Polygon Puzzle

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Objective

Students will be able to use their knowledge of different polygons to solve a riddle in their reflection journals.

Big Idea

Students need to spend time comparing and creating with polygons in order to better visualize their attributes. This lesson engages them in visualizing the attribute of sides.

Warm Up

5 minutes

As the end our year, and unit, approaches, I have chosen to administer a journal entry.  I will use this entry to assess my students perseverance, knowledge, and communication skills.

To begin, I post the journal prompt. This one is from K-5 Math Teaching Resources. The prompt states:

"I found a bag of shapes, all of which were different and had 4, or more, sides. If there were a total of 16 sides, what shapes might be in the bag? Show as many different solutions as you can."

I help the students think of tools in the room that might help them solve the situation.  We have shape templates, posters, math reference books, and the knowledge that polygons just need to be closed, linear figures.

I ask the students to begin the task working independently.  Later, I plan to have the students work as a community to critique and revise their work.

Active Engagement

30 minutes

As the students work, I make it a point to circulate and just watch for a bit.  As the children have time to record more than one solution, I begin to ask questions to understand their thinking.  I am watching for understanding of the prompt, organized solution attempts, and an understanding of concept development.

As this student worked, I realize he did not understand the prompt's rule of all polygons being different. However, as he is an "English as a second language learner", and has to work on reading comprehension skills, my goal is to modify my expectations and find what he does know about the number of polygon sides.

As he works, I realize the arrangement he drew presents a situation that will not work. I decide to make this a class discussion and brainstorming situation.

The following clips show the class working through the dilemma of using a hexagon in their shape set.  You will hear me asking leading questions, but the students do all of the problem solving.

Sharing and Close

10 minutes

To close, I simply ask student to share their various strategies with each other.  In doing so, I watch for revisions, additions, and deletions altogether.

As partners, students are able to share their thinking and are eager, when a peer points out mistakes or ideas, to revise work and add more.  This is a simple, yet effective way to close a lesson and review the concept/skills taught.

However, it is not appropriate teacher technique to sit at a desk and observe this wonderful learning.  It is important to continue to circulate and listen, prompt, and quickly teach or reteach a skill or concept.  Left alone, students may develop misunderstandings or confusions.