3D Figures (and Algebra)
It is a rare lesson that connects the different strands of Mathematics in an academically significant way. I taught one of these lessons last week, and it was definitely a challenge, but it felt great.
For this lesson, students should already be able to use an equation to describe the rule they see in a table (G.E.T.S.). They should also know how to graph the data they see in a table. Students should know what faces, edges and vertices are. Students should know what a triangle, rectangle, pentagon and hexagon are.
Note: If you can do the activity where students construct prisms with pipe cleaners before they do this lesson, it is really useful (and fun).
Me: “Lately, we been counting the number of faces, edges and vertices of three dimensional shapes. Today, we’re going to see if we can notice a pattern in these properties for prisms. Then we’re going to show that pattern with a graph, equation and table. Then we’re going to use that pattern to answer questions.”
Teacher and students complete the table with (a) the name of each prism, (b) the number of sides of each base and (b) the total number of edges. It is particularly important to do two things as you go:
1. Clarify the difference between sides and edges early.
Sides and edges are not the same. When we say “sides,” we mean, “the sides of the base.” A hexagonal prism has six sides on its base. When we say “edges,” we mean, “all the edges of the figure.” A hexagonal prism has eighteen edges.
2. Emphasize your systematic approach to counting the edges.
For a triangular prism, we add 3+3+3 or multiply 3×3 because there are 3 edges on the first base, 3 edges on the body and 3 edges on the second base. We could also write 7+2 and get 9, but that’s not actually connected to the form we’re talking about.
Students will notice the pattern. Then the teacher works with students to write the pattern as an graph, equation and table. The table is already done. The graph is review. The equation is the important part because now students can use the equation to answer tricky questions. You can see that part here:
Part Three and Four
Students complete the same process for a sheet on faces (I let them do this in pairs). The teacher go overs the answers. Then students complete the same process for a sheet on edges (I have them do this on their own for a grade).