Project AMP Dr. Antonio Quesada – Director, Project AMP

LESSON LAB ABSTRACT

SUBJECT: Geometry

GRADE: 9, 10

STRAND: Geometry, Measurement, Data Analysis and Probability, Problem Solving, Communication

TOPIC: Maximizing product packaging cube on a shipping pallet

OBJECTIVES: The students will organize and consolidate their mathematical thinking through communication.

The students will analyze characteristics and properties of three-dimensional geometric shapes and discuss their relationships.

The students will use visualizations, reasoning, and geometric modeling to solve problems.

The students will communicate their mathematical thinking and strategy to others.

MATERIALS: Student worksheet (2 pages)

Graphing calculator

Tennis balls

String

Rulers (measuring in inches)

Multi-media tools (PowerPoint, ViewGraph with links, etc.)


LESSON LAB 1

MAXIMIZING CARTONS PER PALLET

Carla Gross (Cuyahoga Falls) & Brian Reeves (Cuyahoga Falls)

PROJECT AKRON WEB

June 15, 2000

CONCEPT / Perimeter, area, and volume of a sphere, cylinder, and rectangular prism can be determined by numerically interpreting data calculated from formulas.
(OPO, Mathematics: GR 9 - # 6, 8, 10, 11, 12; GR 12 - # 3, 5, 16)
LEARNING OBJECTIVES / The students will organize and consolidate their mathematical thinking through communication.
The students will analyze characteristics and properties of three-dimensional geometric shapes and discuss their relationships.
The students will use visualizations, reasoning, and geometric modeling to solve problems.
The students will communicate their mathematical thinking and strategy to others.
ASSUMED SKILLS / It is assumed that students doing this lab can calculate area and volume of spheres, cylinders, and rectangular prisms through the appropriate formulas.
PROJECT
TASKS / 1)  Each student will participate in small groups (pairs or triads) that promote real-world applications of area and volume.
2)  Students will measure a tennis ball and calculate the size of cylinder needed to package a maximum number of balls.
3)  Students will develop various alternatives on the size of the carton to package the balls given the dimensions of the pallet, which they will be loaded on.
4)  Students will use multi-media tools to present their group's findings.
5)  Students will discuss how to generalize the packaging decision-making process for any shaped product.
LEARNING STRATEGIES / This lesson is designed to be a 2 day or single block self-contained lesson with a student worksheet.
Worksheet steps #1 through #5 are to be completed during the first class period, and the remaining steps to be completed the next class period.
Students will require instruction in using the graphing calculator in developing the list of calculated values.
The teacher prompts and / or assists groups as requested or as needed.
The group roles of recorder, task master, and technician will be defined for the groups. Each group member will volunteer or be assigned a specific role.
The groups will elect a spokesperson to present the group findings to the entire class.
CLASSROOM /
INFORMATION
MANAGEMENT / Group presentation, class discussion, and concept generalization will follow cooperative group work.
Teacher will assume the role of facilitator to oversee progress and intervene when necessary.
Task master will get material and make sure all group members stay on-task.
Recorder will keep track of all results.
Technician will perform calculations.
ASSESSMENT / Students will complete a worksheet through various stages of their task.
Individual groups will receive feedback from their peers.
Each student will submit a personal reflection of his or her learning.
TOOLS &
RESOURCES / Student worksheet (2 pages)
Graphing calculator
Tennis balls
String
Rulers (measuring in inches)
Multi-media tools (PowerPoint, ViewGraph with links, etc.)
RESULT SHARING / Students will gain an understanding of how to apply perimeter, area, and volume in a real-world application. They will speculate and generalize their finding to apply to other novel product configurations.
Students will share their findings and mathematical rationale with the entire class.
Students will individually reflect on their learning and communicate in writing their thought process in solving this problem.