Dot Crazy

   Last month, on the Friday before our spring break, I borrowed Shannon's third grade class.  Inspired by the work both Simon Gregg and Steve Wyborney are doing with dot images...

This week's quick dotty image. How do you see it? pic.twitter.com/SasGGR8GSJ

— Simon Gregg (@Simon_Gregg) December 1, 2015

...I was anxious to see what would happen when our kids were presented with a similar task. I chose this potentially over-ambitious image from Amanda Bean's Amazing Dream, a book I had used as part of a Do the Math multiplication intervention:

I wanted them to count how many bushes there were. 

     We decided to start by modeling the activity with a simpler dot image.  I spent a few minutes playing around with Steve Wyborney's cut slides, and brought one into class for the kids to work on, asking them to figure out how many dots there were and record their thinking with some equations. First working independently...

...and then sharing out on the SmartBoard.

    After this brief intro, we gave them copies of the image from the book, some blank paper, and told them to figure out how many bushes were in the picture.  They could work alone, or choose a partner.  Once they had done it, they were to take another copy and figure it out again, but in a different way, and see if they got the same answer.  If they had time, they could try it again.
     What happened next was pretty amazing.  Right and wrong, neat and disorganized, straightforward and complex, in pencil and in marker, in rows and in columns; it was like we had turned on a fire hose.  Math started gushing out all over the place.  In fact, I don't think I've ever seen so much math happen in one place in such a short period of time:

     Shannon and I stood back and watched, offering feedback when asked.  The activity really hit the elusive sweet-spot: our high achievers loved the challenge of finding multiple ways to compose and express the total, while the strugglers enjoyed engaging with the picture (maybe they were just relieved it wasn't another word problem) and didn't seem to mind that the correct total was elusive.  The persistence level was off-the-chart.  The kids were so involved it was hard to get them to stop.
  We closed by having some volunteers to share their work, and before leaving I asked the students to take a few moments to reflect on the experience.  Some selected comments:

   

     Sensing we had a winner on our hands, I spent some time over spring break creating more dot images (thanks again to Steve Wyborney), and Shannon has left them out for the kids to work on:

Here's why I like this activity:

• It promotes both additive and multiplicative thinking, and is a great formative assessment.
• It puts writing equations into a meaningful context.
• It's a task with a low barrier to entry and a high ceiling, so every student can engage at his or her own level.
• It's simple to implement, and takes virtually no explanation or prep work.  Big return on a small investment.  Everybody wins!  

When Reading Met Math

     This is a common sight in many of the classrooms I visit:

Whether on a poster...

...or displayed on a bulletin board.

     Students are taught to use these strategies in order to help them make sense of what they read...in reading class.

Their independent reading books have post-it notes sticking out all over the place.

     Every math teacher knows that many students have trouble solving word problems.  Looking at these displays day in and day out got me thinking: might these active reading strategies be useful in math class?  Curious to find out, I enlisted Shannon and her third grade class in a little experiment.
    In your typical series of lessons on solving number stories, at least as presented in our curriculum, the kids are given the following:

This is of dubious value.

They are provided with some information:

Animals are a favorite of elementary curriculum writers.  All kids like animals, right?

And then asked to solve some related number stories:

This is sure to kill any interest you may have had in the animals.

   We decided to try something different.  We provided the kids with the animal information, and asked them to use their active reading strategies:

Shannon created the sheet.  The boxes are intended to resemble the post-its the kids stick to the pages of their independent reading books.  In the top right corner they indicate the strategy they've employed.

It's really quite similar to noticing and wondering:

   

Next, we asked the kids to write questions for their classmates to solve.

     Shannon and I vetted them, and threw in some of our own.  We typed them up and taped them to index cards.  Students got to choose which problems they wanted to solve, and each had a sheet where they had to record both an active reading strategy and a solution:

This was a student generated question.

This student used the questioning strategy.   Shannon and I felt that this showed good insight into a curious turn of events for the crocodile.

This was one I wrote.

I think this question came from the book.

A clutch is a nest.

   I tried it out with a fourth grader who has particular problems with number stories.

She predicted, visualized, clarified, and made a text-to-self connection.  Unfortunately she got the wrong answer due to a computation error.

Some comments, reflections, and questions:

• Treating number stories as texts similar to those encountered in reading class could be one way to demystify these often intimidating and challenging tasks.
• This strategy can help kids with the first step in solving number stories: making sense of the problem.
• One advantage was that the kids didn't have to be taught these strategies.  They already knew them.  
• Integrating reading and math builds curricular coherence.  It's second nature for them to "post-it" up their books.  Why not their number stories?  Why can't math have what reading's having?
• I haven't followed up, although I'd like to revisit this activity with Shannon's class before the year is out.  There's a lot happening in the MTBoS surrounding the issue of math and literacy.  How do we help kids make sense of number stories?  What strategies can we provide to help them make sense of text-heavy problem solving scenarios?  Noticing and wondering and numberless word problems are two that have been offered up and that have proven benefits.  Could this be another?  Fire away.