Polygon is a Shape That is Really Big

I am trying to de-unitize my grade 5 math curriculum this year. As we are reviewing subtraction, looking at visual patterns and exploring arrays, we also work on building vocabulary and precision in describing and classifying shapes. We started with a Which One Does Not Belong? board which is the permanent setup now in our hallway with regularly changing prompts.

wodb

Rope Polygons: Body-Scale Exploration

Last Friday, I decided to implement a Rope Polygons lesson from Whole-Body Math Lessons developed by Malke Rosenfeld. I was hoping that my students will have an opportunity to refine their understanding and to develop their vocabulary by working collaboratively; communicating with each other should create a need for more precision and justifications. Malke shared a very detailed lesson plan here.

After students investigated the ropes and noticed the knots, I asked them to create as many regular polygons as they could. Eventually, all the groups started using the knots and created squares, triangles, hexagons. I moved some students holding the vertices of a square apart, and they informed me that it is not a regular shape anymore but struggled to explain why. A few mentioned angles.

After half an hour of building, I asked my students to reflect on the activity. What strategies did they use? What helped them to be successful? What were the challenges? And how would they explain what regular polygon is to someone who doesn’t know? Give me the definition.

Definitions: Polygons Are Big

Here are the (non-exhaustive) list of definitions I was surprised to read after school.

A regular polygon is a shape that has edges.

A regular polygon is even.

A regular polygon is the shape whose angles are the same.

A regular polygon is straight line and symmetrical.

A regular polygon is like a square or triangle.

A regular polygon is the shape that has same perimeter and area.

Polygon is the shape with parallel lines.

Regular polygons have the same angles.

Polygon is the shape that is really big.

Students described all the properties that they noticed while building regular polygons with the rope, including the size. How do I zoom in on the defining ones?

Attack and Counter-Attack: Refining the Definition

I got the idea from the blog post Attacks and Counterattacks in Geometry by Sam Shah. There are still a lot of ideas in this post that I would like to try this year, like finding counterattacks for the altered textbook definitions. I made it into a whole class activity with students working on the small whiteboards.

We started with this example: “A circle is a shape that has curves. Counterattack! Draw a shape that fits this description, has curves, but is NOT a circle.”

counter7

Then we moved on to regular polygons. Here are some counter-attacks.

counter6
“Polygon is a shape that is really big.”
counter8
“A regular polygon has edges.”
counter5
“A regular polygon is even.” This caused some confusion and I asked students to interpret this to the best of their abilities.
counter4
“A regular polygon is like a square or triangle.”
counter1
“A regular polygon is straight line and symmetrical.”
counter3
“A regular polygon has parallel sides.”

We made a list of properties on the board. After each counterattack we had a discussion if this property applies to all regular polygons and if it is essential. I think I overdid it a bit with circling and crossing, so I pretty much had the definition on the board by the time I asked my students to go back and to revise theirs.

definition

Thoughts: What’s Next?

Something that naturally appeared in the discussion was “Never, Sometimes, Always” format. Regular polygons never have curves, sometimes are big and always have edges of equal length. I might pull a few statements for Talking Points (I learned about Talking Points here).  I’ve been thinking about Van Hiele levels. How do I support my students in moving from the shapes as objects of investigation to the properties of shapes?

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I live on Hepta-Shape street

There has been a lot of conversations about disciplinary literacy in recent months in my  professional learning circles. The intent is sometimes going in strange directions in math class towards keywords in word problems and being “ok with writing just to write”.  The whole “incorporating reading and writing into the math class” treats the matter as if reading and writing skills are somehow not intrinsic to math and have to be dragged in forcefully.

There is a lot of reading, writing, questioning, inquiring and thinking critically that absolutely has to happen in a math class for students to learn math in a meaningful way. And I also think that often math topics can lead into some great creative writing, art and discoveries across the disciplines. This post is about the latter.

I have blogged extensively about my geometry lessons this year (here and here). I am working with an amazing teaching partner this year, who is taking care of the language arts teaching part of our fifty students’ community. Working with Megan allowed me to regularly cross the imaginary boarders between the subjects without any teachers being hurt in the process. She developed and implemented the writing/reading part of this polygons project.

Polygons Pen Pals

Students have been exploring, classifying and creating their own polygons from tangrams. I noticed some started drawing eyes and hands, and that’s how the project was born. After identifying the properties of their polygons, students gave them names and considered their personalities and life stories.They wrote letters to their unknown polygon pen pals, and next week we hope to exchange the letters and to write responses. I will leave the rest of this post to my students’ work.

SKITTLES

Poly10
I’m Skittles Decagon. I have 10 soft/fluffy/straight edges, 10 pointy sharp vertices like a sword that’s sharpened. My hobbies are catching mice for dinner and breakfast, reading cat history books and I play catopoly on Monday and Wednesday. What are your hobbies?

LARRY’S SWORD

Poly11
I am a polygon from the dragon slayer realm and I used 7 stones/tangrams to build myself. My favorite food is poutine because the fries are mushy, soft and salty. My favorite drink is Mountain Dew because it is sweet and fizzy like Coca Cola and ice tea at the same time.

LARRY

Poly12
Hello, my name is Larry Decagon from Royal Arena. I am infinity years old because my mom, the Witch, revives me from death every 50 seconds. I am dying all the time because I am always fighting in the royal arena.

SHIRO

Poly5
Hello, my name is Shiro Pentagon. I look like a regular quadrilateral with a triangle on top.  I like cats, every candy, a game called ROBLOX, acrylic art, writing with different fonts, friends, traveling and dancing. I also have a cat named Kanto. He enjoys getting dressed up in tiny handmade outfits!

LARRYO

poly3
I am a hexagon with 6 pointy vertices and 6 straight edges. I look like a heart. Some likes that I have are toys like hex bugs, sports like soccer, activities that are outside and movies that are comedy. What likes do you have? I wonder will the earth come to an end.

BOB

Poly2
I’m not a normal shape because I am concaved. I don’t like annoying people because it distracts me. I like doing experiments, building structures and shapes. I won the science contest last year at my school. When I’m bored, I read a book.

LINDSAY

Poly9
I live in a farm in the middle of Japan. I am a triangle. What I like about Japan are the Cherry blossom trees. I am a convex shape and I have one right angle. I am also a 2D shape which means I have one face.

CENAMAN

Poly8
I like parties and I am always wearing a hat. I’m clever, agile and creative. I don’t like loud people at all. Do you like loud people? Some people call me a monster because I have a big mouth and sharp jagged teeth.

QUAD QUADRILATERAL

Poly1
I am a convex shape because I have no edges that are inside. Are you convex or concave? I am a regular shape because all my edges are equal. I like resting during the winter because it is nice and cooling and moving during the summer when there aren’t many obstacles. Autumn and spring are usually equal because the temperatures are very similar.

KASEY

Poly6
By the way, what do you want to be when you grow up? I know what I want to be. I want to be a shape nurse. Because you can heal a lot of shapes and polygons. I like meeting new people. I also like going to the library and school.

Thoughts and Questions

I know that students enjoyed giving “life” and stories to their polygons.  I admit my worries that it might have been a superficial connection. There was no mathematical need for written communication and there are still many questions that I wonder about.

Did moving towards creative writing still support my students’ mathematical thinking in some way?

What is the value in putting mathematical objects and relationships into non-mathematical context?

Months later, my students keep bringing up our infinity art/writing/reading lessons; they keep asking mathematical questions and making mathematical connections. My students spent time thinking about dragons and favorite food of their polygons, but they were also very careful  making sure they identified their polygons’ “physical” features correctly. Mathematical context created motivation for creative writing which in turn created motivation for mathematical precision. Maybe we do need the whole range of experiences to make sense of the whole range of things and our literacies can be a bit more interdisciplinary.