Draft Scope and Sequencing Release

Greetings, WCSU math folks!  I hope everyone had a restful break.  Just a quick post to let folks know that I have worked up draft WCSU Math Scope and Sequencing documents for grades k-6.  The hope is to get feedback and then be able to roll this out in the Spring so that we can start the year on the same page.

No pressure, but if you are interested in checking it out here is a link: WCSU Scope and Sequencing.  Please realize that this document is in draft form and will be changing as we get feedback from all of you.

Also, I've been using relative down time to pick away at articulating our levels of math knowing.  Look for new links in our WCSU Math Learning Progressions document linked above on this blog.

If you have questions or feedback on this or anything else, please send it along to me at edorsey@u32.org.

Oh, and if you missed it.  Check out my last post on the Loster Mobster game.  If anyone wants me to come teach your class how to play, I would be honored...

Lobster Mobsters (best math game ever!)

Years ago, my colleague Cathy introduced me to a game that she learned from her mother in the UK.  We were pooling our seventh grade math classes together to play a game the last day before a vacation, and she enthusiastically explained this "lobster pots" game that sounded really complicated to me.  I had my doubts, but she insisted it was great.  Then we played, and I was amazed by how good it was.  It became an instant favorite.  It engaged all learners, but was challenging.  It involved higher order math applications and connections, yet allowed students to work on developing number sense, too (keep those calculators away!).

With a few revisions, the game became an excellent "low floor, high ceiling" game capable of inviting in and sustaining all learners.  I have played the game with students as young as second grade, and it would certainly challenge high school students, too.

How to play

Game players are cast as "lobsterpeople" who trap lobsters in "pots" to sell them at the lobster pound.  You can play as a whole class (this is how we prefer it), in small groups or individually. Students can work in a group as a part of a crew or solo.  They start the week with a certain amount of money and a certain number of pots.  Each day, students decide where to place their pots: how many in the harbor and how many off shore?

We've Been Sharma-ed - Mahesh's Visit to Grade 3

It's always exciting (for me, at any rate) to have the opportunity to come together with colleagues to improve our understanding of math and math instruction.  This week we had a special guest, Mahesh Sharma, who came to WCSU for clinical rounds.  Lots of folks were able to attend various "rounds," but since I was able to attend all four rounds, I thought it might be helpful to document and share what went down... 

Monday, December 7 

After some delicious beverages and treats (and I spilled an entire cup of tea all over the lovely spread because obviously, someone needs to have caffeine before leaving home), we started with a discussion of place value...

Ever wonder why the names billion trillion, quadrillion, etc.?  Pictured at left, Mahesh explained that the word "million" comes from mille which means "one" and llion which means "group."  

I was unable to substantiate this (fact checking found that the etymology of million is that mille means "thousand" and  the addition of the suffix -ion changes the meaning to "a great thousand"). 

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!

Engaging in a Math Debate

"One train may hide another."

Recently, Lisa, a sixth grade teacher sent me a link to this Amazing 6th Grade Math Work! blog post that she had written up to document a math debate that she released into her classroom around the difference between ratios and rates.  It's definitely worth reading her post, but if you don't have time, here's a synopsis...

Lisa began by admitting that, although she knew the official definitions of "ratio" and "rate," she wasn't sure what the practical difference was.  So, she put that out there and had her students research the terms, debate the differences and come up with a working definition that they summarized in a table.

After she sent this to me, I had some thoughts, too, and then the two of us debated back and forth over email a bit (for those of you who are riveted by such things, I'll paste these in at the end of this post).  Then, Lisa brought these ideas back to her students.

Making Number Talks Happen

I mentioned in my post Does Automaticity = Timed Tests? that number talks are a great tool for building number sense.  Number talks can be used regularly to engage our students in mental math that puts the focus on developing efficient strategies.

In the past month, I've had the opportunity to facilitate number talks in a few different schools with teachers and with students using the visual cluster of dots shown to the right here.  I am excited to report that teachers have been having success using this strategy with their classes.  In this post, I'll share some general guidelines (nuts and bolts) for facilitating a number talk, and share one teacher's experience using them with her third grade class.