Recyled Definitions

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Students will be able to apply geometry vocabulary to solve problems and test the quality of a proposed definition by looking for counterexamples.

Big Idea

Given a set of definitions, students will try to find counterexamples while applying their understanding of basic geometry vocabulary, particularly types of angles.

Warm-Up and Discussion

20 minutes

Since I do this lesson near the beginning of the year, I find it helpful to continue with some Algebra 1 review.  Either of these Warm-Ups will provide students with opportunities to keep up their Algebra skills in a Geometry classroom.

Homework Review

15 minutes

For this homework review, it is particularly important to set some community norms for how to agree and disagree with each other respectfully because students may have very different ideas about the previous night's homework.  Posting sentence frames like, "I agree with ____________ but would also like to add ________" or "I disagree with __________; while I think he/she is onto something about _________, I think _______________" can really help students to have a rich discussion where multiple views are respected.

Recycled Definitions

30 minutes

In Recycled Definitions, students will decide whether the given definitions are "good"--that is, the definition is correct and no counterexample can be drawn that matches the word but does not show the term itself.  If the definitions are not good, students should provide a counterexample to the proposed definition, as well as improve the given definition.

Students should work individually to get a sense of which vocabulary terms they find easier or more challenging.  After circulating the room for about 10 minutes, I ask students to work with a partner to compare answers, then have them compare with their entire group.  The ultimate goal is for the group to come to consensus and to be able to justify how they know, which develops the kind of thinking students need when writing proofs, where they always need to justify their statements with reasons.

After students have had enough time to work, I facilitate a Whole Class Discussion, having student volunteers share out their answers and agreeing/disagreeing respectfully if needed.