Mathematics

=**Mathematics **= =//"Slice and Dice" //=

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__Meets Common Core State Mathematics Standard: __

Geometry Draw construct, and describe geometrical figures and describe the relationships between them. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

__ Technology Needs: __ Computer – 1 per student Internet access to the following website from the National Library of Virtual Manipulatives at the University of Utah:  []

__Task Description with Technology Integration: __  First direct students to click on the link for “Platonic Solids” under the heading Geometry (Grades 6-8)

 to identify their characteristics and build vocabulary for describing them.

From this first link students will become familiar with Platonic solids, polyhedra whose faces are identical regular polygons. This virtual manipulative allows students to display, rotate, and resize the five Platonic solids. It also allows them to select vertices, edges, and faces, and observe them in colors different from the color of the figure.

This is a screen shot of a three dimensional dodecahedron with some of the faces, edges and vertices highlighted. Note that the application keeps track of how many features have been counted and how many features are still uncounted.

 Next, have students click on the link for “Platonic Solids – Slicing”



to discover the shapes and relationships between slices of Platonic solids. Using this tool, students are able to manipulate the angle, size and depth of the slice through any one of the five Platonic solids. Students could then capture screen shots of the slices and use vocabulary built with other links on the site to describe the slices using Microsoft Word. Their work will then be uploaded to the Glog created for Tech Day. Some examples are shown in screen shots below:





All geometry tool images retrieved from http://nlvm.usu.edu/en/nav/topic_t_3.html __

Supporting Research: __ In a study of sixth grade students pre and post test results showed that the use of geometry software in a unit involving measurement seems to accommodate different cognitive styles and enhances students’ learning. Some of the gains depend on the dominant learning style of the student; students with a high non-verbal IQ tend to score highest on assessments following instruction with geometry software. However, overall small gains were seen by all students.

A meta-analysis completed in 2003 by the U.S. Department of Education found that the use of technology in instruction produces small favorable improvements in learning over traditional instruction. While more research needs to be done, the conclusion of the study stated that the educational gains were higher than expected.

Pitta-Pantazi, D. & Christou, C. (2009) Educational Studies in Mathematics. 70(1). 5-26. doi 10.1007/s10649-008-9139-z

Waxman, H. C., Lin, M. & Michiko. G. M. (2003, December). A meta-analysis of the effectiveness of teaching and learning with technology on student outcomes. A report of the North Central Regional Educational Laboratory, published by Learning Point Associates. Retrieved from http://www.ncrel.org/tech/effects2/waxman.pdf

__<span style="color: #00ff00; font-family: 'Comic Sans MS',cursive; font-size: 16pt;">"Tried and True" or "New and Innovative?": __

I <span style="font-family: Arial,Helvetica,sans-serif; font-size: 144%;">nteractive geometry software has been around since the 1980’s. However, the applets and java-type programs to run them in a more interactive three-dimensional way have only developed within the last ten years. The availability of online drawing tools in the middle school mathematics <span style="font-family: Arial,Helvetica,sans-serif; font-size: 120%;"> classroom using sites such as the one in this lesson is about ten years old, so it is fairly “Tried and True” for the teacher who has the technology available and is willing to incorporate it into lessons.