Grade Level: 4, 5, 6

Subject(s):

• Mathematics/Measurement

Duration: 45-50 minutes

Description: After listening to the story, How Much is a Million? , students work in groups to determine the following: how long one million dollars would be laid out end to end and how tall a stack of one million pennies would be.

Goals:

1. Students will be able to estimate, investigate, and calculate answers to mathematical problems.
2. Students will be able to work cooperatively in groups.

1. Students will be able to measure objects using the metric and English systems.
2. Students will be able to convert and simplify measurements.
3. Students will be able to estimate the lengths of objects.
4. Students will be able to present and discuss their group's findings.

Materials:

• How Much is a Million? by David M. Schwartz
• overhead projector with transparencies of worksheets
• standard rulers with both the metric and English systems on them
• one-dollar bills
• rolls of pennies
• paper
• pencils
• Worksheets and Answer Key

Worksheets and Answer Key in .pdf format; requires free Adobe Acrobat Reader.

Click the icon to obtain the free Reader.

“Today’s lesson requires you to discover how big a million is. Materials will be provided for you. In groups, you will be estimating, investigating, and then calculating answers to questions. At the end of the lesson you will present your group's findings to the class."

Lesson Focus:
Divide students into small groups. “Within your groups, there is a recorder and a presenter. The recorder will write down any of the steps and computations that need to be made. The presenter will present the group's findings in the closure of the lesson. Everyone in the group must work on the problem-solving activity. As a group, you need to estimate an answer to the problem. After you have agreed upon a reasonable estimate, the group should then investigate and calculate the answer. On your desk you should find all of the materials needed for this lesson. On your desk you should find a problem worksheet that has the question you need to solve, a standard ruler for everyone in the group, a one-dollar bill, paper, and pencils. Each question requires that you use both systems of measurement. Use one system first and then use the other system next. I will be around to each group if you need me for anything. Now go ahead and get started." While the students are working in cooperative groups, walk around and monitor their progress. Be available to answer all questions and to give helpful “hints.” If a group finishes the first question, then students can try the second question (using pennies). The groups should work on one problem at a time, therefore eliminating any confusion among the group members.

[ Author's Note: If students were having difficulty, I would give hints on how to make the measuring easier. (Example: Students should measure the dollar bills lengthwise. Instead of measuring 1,000,000 bills, students could take the measurement of one bill and multiply it by 1,000,000.) While the students were measuring the pennies, I would give hints as to how to measure the pennies. (Example: A stack of 10 pennies multiplied by 100,000 would be more accurate than one penny multiplied by 1,000,000.)]

Closure:
Have each group present and discuss their findings to the problem-solving questions. The presenter is the person who starts the discussion. If further explanation is needed, all group members will be available for discussion. While the different groups are presenting their findings, ask the following questions:

• Were your estimates accurate to your actual calculations?
• Which system was easier to convert measurements? Why?
• Do you think your calculations are accurate? Why did other groups get similar but not the exact answer as your group? What could have caused this?
• What strategies did you use to solve this problem? Were there any other strategies thought of and not used? If so, why?

Assessment: Observe students while they are working in groups. Were students able to work cooperatively in groups? Did students use the materials properly and accurately? Were students able to present and discuss their findings? Collect students' worksheets to check for accuracy and completeness.