BYTES IN A BOX

Leo Paveglio Barb Steinbrunner Rich Van Gilst Carolyn Wahl

Class: Pre-Algebra or General Math

Materials: Graph paper, rulers, scissors, manipulatives (boxes, paper objects, etc.)

Goals: The student will be able to stack boxes with minimal wasted space using concepts of area and volume. The student will write a work order with drawing for storing the largest number of computer systems per storage unit.

Time

Required: Two class periods with unfinished work assigned as homework.

Background: Students need to understand spatial relationships and be able to build scale models.

Setting: The school purchased computer equipment that cannot yet be installed. There is a need for storage. Students will determine the number of computer systems that can be stored in different size storage units.

Problem: Your school purchased computer equipment which needs to be stored until it can be installed. Your job is to determine the maximum number of computer systems (i.e., one CPU and one monitor) that fit in each of the given storage units. You must then write a work order for the custodial department explaining how they are to stack the computer systems in the storage units. (Be sure to explain in sentences AND diagrams.)

Storage Unit Sizes Height Width Length

Small Unit 240 cm x 150 cm x 300 cm

Large Unit 240 cm x 260 cm x 300 cm

Computer System Height Width Length

CPU 25 cm x 40 cm x 60 cm

Monitor 50 cm x 50 cm x 50 cm

Teacher Notes: Discuss the need for storage units with the students to familiarize them with the various situations for which this need arises. The type of door or access to the unit could also be discussed or left for the student to consider. The idea of stacking the components should be presented in order for students to see different orientations or layouts of stacks and/or layers. Each computer component has a Athis side up@ arrow printed on the box so students may not turn it on its sides or upside down. There is not necessarily one correct solution. Several different arrangements are possible and may have the same or different number of computer systems stored. The number of computer systems stored will also vary if students take the physical constraints into consideration.

This project may be done in groups or individually. There will be a written work order and a layout (floor and/or layer plans). The main emphasis for this project is communication. Since businesses require their workers to be able to write and read such orders and drawings without explanations, the written work order and layouts need to be self-explanatory. Suggestions for things to be included in the written, oral and reflection reports follow.

A detailed description of the approach(es) to the problem

Conclusion to include the work order and drawings

Oral: Work order and plans to be put on transparencies for class inspection.

Can the class interpret these plans without additional explanations?

Students will then field questions and explain the plans.

What could you have done to make a more efficient arrangement?

How feasible is your arrangement? (Do you have all the monitors on the bottom and hard to get at?)

Can computers be packed to the ceiling?

Can you pack computers in the top row by the door?

Is a walkway needed?

Sample Solution: Through many hours of effort, we arrived at 53 systems for the small unit and 92 systems for the large unit, without taking physical constraints such as doors, inability to pack to the ceiling, etc, into consideration. This was our best effort. We challenge you to find room for more!!

Evaluation: We suggest that this project be done in groups. However, we feel it would be valuable for the reflections to be done individually.

Extensions: The problem could be revised in the following ways:

Arrange the layout so systems may be removed individually with relative ease.

Include printers in the units to be stored. Reasonable dimensions for the printer are: 30 cm x 35 cm x 45 cm. Use a ratio of one printer to every four to ten computer systems.

Include a walkway in the storage unit.

BYTES IN A BOX

Prolem: Your school purchased computer equipment which needs to be stored until it can be installed. Your job is to determine the maximum number of computer systems (i.e., one CPU and one monitor) that fit in each of the given storage units. You must then write a work order for the custodial department explaining how they are to stack the computer systems in the storage units. (Be sure to explain in sentences AND diagrams.)

Storage Unit Sizes Height Width Length

Small Unit 240 cm x 150 cm x 300 cm

Large Unit 240 cm x 260 cm x 300 cm

Computer System Height Width Length

CPU 25 cm x 40 cm x 60 cm

Monitor 50 cm x 50 cm x 50 cm

Restrictions: A computer system consists of one CPU plus one monitor. Each component must be placed right side up.

Task: For each storage unit, create a work order that includes a packaging procedure written in sentences and illustrations or diagrams (layout, floor plan, etc.). Be prepared to present your arrangement to the class. The report should include your assumptions, method(s) and solution for each storage unit.

Funded in part by the National Science Foundation and Indiana University 1995