Interior Angles Discovery Exploration

A whole-group mathematical exploration into the geometric concepts of triangles, quadrilaterals, interior angles, and sums of interior angles. The discovery lesson in this product operates under one premise: that math is not simply a set of rules learners are assimilated to follow but rather an intricate and infinite world of possibility that they can be guided to interpret on their own. Set aside your understandings about how math is supposed to be taught, learned and structured, and open your mind to a whole different kind of math lesson. One where discovery is the goal and the learners are fully responsible for it.

WHAT’S INCLUDED

This resource contains:
-> A 3-task lesson which allows learners to discover ideas about the properties of triangles, quadrilaterals and polygons as well as their interior angles
-> A detailed breakdown of what happens in each task based on what becomes the student’s responsibility and what is left for the teacher to manage
-> Possible discoveries that learners can make along with key transferable ideas they’ll use throughout their future geometry explorations
-> Plenty of possibility for extension, deeper discussion or lesson ideas

STORY

I’ve spent many years reading through textbooks and adapting the content to fit the learners I had sitting in my classroom. The rigid structure the most textbook lessons would often frustrate me as the beautiful and interconnected world of mathematics was boiled down to minute facts to be memorized, repeated and regurgitated in a specific standards-defined order. Over time, I’ve realized that a more authentic learning experience centers around learners exploring mathematical phenomenon and discovering the deeper truths for themselves. And that got me thinking, could an entire curriculum be crafted around this idea that the content could be discovered rather than memorized? And thus, our journey toward REdiscovering mathematics was born.

IMPLEMENTATION

This resource provides a three-task lesson with two extra pages of teacher information for implementing an organic, collaborative, exploratory lesson in geometry. As such, there are many possibilities for implementation. The tasks should be explored in the order they are given, but should not be pushed to be completed in a single sitting. Allowing learners time to make theories about the mathematics is key to the success of the lesson.

POSSIBLE EXTENSIONS

While this lesson does not cover all ideas specifically related to triangles, quadrilaterals or angles, it does give a great jumping off point and is suggested as the start of any inquiry into geometry at this level. Supplement this discovery lesson with problems and other ideas from your school’s curriculum.

MATERIALS/PREREQUISITES

Besides this resource, you may require:
-> Plenty of time and space to explore these ideas
-> Computer and Internet access