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.

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Explain that, please.

Recently, I've given a few teacher workshops/conferences and have had the luxury of reflecting on teacher moves as I facilitate a lesson with the attendees. One of the many things we talk about are teacher responses to students.

Me: Did anyone hear me say, "No. That's wrong. You're wrong. I don't like your answer."

Attendees: No.

Me: Right. Instead, you'll hear me say things like, "Can you explain what you did here? Explain that, please. I noticed you did [this] here, please share how you got [that]. I'm curious how you came up with that. Walk me through what you did."  

I tell teachers that I'm taking the emphasis away from right versus wrong answers and placing an interest on the student's thought process and problem-solving. I continue with teachers:

Me: By telling a student they're wrong, a student can have the tendency to shutdown [I make the sound effect of a machine shutting down, "BOOOOvvvvvvvv"]. By asking a student to explain things, it shows that I'm more interested in how they arrived at their answer. 

As teachers, we know a student can be told they're wrong and it's easy for them to give up. On the flip side, when we validate a kid by telling them they're right, the student can also shut down and never reach the higher levels of Depth of Knowledge.

Recently, a workshop attendee asked me how I respond to students who have nailed the answer to a 3 Act task. First, I have them explain their problem-solving plan to me. Second, I question any details that were unclear, encourage them to be more precise, or have them explain their units of measurement. Third, I ask them if they feel confident in their answer after explaining it to me. Fourth, I validate them by simply saying, "That makes sense to me."

I don't tell them they're correct. I treat them just like as if they got the answer wrong. If that doesn't satisfy them, I respond with, "We'll find out soon if you're correct, but that (their explanation and work) makes sense to me." At this point, I offer them an extension to the task. I'd like to talk more about this later, but usually the extension revolves around the students creating something with the new knowledge or skills they have just recently gained.

After all that, please add your favorite lines when questioning students to this Google doc. I think it's also helpful we create a list of lines we avoid using with students as they explore math.

Here are a few people with other stellar teacher moves/lines to support students.
Max Ray: 26 Questions You Can Ask Instead
Dan Meyer: You Don't Have To Be The Answer Key
David Cox: Creating A Culture Of Questions
Steve Leinwand: Accessible Mathematics

BOOOOvvvvvvvv,
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