13 yrs teaching
Supplies: clay, fishing line, paper towel, handout
Article illustration constructed with Geometry Expression Program. http://www.geometryexpressions.com/
Grades 5-10
On the Cutting Edge of the Third Dimension
I was working through the practice state exam with my sophomore advanced math class, when I was surprised to find them all struggling with a question about cross-sections. I could not convince students of the answers because they could not visualize the 2-d shape within the 3-d image. So, I pulled out the clay. Students were begging to join me in making the 3-d figures. Knowing that our curriculum does not focus on 3-d geometry (other than for volume and surface area), I decided that not only would students enjoy a hands-on 3-d lesson, but they needed the content.
To facilitate the manipulative distribution, have all student pick up a piece a paper towel (about 1.5 feet long), a medium size ball of clay, and a piece of fishing line (about 1.5 feet long) as they arrive. Free is my favorite price from math manipulatives, so I borrowed, with no intentions of returning, a roll of paper towels from the custodians. Fishing line, especially the light-weight type, is a great price per foot. I also use fishing line to hang students created 2 and 3 dimensional shapes from my ceiling such as x,y,z coordinate graphs, or triangles dangled from the centroid (center of gravity). Clay can be ordered from catalogues, purchased from stores with toys, or make your own play dough using a recipes from the web. Students might prefer the homemade material as the ordered clay becomes soft only after students work with it for a number of minutes. Some recipes are even kid friendly so that students could make the manipulative for themselves. (Yeah! More math with measurements!)
I started the lesson by showing students how to form a cube. Roll a sphere. Place the sphere on the table-top and press gently on top of it to flatten to sides. The turn the ball of clay and flatten again until there are 6 sides. I showed students how to cut of a corner of the cube to form a triangle. Students they tried to cut the other cross sections from the clay. After discussing the first row on the table, I had student work independently (or with a couple neighbors if they so chose) on the other table rows. At the end of the class, we took a field-trip for hand washing. (Yes, I really did leave a sign on my door giving our destination and walked my high school class right down the hall to the bathroom. It was rather amusing to explain our instructional purpose to the staff members we passed along the way.)
I suggest using the lesson on a Friday, a day before a holiday break, or any other day when your students would enjoy an out-of-the-ordinary lesson.
Not only will students benefit from the use of these manipulatives during classroom instruction, but they would also benefit from using them during the state exam. Our schools testing coordinator checked with the state and we were informed that students may use clay and fishing line on the state exam. (The typed directions for testing administration allow the use of unlabeled 3-d figures and unlabeled fraction pieces to be available for student to use if they wish. These are similar manipulatives.)