To begin the lesson, read the clever book, The Greedy Triangle, by Marilyn Burns. The book is about a triangle that becomes unhappy with his attributes and how they determine his life's role. Therefore, he seeks a shapeshifter to help him by adding lines and angles, so he can become something different. In the end, he reverts back to a triangle, happy with his role in life.
This is such a fun book to work in the terms and meanings of attributes, lines, angles, various shape names, and vertices. Your students will also love predicting what each shapes' job in the world is and why they are just perfect for their role.
Prior to reading, you may want to pre-read and mark stopping places that make sense to ask the students to explain what they notice, what they predict, and how the shape might change. This visualization is important in the growth of their geometry skills. You will also want to begin using the correct terms for each attribute. Instead of line, use line segment. Instead of corner, it is now, and always, an angle. The points are vertices. This whole reading experience will help your students develop the ability to look for and make use of structure, which is Mathematical Practice 7.
Next, I work with the class to review the terms right, acute, and obtuse. They will need this review for the next activity. If your students are not aware of these terms yet, you may want to write them on the board with a drawing of each type. My students make the connection with acute as "a cute little angle".
Following the book, I put the students into groups of three. If I have to make groups of 4, then the fourth person becomes the "shapshifter" of the group.
Once the teams assemble in a workspace on the floor, I begin calling out challenges. They may be:
I also throw in a challenge, like,
After several minutes of fun, I give the students three straws and ask them to go to their seats. Now, I run through the same activity, but they must individually create the triangles.
Another activity, if you don't want to use straws, or have the room for students to lay all around the floor, is to give groups a long piece of string tied into a circle. The students then become the "vertices" and create large triangles.
All of these activities engage the students in modeling with math, making sense of problems and persevering in solving them. They also create an opportunity to critique the thinking of others, because moving around on the floor together to construct a triangle requires some debate on what to do!
To close the lesson, I simply ask different students to come up and complete a "challenge" in front of the class. I could then ask clarifying questions to prompt a class discussion.
This student explains his acute angles, while the second video shows my students explaining how she knew what a right triangle was.