## Who Wants To Carry a Million?

### Annette NixonSanta Rosa District Schools

#### Description

Students use cooperative learning, problem solving skills, and volume to find the dimensions of a box large enough to hold a million dollars.

#### Objectives

The student selects the appropriate operation to solve problems involving addition, subtraction, multiplication, and division of rational numbers, ratios, proportions, and percents, including the appropriate application of the algebraic order of operations.

The student adds, subtracts, multiplies, and divides whole numbers, decimals, and fractions, including mixed numbers, to solve real-world problems, using appropriate methods of computing, such as mental mathematics, paper and pencil, and calculator.

The student uses concrete and graphic models to derive formulas for finding perimeter, area, surface area, circumference, and volume of two- and three-dimensional shapes, including rectangular solids and cylinders.

The student understands and describes how the change of a figure in such dimensions as length, width, height, or radius affects its other measurements such as perimeter, area, surface area, and volume.

The student selects appropriate units of measurement and determines and applies significant digits in a real-world context. (Significant digits should relate to both instrument precision and to the least precise unit of measurement).

#### Materials

-Worksheet (attached) (one per group of each item below)
-\$1, \$5, or \$10 bill
-Scissors
-Tape measure
-Yarn or curling ribbon

#### Preparations

1. Copy worksheets, one per group.
2. Have students bring in a dollar bill (A copy works fine also, but you aren't supposed to copy money!)
3. Gather materials.
4. Divide class into groups of 2's,3's,or 4's.

#### Procedures

1. This activity is best done twice; once in class, in a group setting, and then again at home, using a different denomination, for a project grade. (See related lesson, Million Dollar Gift.)
2. Discuss with students how large a million dollars would be in ones. What about in other denominations? Is it reasonable for movies and TV to show large amounts of money in small briefcases? As a class, decide which denomination to use to find the size of a million dollars. Point out that this size is actually the volume of a million dollars.
3. Have the class brainstorm for ideas on how to proceed to find the volume of the money. Record suggestions on the overhead or board. The discussion should lead to the following topics:
-How many bills will it take ?
-What are the dimensions of one bill?
-Should be able to multiply the size of one bill by the number of needed bills to find the volume.
-One problem: The thickness of one bill is too small for an accurate measurement. Solution: Measure a stack of bills. Try to allow students to develop these ideas on their own, but direct them, if needed.
4. Allow the students time to work within their group, at this point, to determine the dimensions of a bill and to calculate the volume of the money.
5. Once all groups have found the volume of the million and compared volumes, they might see that there may be differences in answers. Discuss how this happened and if it is okay. (Variations in measurement.) Lead a group discussion to brainstorm for ideas on how to use the volume to find dimensions for a box to hold it. It is more difficult than it sounds.
6. The typical first suggestion will be to divide the volume by 3 to find the length, width, and volume. Try this for the class to disprove it. Depending on the level of the class, cube roots could be used, but for most middle school students, this may not be appropriate. Brainstorm for other ideas. If none arise, suggest the idea of fixing two of the dimensions and finding the third. Use a simple example to illustrate: If the volume needs to be 3000 cubic cm, let the length be 50 cm and the width be 60 cm. What would the height have to be? Ask for a volunteer with the answer and record the correct answer, but don't explain it yet. Try another, volume=3000 cubic cm, length=100cm, width=10 cm, height=? Hopefully students discover the method without explanation.
7. Allow students to focus within their group again and come up with dimensions for their boxes to match their volume.
8. Have students cut ribbon or yarn the length of each dimension. (Warning: If one dollar bills are used, students may need to cut their yarn in the hall, but it is impressive!)
9. Once each group has cut their dimensions, have them present their volume and yarn to the class, defending their reasonability.
10. As a wrap-up, discuss the variances between groups and how changing one dimension affects the others.

#### Assessments

Assess informally as students are working on activity, walking throughout class correcting errors, leading students who are stuck, and affirming good progress. Collect the group worksheet and check to be sure that students can explain how they found the volume and dimensions clearly and completely. Also check to be sure that all calculations are listed.

#### Extensions

The weight of a million dollars can be found in a similar fashion.

#### Attached Files

The group worksheet to be filled out as the exercise progresses.     File Extension: pdf