I’m beginning to teach a dreaded geometry unit chock full of confusing vocabulary such as complementary, supplementary, adjacent, and vertical angles. This is often a difficult concept for students to wrap their minds around since it’s so different from their typical math.
Direct Instruction Is Okay, But…
Teaching each type of angle individually through direct instruction works decently until the students need to start combining angles to complete problems. Then we have to go back and clarify misunderstandings and inevitably, students become lost in the vocabulary memorization. Plus, it’s a bone-dry way of teaching what is essentially a puzzle.
This year, I’m going to use a new tactic: cooperative reasoning with a set of “clues.”
I put students into groups of four, carefully matching students to help promote success. This means considering abilities as well as personalities.
Then, I wrote the following “clues” on notecards, one set per group:
- All straight lines have a measure of 180°. If you cut a straight line into pieces, the pieces still add up to 180°.
- If you split a right angle into pieces, the pieces still add up to 90°.
- The angles of a triangle add up to 180°.
- Two angles that share only a vertex (and no sides) have the same measure. They look like they’re “across” from each other.
My goal is for students to understand the concept before introducing the mind-numbing vocabulary, so no one has even mentioned “supplementary” or “vertical” angles yet.
Use The Clues
26 delightful mathematical curiosities - simple enough for elementary students, yet rich with deep possibilities. Learn more...
I then give increasingly difficult problems for the groups to solve using their clues. I put these on the board and note the number of steps that are required. The group is expected to label each step with the clue they used, and they solve for the answer.
I then went around the room and gave tickets (our class currency) to groups that could successfully label the next step in the puzzle.
The catch: everyone must “own” their clue. That is, nobody can take all the clues and solve the whole puzzle. This is designed to ensure participation and cooperation.
By holding a potentially necessary key to the puzzle, each member of the group is vital. Even if they only read their clue over and over to the group, the have a stake in the process and the other students must include them in the discussion.
At least that’s the idea 🙂 So far, I’m pleased with their level of understanding. We’ll see how the homework comes back tomorrow!
Once students have become comfortable with using these clues, I will “name” the clues and formalize what they have learned through inquiry and induction.
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