls and springs are assembled and hung from the ceiling in advance, each team will only need a tape measure, three copies of the activity packet, a calculator, a bag of bingo chips, and a bag of marbles. If the bowls and springs are not assembled in advance, each team will also need two bowls, two springs, string and scissors.

Read the problem out loud to your students. Ask a student to describe the problem in his or her own words. (Note that to save paper, you can choose not to distribute the first page of the activity packet to students. Similarly, you can either not distribute the last page to students, or you can withhold the last page until the end of the lesson, when students need it.)

Explain to the students that you have two bowls set up in the front of the classroom. Tell them, "This set‑up represents the baskets in the Escape from the Tomb problem. After you have finished the activity sheet, I will give you one bit of information, and you will determine the number of items that must be placed in each bowl so that they will be at the same height."

While the students are actively gathering and recording information, circulate around the classroom. Randomly ask different teams to explain how they arrived at their responses. If you are not satisfied with their response, ask some probing questions, such as,

• How do the slope and y‑intercept relate to the problem situation?
• What is meant by "average displacement"?

Continue to question until you feel that they are making a connection. Visit each group at least once.

When ALL teams have completed Questions 1‑20, conduct a whole‑class discussion. Discuss questions such as:

• What was the purpose of this activity?
• What did you learn?
• Was it what you expected?
• Can you help Bart and Lisa solve their problem?

After the whole-class discussion, point to the two baskets that you have hanging in front of the room. Give students the difference in height between these two baskets, and tell them that they have only two minutes (just like in the Escape From the Tomb game) to figure out how many items should be placed in each basket. Allow students to begin working, and while they are working, give an index card to each team. At the end of two minutes, each team must write the names of their team members as well as their answer on the card. Then, the cards should be given to you. One by one, allow the teams to come to the front of the room to test their solutions. The team(s) with the most accurate answer can be given exact credit points or some other reward.

After the completion of the question about your baskets, read the last question on the activity packet in the Solving The Game section. Allow students to complete this question during the remainder of the period, or as homework.

Assessment Options

1. Have each team give a short presentation on how they solve the problem before they test their hypothesis using your baskets.
2. Use the Escape From the Tomb Activity Packet as a form of assessment.

Extensions

1. Change at least one of the items so that students have to solve the problem again, this time not using both bingo chips and marbles.
2. As students test their solutions, begin a discussion about human error and uncertainty. Talk about the fact that not all the individual objects weigh the same, or about how measuring the distance to the floor can attribute to calculation errors.

Questions for Students

Refer to the Instructional Plan.

Teacher Reflection

• Was students’ level of enthusiasm and involvement high or low? Explain why.
• Was the lesson appropriately adapted for the diverse learner?
• How did the students demonstrate understanding of the material presented?
• Did you find it necessary to make adjustments while teaching the lesson? If so, what adjustments, and were these adjustments effective?

Learning Objectives

Students will:
• Solve a system of linear equations.

NCTM Standards and Expectations

• Generalize patterns using explicitly defined and recursively defined functions.
• Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.
• Draw reasonable conclusions about a situation being modeled.