Reflection: Shared Expectations Definition of Similarity and Similar Triangles - Section 2: Practice: Similar Polygons


Since my students have solved problems using proportional reasoning prior to entering this class, I didn’t want to re-teach skills I knew they would be able to bring back on their own.  Instead, I wanted to focus students’ attention on why and how they could solve similar polygons.

As students worked through this set of practice problems, I asked them to consider a pair of questions that would encourage metacognition, which I posted on the board using the document camera.  I posed two questions to them: why can I do this? (when they used a particular solving strategy) and how do I know I can compare these sides? (when they looked for pairs of corresponding sides). 

By giving students a frame for working through these problems, I hoped to encourage them to solve in multiple ways that would make sense to them so long as they could justify which sides were corresponding and why their problem solving method made sense.  As I circulated the room while students corrected their work, I could see them connecting their work to the approaches shown in the answer key, which allowed me to see how they made sense of solving polygons in multiple ways.

  A Frame for Working Through the Task
  Shared Expectations: A Frame for Working Through the Task
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Definition of Similarity and Similar Triangles

Unit 12: Triangle Similarity and Trigonometric Ratios
Lesson 1 of 11

Objective: SWBAT apply the definition of similarity to identify measurements in similar figures. SWBAT to argue that HL is a “similarity shortcut” for right triangles.

Big Idea: Students' prior knowledge of transformations and congruence helps them make connections as they learn to use similarity shortcuts.

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