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## Diving in Head First: Finding the Volume of Norris Lake

Using a Journal Article as a Professional Development Experience

Measurement

Author:          Drew Foster

Journal:         Mathematics Teacher

Issue:            September 2008, Volume 102, Issue 2, pp. 90-97

Rationale/Suggestions for Use

This article provides mathematics teachers an opportunity to reflect on practice by exploring: How real-world problems can be used to enhance student learning and understanding of student learning.

• How physical and graphical representations can be connected in a lesson
• Connections across geometry, measurement, problem solving, and technology
• Connections among different subject areas – mathematics and geography
• Use of graphic imaging technology to analyze data

This activity may be used when working with pre-service teachers, or by in-service teachers interested in exploring ways to extend student's understanding of area and volume to a real-world situation.

Materials

• Copies of the article
• Copies of a local map with body of water (if possible – if not, use those referenced in the article)
• Copies of body of water partitioned for each groups
• Transparencies of centimeter grid paper to complete the problem
• Extension: The Geometer's Sketchpad or Image J Technology

Procedures/Questions

Goal: Participants will discuss strategies for finding surface area and volume of irregular shapes in the real world

Note: It is intended that participants not read the article beforehand

1. Lead a preliminary discussion on strategies to calculate the surface area and volume of irregular shapes.
Suggestions
• Have some slighty irregular basic shapes to display and discuss the strategies on finding their surface area and volume. (i.e., displacement, estimation, composition of basic shapes)
• Consider when to use surface area, volume and the differences in dimensional measurements (linear, area, volume)
2. Extend the discussion of calculating volume to using the depth features of the topographical maps.
3. Present the problem in the article; include a discussion of the real-world needs for knowing the volume of a body of water. If possible, use materials from a local body of water.
• Have materials ready for each group of participants to calculate the surface area and volume for their portion of the body of water.
• Have groups present their strategies for finding the surface area and volume.
4. Lead a discussion on the strategies used to solve for surface area and volume.
• Did all the strategies produce reasonable answers? How do you know?
• How were the strategies similar/different?
• Were some strategies more efficient than others?
• Were some more accurate than others?
5. Have participants read the entire article and discuss.
Sample questions:
• How are the strategies in the article like/unlike the strategies they used?
• What are some of the ways students might solve it?
• What misconceptions might they bring?

Next Steps/Extensions

Calculating Surface Area and Volume with Technology

• Import scanned copies of the maps into Geometer's Sketchpad and superimpose a rectangular grid.
• Have the participants calculate the surface area.
• Use the surface areas and the water depth features of the map to determine the volume for each section of the body of water.
• Have groups present their findings for surface area and volume.
• Calculate the surface area and volume for the entire body of water.

Using Image J:

• Reread the process outline in the article, pp. 93-97, for calculating area and volume.
• Calculate the area and volume for each section of the body of water.
• Have groups present their findings for surface area and volume.
• Calculate the surface area and volume for the entire body of water.

Discuss as a group how real-world problems and the use of technology might be used to extend and enhance students' understanding of area and volume.

Connections to Other NCTM Publications

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