**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 isnotthe 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.**What about those other two inequalities, right?

*Now*what?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

180 ways,

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