## Wednesday, April 22, 2015

### The Fact Platter Gets a Makeover

I like to cut things apart.  Game boards, worksheets, problem-solving tasks; nothing is safe.  The latest activity to fall victim to my scissors was the unsuspecting Fact Platter.

 I found some first graders in Jen's class working on this at a center one morning.

Now I've seen this activity many times before.  But that day, as the kids were filling out the Fact Platter, I happened to look up at Jen's desk.  I saw a pair of scissors, and a light bulb went on.  What if...

 ...you cut the platter apart...

 ...and put it back together like a puzzle?

I tried this out with a kid and liked the results.  It required more thought than simply filling in the sums.  I called Jen over, and we started experimenting with ways to differentiate the task.

 Here's a version with just the outer ring of sums cut out.

 Jen had the idea to cut out the inner ring.  Here the kids needed to find the missing addend.

As a challenge, I took two platters, cut them both apart, and mixed them up.

 It took two kids about 10 minutes to put them back together.

 They had to make sure that each one had the digits 0-9 in the inner ring.

 It required quite a bit of cooperation.  When they were finished, Jen put the pieces in envelopes to use at a center.
So the next time your kids are working on an activity, and it seems a little drab, reach for one of my favorite teaching tools and give it a makeover:

 It just may do the trick!

## Wednesday, April 15, 2015

### Between 6 and 8

It started, as it so often does, with an estimation180 prompt.  A "do now" that leads to an unexpected place.  An innocuous math message with a powerful punch.
A few minutes late to grade 5, and Rich's AM class, all 21 of them, are already busy at work on Day 201:

This particular opening routine is well established.  Draw an open number line.  Plot a "too low", "too high", and a "just right" estimate.  Provide justification.  Turn and talk.  Share some responses.  This takes maybe 5 minutes.  And the reveal:

Cheers, groans, and purposeful talk as the kids place the actual measure on their number lines.  And with the picture still up on the SMART Board screen, the kids get ready to begin a round of guided groups.
Now there are many ways to structure time in math class.  But when we use the guided group model, I like to try, whenever possible, to start with a quick whole class activity, break about half-way through with a short, whole class "mid-workshop interruption" (something I stole from my ILA colleagues), then end back together as a whole class for a wrap-up.  The opening activity, as well as the guided groups, should be planned in advance.  This is also true for the mid-workshop interruption and lesson close.  But a good teacher should be ready to change on the fly, and allow the teaching points for the mid-workshop interruption and the wrap-up to be informed by what he or she sees happening during the day's activity.  These are times when concepts can be reinforced, misconceptions addressed, and classwork analyzed.
On this particular morning, when the clock strikes noon, Rich and I give each other a look, a look that means: "You got anything for the mid-workshop?"  Nothing of any significance has come up with the kids I've been working with and, as I watch him shrug, it seems the same can be said for him.  My eye catches the picture of the hot cocoa reveal still up on the SMART Board, and I've got it.
I nod to Rich.  He gives the groups a two-minute warning, and soon they're all back in their seats.

Me: Take a look back at the picture on the SMART Board.  We know that the cup has 8 fl oz of water in it, but the package says we could use 6-8 fl oz.  What does that mean?
Them: There's enough cocoa mix in the package for as small as a 6 and as much as an 8 fl oz glass.  Maybe some people like their cocoa stronger than others.
Me: Let's count from 6 to 8.  If Ryan says the number 6...(here I point to the student sitting in the first seat at the first grouping of desks to my right and sweep my hand around the class)...and we count all the way around the room and end with Kelly who will say 8, what will we have to count by?  Who will say 7?  Turn and talk to your table and figure it out.
The class is pretty sharp.  It doesn't take them long to figure out that because there are 21 of them, and because Ryan will say 6, they will need to take 20 steps to 8.  Ten tenths will get them to 7 (that's Jake), and then ten more tenths will get them to Kelly at 8.  It works!

 I recorded the count on the whiteboard, switching to decimal notation after 7 because it was easier for me to keep up with them!

The kids got back to work, moving through their group rotations.  And to wrap up the morning, we spend the last few minutes of class talking about the advantages of writing in decimal notation:

There are 19 kids in the PM class, and they follow the same routine, with the same counting circle activity for the mid-workshop interruption.  This time, however, the results are quite different.  The kids cannot agree on the appropriate counting interval:

 I found their responses fascinating.  19ths because there were 19 of them.  38ths because, well, double 19!  37ths because one less than 38ths, an attempt to account for the first student starting at 6.

There was nothing left to do but try each one, and hope they could, by trial and error, come up with the correct response.

 Counting by 37ths didn't even get them to 7. That eliminated 38ths as a possibility.  We tried counting by 19ths, but that didn't work either.

 Finally!

This process took up much more time than we had anticipated.  We decided to make hay by shortening the meeting time for the final guided group session and ditching the wrap-up, an example of the flexible decision-making that goes on in classrooms every day.  All told, I felt it was time well spent.
That evening, reflecting on the counting activity, I was plagued by a thought:  What if there had been an even number of kids, say 20?  What would we have done?  Did we just get lucky?

I spent the next few days trying to puzzle this out.  My somewhat inelegant solution was to split the difference between ninths and tenths and count by "nine and a halfths".

 It wasn't pretty, and I couldn't hit 7 exactly, but it worked.
Nevertheless, it didn't seem appropriately math-like to me.  So, as I have in the past when I get confused, I asked my supervisor for some help.

 He liked my thinking, but not the notation.  Here's what he showed me.
 I tried it out.  Counting by 2/19s worked.  I realized that my difficulty stemmed from the fact that, 1) I was trying to count by a unit fraction, and 2) I was trying to hit 7 exactly, which was not possible.
So yes, we did get lucky.  Score another point for the power of estimation180: from that one prompt we drew out a counting circle, a refresher on decimal notation, and an interesting problem solving experience for both the kids and their teacher; a teacher who now knows there's a lot more between 6 and 8 than just 7.

## Monday, April 6, 2015

### What Happens In the Faculty Lounge (Doesn't Necessarily) Stay In the Faculty Lounge

Some of the most interesting math action in my school takes place, not in a classroom, but in here:

 The Faculty Lounge

Recently, I blogged about how seeing this on one of the tables...

...inspired a 3-Act problem solving task.

And earlier this year I described how seeing this Thanksgiving leftover...

...inspired some interesting noticings and wonderings.  Here are a few more examples of what I think of as "Faculty Lounge Math":

The Soda Machine

Did you notice the soda machine in the back right corner?  One afternoon a few months ago I caught the delivery guy in the process of refilling the machine.  I snapped this picture:

Thinking I might use it as the basis for another 3-Act, I found out that the machine holds 288 bottles, which is 12 cases at 24 bottles per case.  One of our grade 5 teachers has already used it as a noticing and wondering prompt.

Candy

Here's something a teacher left on the table after Valentine's Day.  I used this as an estimation180 task:

 How many candies inside?  Give me a too low, a too high, and a just right.  On an open number line, of course!

 I opened the box and took this picture for the reveal.  It also suggests fractions, arrays, multiplication, and subitizing.
Later that afternoon I found that someone had been at the candy!

Speaking of subitizing and candy, one morning in early November I found this bag of left over Halloween treats...

...and brought it back to my room.  I arranged them in different configurations...

...and downloaded the pictures onto our school's shared drive for the primary grade teachers to use as subitizing prompts.  OK, I confess.  I ate the candy.

Supplies

Several weeks ago I found myself in Aimee's first grade classroom, working with a group of kids trying to make 2-dimensional shapes using play-doh and what looked like over-sized collar stays. Things were not really working out.
"I wanted to use coffee stirrers," she explained, "But I left them at home."
"Just a sec!"  I told her.  A quick trip to the Faculty Lounge...

...and the kids were good to go!

Donuts

Some kind soul brought these in one morning:

 I thought this would make another nice subitizing prompt, or maybe start an array chat.
But food doesn't last long in the Faculty Lounge, and as the day progressed I took this series of pictures, hoping it might inspire the kids to write and solve some number stories:

So there you have it.  The Faculty Lounge is many things: a sanctuary, a meeting place, a destination where a hungry teacher can find some much needed sustenance.  And it's one of my go-to spots for mathematical inspiration.  Now you know what's in my Faculty Lounge.  What's in yours?