Using a Journal Article as a Professional Development Experience

**Measurement**

PDF

**Title: **Diving in Head First: Finding the Volume of Norris Lake

**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

- 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)

- Extend the discussion of calculating volume to using the depth features of the topographical maps.
- 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.

- 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?

- 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

**Using Geometer's Sketchpad:**

- 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**

- Edwards, M. T., & Reinhardt, J. A. (2007, February). Technology tips: Approximating irregular areas with Monte Carlo simulations.
*Mathematics Teacher*, *100*, 408-411.
- Hall, R. (2008, April). Activities for students: Get the most pop for your buck!
*Mathematics Teacher*, *101*, 609-613.
- Matthews, M. E., & Gross, G. (2008, December). Illuminating the mathematics of lamp shades.
*Mathematics Teacher*, *102*, 332-335.
- Mihaila, I., Barger, E. (2008, December). Area by dissection.
*Mathematics Teacher*, *102*, 350-355.
- Nowlin, D. (2007, January). Precision: The neglected part of the measurement standard.
*Mathematics Teacher*, *100*, 356-360.