Estimation180 site

Its official: I've launched estimation180.com

The Google doc was a temporary holding place for my daily estimation challenges. I'm proud to announce that I will be updating my daily estimation challenges through this site. The site is way more interactive than a Google doc spreadsheet... and quite possibly, more fun too. You can make estimates, share your reasoning, see how others estimate, and more.

The goals of the site:

1. Document my daily estimation challenges.
2. Create opportunities for teachers & students to build number sense together.
3. Share!

What you can do:

1. Click on a picture.
2. Read the question.
3. Look for context clues.
4. Make an estimate.
5. Tell us how confident you are.
6. Share your reasoning (what context clues did you use?).
7. See the answer.
8. See the estimates of others.

The most important part is step #6. It's so valuable to a classroom when students share their logic or use of context clues when formulating an estimate. After you make an estimate, feel free to give us a brief description.

I've posted the first 15 days and will continue to update the site. Go do some estimating, build some number sense with your students and throw me some feedback if you find any glitches or ways to improve it. I want to sincerely thank Fawn Nguyen, Nathan Kraft, Chris Robinson, Michael Pershan, Dan Meyer, and Steve Leinwand for any help, inspiration, and/or feedback you've given me regarding estimation180.com You all are amazing!

Happy estimating!

Estimation vs. guessing Part 2

Yesterday I blogged (part 1) about visiting a fourth grade classroom and their lesson on estimation. After her lesson and her students left for lunch, the teacher and I debriefed. I really hope I complimented her enough. I was inspired. She asked me for some feedback. To remind you, she started the lesson by picking up a small cup, about half full of cubes, somewhat concealing it and asked students how many cubes were inside. She wanted to demonstrate that their initial answer would be a "guess" and not an "estimate". However, she had many observant students who already saw the size of the cup, the fact that it wasn't full of cubes, and even from my seat in the back I could tell that the cubes were small enough to fit inside the small cup. I told her I loved everything. The only additional thing I would have done was this:
Don't even show the kids anything. Don't go and pick up the cup. Simply say to the students:
Students, I will have a cup in my hands very soon. There will be cubes inside. How many cubes do you think will be in the cup?

Okay, look how simple this uninformative setup was. If I were a student, a bunch of questions would have just popped into my head: Hey teacher, what size is the cup? Is it a small paper cup? A medium coffe cup? or a large Big Gulp cup? What size are the cubes? As a fourth grader, I know what base ten cubes look like. Are they bigger like the size of snap cubes? Are they the size of ice cubes? and how about the amount of cubes in the cup, teacher? Are there just two at the bottom? Is the cup half full (or over half empty for you pessimists)? Is the cup full of cubes?

Any number the students produce would simply be a guess. It's a low-entry point, but doesn't hold much strength for long. How many cubes are in the cup? It could be two. It could be two hundred. Two thousand. You get the point. This strategy reminds me of a couple engineering classes I took in which we discussed a black box. In other words, there's something inside this black box that serves a purpose or function. However, you have no idea what's inside or the parts that make it function.

Students are guessing blindly at this stage. However, I wouldn't want them to just guess. I want them to beg for more information. Even better, I want them to think what information would help them solve this question. Let's move to the next stage.

Let's spiffy up our description, but still refrain from showing students the cup, cubes, or content level:
Students, I have a small drinking cup in my hand that's about 8 oz. Inside are cubes that are slightly smaller than six-sided dice. The cup is a little less than half full. How many cubes are inside?
By this time, I hope students would be falling out of their seats trying to sneak a peek at the cup. They're lusting after more information to make a more accurate assessment. You're simply adding some labels to the black box. Heck, put the cup inside a brown paper bag for this part.

What stage is this? I think this is the in-between stage. Shall we call it guesstimating? I used to really loathe this term as I want my students to use estimation. I thought it was a silly verb and should be eliminated from our vocabulary. I no longer think that. A guesstimate implies we could make a better attempt. We could use better clues. It's the bridge between guessing and using sufficient clues and observations to make a reasonable estimate. In other words, we must encourage our students to demand better information. Demand facts. Demand relevance. Don't SETTLE! Okay, so what takes us to that next stage, estimation?

Reveal the cup. Take it out of the black box and put it in the display case. That's right, put it in the display case. Don't let them touch it.

Demand they use their intuition, their available senses, and rely less on the sense of touch. Show a picture of the cup, a cube, and a birds eye view of the cup. Remember, it's in a display case. An even greater challenge to your display case would be to put the cup on the students's desks, but don't allow them to touch anything. Hold onto any last shred of information you could provide them with. Guard it. Be stingy. Let them use their sense of sight and intuition to build their number sense. Help students build up a thirst for relevant information. Build a problem solving plan or strategy. Don't be mean about it or covet the information for malicious reasons. Give students time to respond to the clues provided. The display case is a prime stage for estimation. Students have many context clues from either a picture or physical model. This should be enough for students to really build a strong theory and/or problem solving plan. As we saw in yesterday's post, students came up with a couple of theories on how to more accurately estimate the cubes in the cup by counting the top layer or cubes on the sides. The teacher didn't just hand her students the cup. She helped them climb the ladder of abstraction.  I think the key to this is encouraging students to demand more information. Don't inundate them with all of the context clues immediately. Make them demand the clues.

Hands-On is the last stage of estimation. Without counting, allow the students to pick up the cup. I'm not saying students will change their estimate. However, it will give them opportunities to consider another perspective of the task. They are including another component: weight, size, etc. There's only one place to go from the hands-on stage and that's revealing the answer: the payoff.

Recap:

1-Black box: Keep that description minimal. Avoid a visual.

2-Label the black box: gradually reveal some information

3-Display case: Look but don't touch

4-Hand-On: incorporate one last sense in order to bring one last perspective to the estimate.

By the way, did you know that Stevie Wonder played many of the instruments on his Innervisions album. I read somewhere that he virtually played all the instruments on about six of the nine songs. That's one of my favorite Stevie Wonder albums. If he can do that without the use of sight, imagine what we can do with all of our senses. 

Part 3: Why should we be the gatekeeper of information for our students? How can you help your students build their number sense and demand more information to make a reasonable estimation? How do I incorporate estimation in my classroom?

Part 2,
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Estimation vs. guessing Part 1

Estimation vs. guessing and the space between, let's talk about it.

If you've been following my thoughts lately, via Twitter (#estimation180) or this blog, I've really been investigating the relevance of estimation for some time now. However, the past few days have really had a great impact on my approach with students, leaving me even more intrigued with the relevance and application of estimation with students. Over the next few days, I plan to share a few of the interactions: here's part 1.

Today, I visited a fourth grade classroom at my school. It's a personal goal of mine this year to visit as many classrooms as possible during my prep period and learn, learn, learn from other teachers, especially elementary teachers. I love observing elementary classrooms and seeing how so many children are still excited about learning. I'm constantly looking for strategies to bring back to my own classroom that will create a sense of excitement with my middle schoolers. The fourth grade teacher and I will be working on creating and implementing 3 Act lessons this year, so I was getting acquainted with the climate of her classroom. It was destiny: the class was discussing estimation and guessing.

First off, she's a fantastic teacher. Second, she did a wonderful job comparing and contrasting what the students thought estimation and guessing meant in their own words. She created a list for each on a huge giant sheet of paper, like a giant Post-It note. She does this often and sticks them around the class for students to refer to. The fourth graders decided that guessing could be something:

1. you don't know
2. you think could be the answer
3. 50% sure
4. or anything

As for estimation, the fourth graders decided it could be something:

1. you round
2. you think is close to the answer and reasonable
3. you look at and use clues to carefully give an answer

This last definition was very insightful for a fourth grader.  The teacher proceeded to pick up a cup in front of the class and tell the class there were cubes inside. She asked them to make a guess and students were stretching their necks to gather any information about the cup in her hands. She did a great job concealing it, but many students had already mentally logged characteristics of the cup. She had a low-entry point for the students. They all wanted to know how many cubes were in the cup. They wrote down guesses in their journals and she took them to the next level. She showed the students how full the cup was with the cubes and asked them if this would be a good time to keep guessing or make an estimate. Students agreed, they had more information to make an estimate and they jotted this new number down in their journal. Lastly, she passed out cups, requesting students to not touch, but think of a strategy with their small group to get an even better estimate of the cubes in the cup. Students shared their theories:

• I counted the cubes in the top layer and then counted the layers down and multiplied the two numbers.
• I counted the number of cubes around the cup on each layer and made a reasonable guess for the hidden cubes inside.

The teacher asked the class who had similar theories and many of them chose the first. I really enjoyed how the teacher didn't once offer her theory on how to estimate. She let the students take ownership. As the lesson drew to a close, she requested the students work together to quickly count the cubes inside their cup and compare it to both their guess and estimate. The teacher had a low-entry point for all students, she let the students define their own vocabulary, she took them up the ladder of abstraction with gradually revealing information they needed/wanted and going from guessing to estimation. Lastly, the payoff was huge as she allowed students go hands-on with the cup and cubes to validate their learning for the day. I left her class inspired. But before I left, the teacher and I had a valuable brief discussion. A few things came out of that conversation I will touch base on in part 2.

Part 2 will connect estimation with guessing and the space between, sometimes referred to as a guess-timation. I want to create a low-entry point that's even more inviting for students. Lastly, I want to discuss how number sense can be strengthened as we transition from guessing to estimation before the payoff.

Part 1,
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