Sometimes, in education, we lose the art of exploration. Especially in the middle grades. The standards are so challenging, the class times so short, the demands so many that we deliver canned notes and a textbook assignment and move on.
But it could be so much more.
When kids learn by exploring and investigating, they come to understand the concepts naturally on their own. They're invested. They care. And they like it. Sure, you're thinking, "Really, Katie? My 8th graders can LIKE cross-sections of 3-D figures?"
I wager, if you try it, you'll eagerly ditch the lecture and never look back.
Here are some ways we've explored and investigated the properties of 3-D figures in my class. These activities cover properties of figures, nets, surface area, cross sections or slices, and views of models or figures. You can easily scale each up or down for your level.
Properties of Figures, Nets, and Surface Area with Magna-Tiles
Magna-Tiles (http://www.magnatiles.com) may be my favorite. I bought them for my youngest son one Christmas but routinely borrow them for class.
Divide students into small groups and give each 6 squares and 4 triangles.
Give them a couple minutes to just build with the blocks. Inevitably someone makes a shape and unfolds it into its net without me prompting. And the magnetic properties are just fun :)
Then have each group build a cube. Ask questions about the properties. "What shape is the base?" "What do we call each square of the cube?" "How many faces are there?" Etc. You've just taught or reviewed the vocabulary and properties of 3-D figures. And, GASP, without a textbook! Score!
Then have them unfold the cube into its net. I like to have them draw it on a small whiteboard and hold it up so we can compare. Were they the same? Similar? Can we make another net that still works? How many can we come up with? Can we tell how the faces must be arranged for it to work? Now you've upped the rigor by having them draw conclusions and allowed students with strong understanding to keep going.
And watch. Are they smiling? Talking on task? Willingly trying to do more? Extending their understanding without you prompting them? Woah.
Then repeat the process with triangular prisms and pyramids.
Wanna take it a step further? With each shape, while it's unfolded into its net, ask them how they could find the surface area. Give them a ruler and let them try. Can they find a more direct way?
You've now covered several standards without cracking a book. And they were actively invested and interested every step of the way. A great closer? Have each group make a set of notes for a figure based on their exploration and what they found important and then compile a class set. Discuss. Anything to add? You can assign homework to practice the skills independently as you see fit, but I bet they remember more of this than anything we lectured at them or they copied off the board.
Cross-Sections and Slices with Play-Doh
Ok, so the first time I did this, I learned something I didn't expect. Middle schoolers LOVE Play-Doh. Like, seriously. Even the uber-cool athlete boys. Even the boys who you know are doing drugs after school. No joke, they beg to take it home. It's a big deal.
Now, that said, I like to get something out of the way right up front. "Just so we all understand, this is Play-Doh. We're making shapes. Not human appendages. Especially not those typically covered by underpants. Understood?"
Trust me. It's a needed conversation.
Give each group one canister and let them play a minute.
Then give a task. Have them make a sphere. They can make one for the group or divvy the doh up among each member.
Then I give each group a plastic knife. I have a similar conversation about the knife. "This is a knife for cutting Play-Doh. Not people. Not materials. This is not Orange is the New Black. Understood?"
Have them slice their sphere in half. What shape is revealed?
Then issue a challenge. Can they slice the sphere with any single straight slice and get anything but a circle?
Repeat with other figures and slices. Most figures can be made by starting with a ball or snake and then smushing edges against the desk. Talk about slices parallel to the base vs perpendicular. What about diagonal cuts? Ask them how they would need to slice a figure to get a certain shape and let them try until they get it.
Again, you can have them generate notes or do an assignment as you see fit. But they just learned a LOT of content willingly and maybe even happily.
And little cups of Play-Doh would make great end-of-year gifts later :)
Views with Katie Kubes (or Other Connecting Blocks)
I bought a set of Katie Kubes (http://www.eaieducation.com/Product/520395/Advanced_3D_Cube_Models_Grades_6-8.aspx) from EAI one year and really like them. I use them just for this skill, but even then, they've been worth it since so many kids just can't visualize these kinds of problems on their own.
You could probably improvise this with other linking blocks.
I start by showing everyone an example. Many of them have no idea what it means to draw the "top view" of something. And the blueprint can be a bit challenging. Then I give each group an easy model and a blank or digital grid to draw the views on. Then I just let them keep going, advancing through the models as their skill allows. If they've REALLY got it, I give them a reverse model--they get the drawn views and build the block model from them.
Getting to see, turn, and manipulate the models really helps them visualize and understand what these kinds of problems are asking.
So, there are some ways we explore and investigate 3-D figures using hands-on materials. Every time, I hear things like, "Class is over already?" "That was fun!" "When can we do Play-Doh again?" This approach is definitely worth the risk. I have virtually no off-task behaviors when I do this because everyone, even my reluctant learners, are engaged and curious. They don't even know they're learning so much! If it's too out of your comfort zone, start with a one-shape, one-concept mini-activity (boy, that was a lot of hyphens...) and see how it goes. And share your ideas! How do you get students hands-on with upper-grades math concepts?