Three years ago, a number-phobic girl in my class sighed with relief when I announced our upcoming geometry unit. “Geometry is math for artists,” she explained. Right then I decided to plan a unit that would be an artsy, hands-on exploration of the shapes inhabiting our world, not a vocab-heavy slog through rules and attributes. Here are some of my students’ favorite geometry activities, with even more geometry ideas coming next week.
Why spend time talking at my students when they pay so much more attention to on-screen animations? To kick off a symmetry lesson with some direct instruction, we work through Scholastic’s Lines of Symmetry Study Jam.
I loved perler beads as a child, and my students enjoyed using these "fuse" beads, too! Perler beads are small, plastic, tube-shaped beads that you place on a plastic peg board. After you've covered the peg board with a bead design, you iron the beads under a sheet of parchment paper and the beads melt together to form a solid plastic shape.
I challenged my students to create symmetrical designs using their perler beads. After I carefully ironed their bead designs, far from their fingers, of course, we threaded the shape ornaments with yarn and created a hanging symmetry display in front of the classroom windows.
Oh, pattern blocks, how I love thee! These small wooden shapes are my favorite math manipulatives. They're useful for everything from multiplication arrays to equivalent fractions. My students love building with pattern blocks while exploring a wide range of geometry concepts.
When first introducing pattern blocks with your students, make sure to leave plenty of time for open exploration with the blocks. I find my students need a full period of free exploring before they are ready to get down to my business. This exploration period isn't wasted, though — while working in small groups, my students naturally practice naming the shapes, discussing the attributes, and testing how the pieces fit together, building an intuitive understanding of angles.
Once my students understand symmetry, they enjoy creating complex pattern block designs. I give them little hand mirrors to test the symmetry. I also ask them to solve symmetrical puzzles such as these from Mathwire.com. Once a student has created a symmetrical design, another student is invited to "draw" the lines of symmetry with pieces of yarn.
Some students prefer to make symmetrical cities and buildings with their pattern blocks. I try to leave room for the students to "play" while engaging with these math concepts.
For a cross-curricular connection, my students invent their own symmetrical creatures and then write creative descriptions about their creatures.
Three dimensions are all the rage at the movie theaters — and can become the highlight of your geometry unit as well! To prepare for the first exploration, you’ll need a collection of geometric solids. You can use a set of wooden or plastic solids, or you can collect items in the shapes you need. (Cans for cylinders, small boxes for rectangular prisms, and so on.) I’ve also asked my students to bring in objects from home to build our geometric solid collection.
As with the pattern blocks, I give my students time to explore their geometric solids before we begin categorizing the solids based on their attributes. Then we set up eight stations around the classroom for our eight categories of solids. For example, at one station I put a group of three to four triangular prism blocks. The students rotate through the stations in groups, filling out this chart. Then we meet as a class and chart their observations about the faces, vertices, and edges for the solids they explored.
My students were understandably confused about whether the rims of a cylinder count as edges. After some research, we decided that an edge must be where two faces meet. The curved surfaces of a cylinder meant that it didn't have any edges by our definition.
Students need experiences constructing geometric solids using "nets," two-dimensional outlines that fold into 3-D solids. Constructing solids from nets is also a fun way to review the shapes of the faces of the solids.
You can find many printable polyhedra nets online; I particularly like the nets on this Web site. For an even greater challenge, check out this NCTM lesson that asks students to create their own nets for cubes. After my students folded their geometric solids, they hung them from wire hangers using yarn to create mobiles.
By the way, if you're puzzled about geometric solids versus polyhedra, not to worry. The faces for a polyhedron are all polygons — no curves allowed. The faces for a geometric solid do not need to be polygons, so spheres, cones, and cylinders all count as solids, but not as polyhedra.
With a few bags of gumdrops and boxes of toothpicks, you can plan several lessons about polyhedra, (curved surfaces need not apply). Begin by inviting your students to compare polyhedra structures built with square faces versus triangular faces. Which structures feel stronger? Hopefully, the students begin to naturally understand the value of using triangles in their construction designs. Here is my worksheet for our first gumdrop construction activity.
Next, I challenge my students to apply what they learned about building strong polyhedra structures to building bridges using 30 gumdrops. I give the students five minutes to discuss their plans with their group members, and then they have 25 minutes to build their bridges.
We test their bridges using a stack of same-sized hardcover books. (The books evenly distribute the weight, giving their bridges more of a fighting chance.) The students boisterously count the books as I dramatically layer them on top of the bridge one by one. I quickly pull the books off when the bridge is on the verge of collapsing, sparing the bridge — and my students' sensitive feelings.
Do you have favorite geometry lesson ideas to share with us? Write about your ideas for hands-on geometry explorations in the comments section below. And stay tuned next week for even more geometry fun as I share my lesson ideas for 2-D geometry.