The Greedy Triangle

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The students will be able to recognize and draw polygon shapes from three sides and angles to ten sides and angles.

Big Idea

Integrating literature, writing and art into math makes it stick


This is one of my favorite lessons, okay one of many of my favorite lessons and was originally created by my teammate, Cathy Mooney.  But as good teachers, we always borrow ideas and lessons and tweak them for our own when we see good ones!

This lesson will integrate literature, writing, math and art in one final student created book - which goes into the students portfolio of work (summative assessment). It also supports the 5th grade Common Core Standards where students need to understand attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. 

In the story "The Greedy Triangle,"  the main character is dissatisfied with being a triangle, and asks a shape shifter to have one more side and one more angle.  He's not satisfied, and his journey continues from the three sided, three angled shape of the triangle all the way to a dodecagon, 12 sides and 12 angles. 

Literature, and this book in this case, gives me an excellent opportunity to support student conversations wherein they refine their mathematical communication skills, by using clear and precise mathematical language in their discussion (MP3). 

The book also leads to wonderful discussion about self-esteem and accepting who you are, a theme that we identify and discuss (5.RI.2 Determine a theme of a story from details in the text, including how characters in a story or drama respond to challenges). 

Inclusion - Engaging Students

3 minutes

I start all lessons with a "hook" to activate prior knowledge and link the upcoming math lesson to the students personally.  Today I ask my students to discuss for one minute,  

"What 2D regular shapes do you see around you?"

From the start of the year, I have set up how students should share in small groups.  They know they have a small window of time for everyone to share and that every student in the group must participate. This keeps them focused and using accountable talk.

One strategy they use is to go around the table with everyone quickly sharing, if a student isn't ready to share they can pass and the group will come back to them.  It's November, and we have moved this type of sharing from 3 minutes down to one minute.  Practice makes permanent, but not always perfect. 

While the students are sharing I suggest you walk around the room listening in, gaining insight into the students level of knowledge on the subject.  I do not participate in these inclusion discussions because if I do, I know my input will influence the group sharing. Once I enter their "space", the teacher has the influence or power, not the students. 

Exploring Through Literature - The Greedy Triangle

10 minutes

When I read the book The Greedy Triangle by Marilyn Burns, I have my students sit on the carpet up close to the Smartboard.  I put the book under my document camera so the students can see the pictures better than if I was holding the book up.  My challenge is my document camera is on my desk and I have to sit off to the side away from my students.  This can create a spot where I cannot see some students.   When I am able to see my students I can read their body language to tell if they are understanding and attentive listening. 

I like to sneak in some geography and mapping by telling the students they have to sit north of my set equator - an imaginary line in the classroom. For a story they sit north (actual compass north) of the closest desks and for a video they sit south of the equator. 

While I read the story, I am using it as math, so I guide students through questioning to recognize the pattern (1 more shape, 1 more side).  My goal is to create a framework where students begin to look for this repeated reasoning, and can express this understanding (MP8).  I draw this reasoning out through questioning early in the book...

What have you noticed?

What has changed?

What has stayed the same?

One more angle and one more side is being added. To clarify my students thinking I ask

How do you know this?

Can you predict what happens next? 


On page one I ask students about the setting of the story - because I want them to be thinking about possible settings for the story writing they will do later.  One student said the Golden Gate Bridge, another Paris. 

On the next page, I ask them to consider if the triangle's favorite thing about sharing gossip was a good thing.  A few heads shook no and a few whispered comments about "That's talking behind someones back." 

When we get to the page where the triangle has changed to a decagon and on and on, I point out that the triangle is trying to become something he is not - himself - and he is so different and strange to his friends they don't know how to be around him. The students in my class are 4th and 5th graders and this message resonates with theme because they are at the age where they are trying to exert their independence, but what their friends say and think about them is very important. 

When we finish the book, students are sent back to their seats to get out their math journals.


Math Journals

15 minutes

I list on the board, and the students copy in their journals, the sides and names of each shape.  Because we are all teaching literature every chance we get I tell my students a story about a former student I had who spoke Greek and how she pointed out to me the root words for each term is also part of the Greek word for that number.  I have the students underline the root words and I ask myself a question out loud - "I wonder if gon is an affix?" I have really worked hard to get students to go home and find answers to my out loud ponderings during class.  This year it has really taken hold - to the point parents are commenting about all the "extra" work their children want to do.  When I get a chance I write down my question - for me to remember - and ask students to bring it up in the next community circle or before the lesson. 

I also take the time to read portions of the parent and teacher notes at the end of the book while the students are copying the vocabulary.

As I mentioned at the beginning, I suggest having a few writing periods open for students to create their own books.  This is a great assessment to put into portfolios to show math vocabulary and standards in writing (W3,W4, W5).  One of my favorites is encouraging students to integrate science into the book - see the example of the Greedy Triangle in Space!  I've included a few different examples of student work to get you started.  

Wrapping It Up

This lesson is very powerful in helping students understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. All of the shapes are polygons but can be broken up into separate groups based on the number of sides.  This lesson also had every student looking at prefixes and root words and they still are 3 months later!