Tuesday, January 14, 2014

That's Gold, Jerry! Gold!!

   Readers know what a big fan I am of Andrew Stadel's estimation180.  I've blogged about it here and here.  But the more we dig into the site, the more amazed I am at how rich the activities really are.  Here's an example from last Thursday.

Class opened up with the activity from Day 55.

What's the capacity of the cylindrical vase?

First of all...

  • What's a cylinder?
  • What's capacity?  How do we measure it?
     OK, now it's time for the number line.  Kids have gotten used to this routine.  They've already got their notebooks out and are working on their boundaries (too low, too high) and their "just right".  They still think it's funny that the teacher is actually asking them for wrong answers!  We have a general discussion of strategies.  Where are your numbers coming from?  It's now automatic:  they use the can as a referent.  They use the other vases and glasses and containers they've seen on previous days to inform their estimates.  They describe the attributes of the vase.  They compare.  They imagine.  They agree with each other.  They disagree, too.
     Next we start the video.  We pause it at the 14 second mark.  Time to evaluate estimates and revise.  This is important: the original estimate is not crossed out or erased.  Your response was not "wrong".   The new estimate must be placed on the number line. 

The video is started again.  Another stop at the 21 second mark.  (Mr. Stadel has disappeared!  Where did he go?  Let's make an inference!)  Time to reevaluate and make a final estimate.

Now we play it out to the end.  Cheers, applause, groans.  The answer is 41 ounces and that is also placed on the number line.  General discussion about strategies.

The original estimate was actually the closest!
     We're ready to move on to the day's lesson (something to do with polygons), when a normally quiet girl in the back of the room pipes up, "So how many cans of soda would fit in the vase?"
Great question!  What do you guys think?  Turn and talk and figure it out!  The vase holds about 3 1/2 times as much liquid as the can?  How do you know?

     15 minutes has gone by since the beginning of class.  I'm breathless.  Instinctively I know that a lot has been covered in that short period of time, and none of it was contrived.  It was all embedded in an engaging activity that all students could access.  (Later I counted 4 separate content standards and all 8 standards of mathematical practice.)  As the kids put their notebooks away, Jeff turns to me to me and says, "That was more worthwhile than anything else we could have done in those 15 minutes."
 I turn and respond with what has become our signature line this year:


  1. I really like how you have the students revise their estimate on a number line. This will help to increase number sense for your students.

  2. Hi Joe,
    With Andrew Stadel's permission, I'm writing about Estimation 180 in a professional development book for teachers. It's called Becoming the Math Teacher You Wish You'd Had: Ideas and Strategies from Vibrant Classrooms. I'm so excited to share Estimation 180 in a chapter about mathematical intuition. I love this blogpost, and am wondering if you would mind if I included the link so teachers could see it in action?

    If you'd like more information about the book, don't hesitate to email. tracyzager at gmail dot com. Thanks!