Fitting It Together: Another Take on Number Visuals

A visual number pattern created by artist and scientist Stephen Von Worley forms the backbone of day two of youcubed.org's week of inspirational math.   

The lesson envisioned by the youcubed team is here and starts with a video of Jo Boaler talking about the importance of "brain crossing" - connecting visuals with symbols - followed by exploration of the number pattern, finishing with summarizing and sharing out.  The whole shebang in one day (possibly followed with an exploration of consecutive number patterns).  Whew!  

I had the opportunity to test this out with various classes ranging in age from 3rd grade to 9th grade, and some adventurous 3rd grade teacher colleagues of mine tried it out with their classes, too.  Low floor high ceiling problems like this have great potential to encourage creativity, build stamina, make and test conjectures, and apply and connect math concepts.  Although we found the youcubed lesson fun, and yes, inspiring, it felt a bit... unwieldy and unfocused.  

We found ourselves asking: How could we use it to hone our conceptual goals?  In this blog post, I am putting forth a possible answer to this question with this overall plan:

An overall instructional plan for Tier 1.  From beginning to end this could span about 2 weeks (more or less depending on how solid and flexible the students' grip on additive reasoning is). 

Low Floor, High Ceiling - Math Coach Attempts Math Art

How often do we (as teachers) hear about something that sounds pretty great, but then we can't picture how it should fit in with all of the other great stuff that we do?  

Last week, I had the opportunity to hear David MacAulay (illustrator and author of visual feasts such as The Way Things Work) speak, and he said something that resonated with me. 

In order to really see something, I need to draw it.

 Well, I'm no David MacAulay, but I thought I'd give it a try... So, for a training session yesterday, I made this poster to explain the difference between high floor, low ceiling and low floor, high ceiling math activities and questions:

Then, I created a visual of what integrating low floor, high ceiling activities into a math class could look like.  

I based this on my own experiences threading these problems into my teaching, but I tried to build it bigger and better.   Then, I made it into a "Thinglink" to add some depth to it. Check it out below (here's a link in case you can't see the "thing").  Each information "i" should be clickable and will provide a little more information about the parts. 

This isn't the only way to do it though.  It's just one way.  How would you improve it?  Thoughts?  Questions?  Comments?  Please send them in... edorsey@u32.org.

Meanwhile, here are some resources I created to analyze and revise our questions and see here for my original post on how to do a low floor, high ceiling makeover.  

Hope you enjoy!