Reflection: High Quality Task Angle Relationships Review and Focus on Justification - Section 1: Warm-Up


This warm-up features two problems, one with parallelogram ANUT, and the other with a pair of parallel lines that are intersected by two transversals such that there is an isosceles triangle and trapezoid has been created (students do not need to notice or know about properties of isosceles triangles and trapezoids to solve this problem).

I was glad that I encouraged the idea that there are multiple ways to solve throughout the warm-up discussion.  Because students sometimes feel discouraged when they don’t see a particular way to solve, I wanted to emphasize the idea of having multiple pathways to a solution to encourage students to pursue other paths when they face a dead end and to ultimately make connections between different approaches.

For example, some students noticed ANUT was a parallelogram because it was created by two distinct pairs parallel lines, while others felt they could extend sides to better see lines intersected by transversals.  I thought it was really important to point out that students do, in fact, have the power to extend lines to make an unfamiliar context look more manageable—this, after all, is how students look for and make use of structure, which is not always intuitive to students and is certainly an action that not all students feel empowered to take. 

A real-life analogy that I thought was quite helpful was to ask students to imagine walking from our classroom to the library.  My students could all think of the shortest path to get there, but they could also imagine several different courses that would still get them to the library (some might even be more scenic or interesting!).  This analogy also helped to set the tone for the Collective Proof, where students sometimes worried about whether they would be able to write their proofs in the most direct way possible—to ease their worries, I would simply say, “just find a way to get to the library.”  

  Reinforcing the Idea that There are Multiple Ways to Solve
  High Quality Task: Reinforcing the Idea that There are Multiple Ways to Solve
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Angle Relationships Review and Focus on Justification

Unit 4: Discovering and Proving Angle Relationships
Lesson 5 of 6

Objective: Students will be able to justify their reasoning about angle relationships.

Big Idea: By collaborating on the Collective Proof, students will bring individual pieces of reasoning to write their first lengthy proof.

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collective proof
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