Going Round In Circles

Whenever I start talking about circles with my students, I use this little wager.

I get students to pick one of the three choices and work the room, looking for a brave student I know will deliver my nachos. I talk up the nachos (and the circumference) as much as possible. Anywhere from 90 to 100 percentage of students will say the circumference is shorter than the height of the water bottle. Let's see if I win nachos or I let my students go to lunch early.

Okay, so double or nothing? I don't bring in this glass, but I do use a taller cup with a really small circular base. Where do you stand on the double-or-nothing wage? Did I give you enough information to take the bet? With a glass like this, you should get at least one student to keep you honest and ask which circumference of the glass you'll be measuring.

This little wager (activity) allows me a quick introduction and fun application of circumference. Somewhere I'll discuss vocabulary and formulas with students while giving them a graphic organizer they can fill out.

I'll usually do an activity where students measure the circumference and diameter of objects in order to discover the relationship of Pi. Stuff very similar to Fawn's Friday Bubbles. Note to self, use Excel (or a spreadsheet) to keep track of those measurements. I've also explored Rolling Tires in the past. This year, I brought the wheel to the class for a small activity. A physical wheel. The wheel from my son's wheelbarrow.

The small activity was for students to guess how many rotations this wheel (8-inch diameter) would make from one wall of my class to the other wall. Students were able to see how circumference can take on the meaning of a tire rotation, hence the graphic I made above. It was sweet to see students roll the wheel across my 21-foot long room and actually get 10 rotations like the math predicted. If you have a wheel like this, bring it in and do this activity.

We also did these awesome lessons. And. I. Mean. AWESOME!
Pizza Pi by Mathalicious and
Penny Circles from Team Desmos and Dan Meyer.

There's so much to do with circles and so little time. 

Round and round,
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Fun With A Sticky

Earlier this year, I wrote about Fun With A Dot and A Line, a Math 6 lesson I loved because it had:

• A simple question/task.
• A competition.
• Student creativity.
• Students assessing the work of each other (accountability).
• Students defining the necessary vocabulary/rules.
• Students determining the necessary tools to help solve the task. 

As my 7^th graders approached surface area, I prepared a few activities in preparation for File Cabinet. Here is one of those activities. I give you Fun With A Sticky:

Launch:

Hand each student a 3” x 3” sticky as they enter. Post the following on the board:

Explore (creativity):

A few students might do something like this.

Give the class a hint or two (if they need it):

1. This can be done with four lines.
2. Think Tic-Tac-Toe

Here's what we're going for:

If a student is still clueless, encourage them to look around and see what their classmates are doing. As the teacher, keep your eyes peeled for students who are approaching this with some creativity. Sarah and Pricila used the straightedge of their binders to draw lines. Gerardo tried folding the sticky in thirds like this.  

Student accountability:

When done, have each student write their name on the back of the sticky. Have each group of 3-4 students decide who has the best 9 squares and bring that one sticky up to the teacher. In no particular order, place them under the document camera for all students to see. Without sharing, ask each student to quietly (mentally) pick the top 2 stickies they feel have the best 9 squares. 

Vocabulary/Rules:

Ask students for input. 

Me: "Without telling me which stickies you’ve picked, how are you determining which sticky has the best 9 squares?" 

Jesus: They drew straight lines.

Carla: They are perfect squares.

Have the class define a perfect square.

Carla: Each side is the same length

I now had students take their top 2 and pick their favorite one. Somehow get your students to vote; little sheets of scratch paper, SmartBoard Responders, iPads, etc. I labeled each sticky alphabetically to avoid “this” sticky and “that” sticky. I had each student stand up. I then said, "Sit down when I say the letter of your sticky with the best 9 squares."

Necessary Tools:

They narrowed it down to about 3 stickies and gave great rules for finding the best 9 squares.

Me: What tools can I use to make it even more precise?

Student: A ruler. 

Me: Ok. What do I measure and what am I looking for on these stickies?

Here’s where you get students to discuss (or discover) how each square should have a width of 1 inch and a length of 1 inch. In other words, you’re defining a square inch with your students. Okay, there will be some "squares" that are just garbage and can be eliminated by eyeballing them. However, here's where you get to be dramatic with your students. Get them worked up. Ask them which ones you should measure. Mess with them a little and joke with them how they're unable to determine the correct "squares". Have fun with it. Either way, make sure students see the squares being measured. If I had more time, I could have redistributed the stickies and passed out rulers for the students to measure each other's "squares". You can see from this picture that the winning sticky note had a total of 3 "perfect squares."

Congratulations to my winners! They received a brand-new whiteboard marker.

Here’s the icing on the cake (and lesson design telling me something wonderful just happened):

• Itzco wanted a chance to do it again. He'd been sleepy in class all week.
• Genesis wanted a ruler if we did a second round. Let's just say her attitude toward math all week was subpar and she has difficulty being a self-starter.
• Students wanted a chance to improve and try again. Especially students who initially drew ridiculous "squares".

There it is, Fun With A Sticky. Here's that list one more time:

• A simple question/task.
• A competition.
• Student creativity.
• Students assessing the work of each other (accountability).
• Students defining the necessary vocabulary/rules.
• Students determining the necessary tools to help solve the task. 

Sticky,

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