Carnival of Probability

This past week, my awesome partner, Hannah, and I hosted a Carnival of Probability for our 7th graders in our school's multi-purpose room. Let's get to it:

Station 1: Spinner 1

Pick a side. Will the spinner (arrow) land on the 5 or the 15? If you choose wisely, you win that many tickets.

Station 2: Spinner 2

No need to pick a section. You get three spins. Land on the 1, you get one ticket. Land on the 100, you win 100 tickets. BAM!

Station 3: Rolling a die

Pick a game. Grab the six-sided die and roll. 

• Roll an even number, win 8 tickets.
• Roll a multiple of 3, win 15 tickets.
• Roll a one, win 30 tickets. 

Station 4: Rolling two dice

Pick a game. Grab two dice and roll. 

• Roll two sixes, win 45 tickets.
• Roll an even number and a five, win 45 tickets.
• Roll two multiples of three, win 32 tickets.
• *Roll the same number on our twelve-sided dice (pictured below), win 70 tickets.

See the blue 12-sided die? There's a 12-sided die inside. Cool, right?!

Station 5: Bag of letters

Pick a game. Reach inside the bag of 26 chips chips (pictured above) and pick one chip. 

• Pick a vowel, win 25 tickets.
• Pick a consonant, win 21 tickets.
• Pick the first initial of your first name, win 40 tickets.

Station 6: Ball toss

Take a ball. Toss it in the direction of the cups. If it goes in any white cup, win 3 tickets. If it lands in the red cup, win 35 tickets. Just like that!

Station 7: Deck of cards

Decide on a game. Pick a card or two. Win tickets!

• Pick a red or black card, win 1 ticket.
• Pick a red card and a queen, win 40 tickets.
• Pick a Jack, Queen, or King and win 22 tickets.

Station 8: Coin toss

• Flip it once and land on heads, you win 8 tickets.
• Flip it twice and land on heads both time, you win 20 tickets.

You might ask, "Did you really pass out all those tickets?"

The simple answer is, "No!" You don't think we're that crazy, do you? We assigned one to two students as captains for each game. The game captains gave each contestant one ticket with the number won written on it. 

The math: we spent a few days leading up to the carnival talking about probability and identifying "and" statements along with "or" statements. Station 4 was all "and" probabilities which made your chances of winning more challenging. The 12-sided dice game had a less than one percent chance of winning. Station 7 and 8 had a couple of "or" probabilities. Our goal here was for students to have a concrete introduction and application of probability. To enter the carnival, students had to represent the probability of each game as a fraction, decimal, and percent. 

The students had a blast. It was fascinating to hear from them about the carnival the following day. They explained which games were the "easiest" and "hardest." The games (as you can see from the pictures) were nothing fancy, but they did the job. Students will get to cash in their tickets for prizes such as candies, pencils, pens, and Expo Dry Erase Markers. What would your carnival look like? Please share.  Head over here for the paperwork/handouts we used. 

Carni,

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180 Ways to Use Estimation 180

New challenge: Find 180 ways to use Estimation 180. Wait a minute. That's seems a little extreme, yet I still love the idea. Here's one use I came up with this week: inequalities.  Click on any picture to enlarge.

Me: Hey guys, here's a piece of paper. Fold it into fourths for me like this.

Me: Great. Now, who remembers how tall I am?

I know, silly question, right? If these guys don't know my height by now, I'll send them back a few grades. Then I show them this picture and ask: What's the height of Mrs. Stadel compared to Mr. Stadel?

I take about 4-6 guesses and write them on the whiteboard. It’s been awhile since we’ve done this specific estimation challenge in class. Many have forgotten my wife’s height. Great! However, it’s quite obvious her height is less than mine.

Me: Let me step back. Let’s all look at these guesses. Is it safe to say that all of your guesses put her height less than mine?

Class: Yes.

Me: Okay, so before I reveal the answer let’s put this in our notes for today.

Me: Before I reveal the answer, who can remind me why we used an open circle?

Student: Because we know her height is not the same as yours.

Reveal Mrs. Stadel's height. Wait for it... Wait for it... Here it comes... Student responses: 

“Yes, I was right!” 

“Ohh, I was close.”

“Ohh, I was off by an inch.”

Next up, our beloved Mr. Meyer.

“Woah! He’s tall!”

“Someone is actually taller than you, Mr. Stadel?”

Again, toss 4-6 guesses up on the whiteboard. Step back. What do we notice? Yes, all the guesses should be greater than my height.

Walk through the notes on this new section with more student confidence and participation.

Ask students:

• What type of circle should we use this time?
• If we’re talking about guesses that are greater than my height, how will that affect the inequality symbol?
• What are ways to remember this inequality as greater than?
• Which direction will we shade now?
• Someone give me a variable we can use for Mr. Meyer's height.

Reveal answer. Same responses as my wife, but usually a different kid was right this time.

Okay, great. Now what? What about those other two inequalities, right?

Me: Before I show you this next picture, last year the 6^th grade English teacher (@mrkubasek) at my old school read this novel with his students and came across these two books he found interesting. I found it interesting too and took a picture so we could talk about it in math.

Show picture.

Me: How many pages in the book on the LEFT?

No need to write anything down. Just get 6-8 guesses out loud. Don’t spend much time here. Reveal the answer. Give some math love [one clap on three: 1, 2, 3, CLAP!] to the closest student. Seriously, it’s pure gut instinct here people.  

NOW, show this picture and ask how many pages in the book on the RIGHT.

They don't know it yet, but you just broke their brains for a bit. Yup, you’ll get a lot of guesses below 307. But wait for it. I guarantee in a class of 35-40 students like mine, one student will say 307. If you do, treat it like every other guess you've gotten.

...and if no one guesses 307, step back after about 6-8 guesses and...

Me: You know all of your guesses make sense to me. I'm curious though guys. This is the same novel here, right? What if? I mean, WHAT IF? What if these books had the same amount of pages? Do you think that's possible? Do I have your permission to add it to your guesses?

Step back again. Look at all those beautiful guesses. 

Me: So if I'm looking at this right, you guys think the number of pages could be equal to 307, or could be less than 307? I wonder how we could represent this mathematically?

BAM! Focus here on the circle. Why are we shading it in this time? What's up with that line under the less than inequality?

Me: Okay, before I reveal the answer, someone remind me why we shaded in the circle. 

Reveal!

Brains broken! Now repair. 

Me: What's up with that? Anyone have any ideas/theories why they have the same amount of pages?

Alright. That fourth and final inequality. Here are the goods. Repeat all the other moves from above. 

Initial guess of one bar.

Take some guesses out loud. Reveal the answer.

Toss up new picture.

Write down some guesses on the board. Play up the "what if" again. Complete the notes. Ask a few questions before revealing the answer.

BAM!

That was fun. Boy, I wish it didn't have to end. But it did. Okay, let's find other ways to use Estimation 180 in the curriculum. The full lesson will soon be is available on the lessons page at Estimation 180.

180 ways,

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Presentations & Workshops

Last month I added the Lessons page to Estimation 180 so you can quickly access lessons I've made. I will continue to add lessons as I make them and host them in that space.

This month, I'm adding a Presentations & Workshops page to the site. Since last November, I've been fortunate to work with some amazing math teachers at conferences and workshops. I've learned a lot and have truly enjoyed doing math with teachers as we share instructional strategies and lessons. My goal is to help support math teachers in strengthening their instructional tool belt for the Common Core classroom. 

I'm excited about this new chapter. Drop me a line if you're interested.

PD,
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