I-MATH

Volume

The National Council of Teachers of Mathematics Standards for School Mathematics in geometry says: "Geometry and spatial sense are fundamental components of mathematics learning. They offer ways to interpret and reflect on our physical environment and can serve as tools for the study of other topics in mathematics and science.

Instructional programs from pre kindergarten through grade 12 should enable all students to analyze characteristics and properties of two- and three-dimensional geometric shapes. Additionally, students are expected to be able to use visualization, spatial reasoning, and geometric modeling to solve problems."

Students usually find 3-dimensional figures very intriguing, and they enjoy playing with models of 3D solids. There are some very exciting 3D models on the Zome System website. The Zome System is a clever construction toy designed for kids, and you can learn more about this visualization and model-making tool by clicking on the link below:

http://www.zometool.com/

Although students enjoy 3D models and pictures, many say that they "just can't draw 3d!" I just think that nobody has ever shown them how easy it is! As an online participant in a Math Forum a few summers ago, I indulged my interest in geometry and 3D drawing by creating the following web pages:

http://forum.swarthmore.edu/workshops/sum98/participants/sanders/

There are a number of student activities on this website, which will help your students to visualize and draw in 3 dimensions. I believe that students can understand volume and surface area much better if they can visualize and draw prisms, pyramids, cones and other 3-dimensional solids. I would suggest that you have your students read the above web pages, and print out the grids. They can then tape a piece of tracing paper over the grids and practice drawing their own 3D figures. The link below will take you to a worksheet my students do at the beginning of our study of geometric solids, in the volume and surface area chapter of our textbook.

3D Sketching Worksheet

Another activity that my students find enjoyable as well as a learning experience is one I call the "3D Scavenger Hunt". I send my students outside, in teams, to find and sketch objects that are approximations of the 3D solids we are studying. You will find a printable copy of this worksheet at the following link:

3D Scavenger Hunt Worksheet

The Math Forum is a fascinating website, formerly funded by a National Science Foundation grant. The Math Forum is, in my opinion, one of the very most valuable resources on the internet for mathematics students and teachers. Please take some time to explore the Math Forum, starting with their welcome page. Be sure to check out their Teachers' Place, Student Center, Ask Dr. Math, and the Problem of the Week:

http://www.mathforum.com/

Another interesting volume and surface area project that connects to "real life" is a package design project that my geometry students work on near the end of the school year. In this project, they design a package for an imaginary product (such as perfume, or sport shoes) and draw the pattern, build a model, and find the volume and surface area.

Packaging Project Worksheet

 

There are many, many sites on the internet that will give you and your students opportunities to explore 3-dimensional geometry. On the website below, click on the graphic in the center of the page (polyhedron) and you will see a beautiful graphic, that you can drag and it will move. This is an interactive website that your students will really enjoy:

http://mathworld.wolfram.com/

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