Reflection: Transitions Discovering Triangle Congruence Shortcuts - Section 3: Debrief/Notes: Triangle Congruence Shortcuts


In the past, I have debriefed this investigation by passing out note takers to students, asking questions about what kinds of observations and conjectures students had made, and facilitating a whole-class discussion about the key ideas of the investigation—in this case, which constructions produced one distinct triangle and which did not.  This discussion can be a bit dissatisfying in that there are times when it feels that I, the teacher, am the one who gives all the answers.

This year, I tried something slightly different.  I passed out the note takers to students after they had finished the investigation with their partner and asked them to try to summarize their thinking on the notetaker.  This is a shift from what I have done in the past, and a good one, I think.  By giving students six pairs of triangles that show all six of the triangle shortcuts, I enabled my students to critically examine the triangles’ given information (to distinguish SAS from SSA, for example) in order to formally record their conjectures.  Furthermore, in the case of ASA, for example, students had to draw on prior knowledge in order to make a decision about whether the shortcut guarantees triangle congruence (if two angles in one triangle are congruent to two angles in another, then the third angles are congruent, thus allowing students to rely on their understanding of AAS as a congruence shortcut).  

The idea of giving students time to think, do some sense making, and make some connections BEFORE facilitating a whole-class debrief discussion is not new.  However, this small decision reminded me that even the smallest decisions (giving students more think time) can increase cognitive demand and encourage higher order thinking as students construct viable arguments and critique their partner’s reasoning.  

  Thoughts on How to Jump into the Debrief
  Transitions: Thoughts on How to Jump into the Debrief
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Discovering Triangle Congruence Shortcuts

Unit 7: Discovering and Proving Triangle Properties
Lesson 4 of 10

Objective: Students will be able to conjecture about the sets of three sides and angles that will guarantee triangle congruence.

Big Idea: Through construction, students will work in pairs to test "shortcuts" to use when proving triangles congruent.

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17 teachers like this lesson
Math, Geometry, Triangles, reasoning and proof, Triangle Congruence, triangle similarity
  60 minutes
warm up
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