In my last post I discussed some of the things I learned about mathematical modeling at a recent Math for America professional development.  At that same professional development, I had a conversation with a few people about modeling and developing great tasks.  I mentioned that I have to practice looking for great questions, but until I'm able to come up with all of them on my own, I steal (borrow) a lot of great content that people share online.  Over the next few weeks, I will write blog posts to share with you some of my very favorite modeling and number sense resources.  Let's get this party started by discussing my all-time favorite number sense resource:

Estimation 180

Website url: http://www.estimation180.com/

Author: Andrew Stadel @mr_stadel

Description: "Each day of the school year I present my students with an estimation challenge. I love helping students improve both their number sense and problem solving skills. I'd like to share the estimation challenges with you and your students. Michael Fenton and I have collaborated on this handout for your students. Happy Estimating!

Enjoy,
Andrew Stadel"

Why I Love It: 

Honestly, I first started using Estimation 180 because I was looking for an easy time-filler/warm-up for a class of students that was way below grade level. I needed something that I knew everyone could do no matter their mathematical skill, that would keep them busy for a few minutes at the beginning of class while I took attendance. I'd heard some buzz about Estimation 180 on Twitter and on some blogs, so I decided to try it out. I got a whole lot more than I bargained for!  Here's a few reasons why this site is so awesome:

1. Low-Threshold
Everyone can estimate. Everyone!  That kid who says, "I don't know how to do this," every time you call on him?  Yep, he can estimate too.  I have 100% student participation when we do an estimation challenge.  On some days, it might be the only 5 minutes of class that everyone is participating, but at least everybody was thinking mathematically for at least 5 minutes. 

2. High Ceiling
Not only can every kid DO the Estimation Challenges, but every kid can LEARN from the estimation challenges. I find that the best learning often happens when I ask kids the 'why' behind their estimates.  Other good teaching moments come from having students calculate their error.  For example, I had no idea how difficult it would be for my students to calculate their errors of estimating Mr. Stadel's height and the height(s) of his family and friends.  First we had a discussion about all the different ways to correctly write out his height (6 feet 4 inches) and why it couldn't just be written as 6.4.  Then we had some interesting discussions on how to calculate error if someone had estimated that Mr Stadel was 5 ft 9 in.  Why can't we just do 6.4 minus 5.9?  Students brainstormed several strategies to determine the error, including counting up and regrouping to write his height as 5 feet 16 inches.  Was this part of my lesson plan?  No way!  Is it in the eighth grade core that I teach? Not exactly. Do my students need it and does it help them improve their number sense? Absolutely!  I consider it to be time very well spent.

3. Kids Love It
I wish I could record for you that moment that I 'reveal' the correct answer!  There is often shouting, occasionally there are fist pumps. There are sometimes exclamations of disbelief! "What?! There's no way that is only eighteen napkins!"  When a student's estimate is perfect, it's as though he or she had just won The Price Is Right?  I usually try to take a moment to acknowledge the person with the smallest error.  That's all they get - no candy, no extra credit - just a moment of verbal praise, and the knowledge that for that moment they had been more successful than every other person in the room.  You wouldn't believe how motivating that is.

4. Estimating and Problem Solving
As a math student and, until fairly recently, as a math teacher, I always thought that teaching estimating was a waste of time. You know what I'm talking about - those worksheets that teachers gave kids where they had to use rounding to find their answers before they learned the actual algorithm.  Students' answers are invariably different from those in the textbook because they'd rounded to a different place value than the textbook had used.  In all honesty, I still don't see any value in the 'kill-and-drill' form of teaching estimating.  However, I see a lot of value in teaching the Estimation 180 form of estimating.  When I give my students a task like Noah's Ark or Styrofoam Cups, I now begin the task by asking my students to tell me something that is too high, something too low, and then an estimate.  This starts them thinking about what the answer should be.  For my students, choosing the appropriate mathematical operation is often the most difficult part of a problem.  If they already have a good estimate in their head before they start to problem solve, the students are able to figure out much more quickly if their strategy is leading them down a wrong path.