Wednesday, February 26, 2014

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 whiteboardStep 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 6th 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. 
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.

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,


  1. I think this is a great idea to connect the estimation to something that makes sense. I wonder if you could have extended to the graph of a compound inequality b/c obviously there are heights that wouldn't be realistic and you could have had them estimate on that end as well...and then connect it back to the graph and what would it have to look like.

  2. Thanks Andrew. We've been playing around a little. We've used a new number line each day, for each estimation task. But for the last series (I made one with various amounts of money, no more than $3.00, this to practice decimals) and we used the same number line, adding as we went. No too high or too low, but a just right and the actual amount each day. Great practice ordering decimals. I also did one with grams of sugar in various sizes of cokes and then with pieces of candy that had fractional amounts (like a skittle 3/4 g and a starburst 2 1/2 g). Also good for fractions and mixed numbers on a number line.
    We've also got a little production studio going, with the 4th graders submitting estimation180 proposals to be made to use with the third graders. They create the scenarios and use my ipad to photo or video and then we download it to the district shared drive. We've had some that were pretty creative. I'll be blogging about this soon.

  3. Can I ask what were their reasons for the books having the same pages? How did you explain it to them?