# Archive for

## The eyes have it …

On his blog, Reflections in the Why, Chris Hunter posted some photos of eyeballs and ice cube trays.  Wonderful!  Marvelous!  Fabulous!  Had me stop what I was doing, take photos of my own stuff, and post on twitter and Instagram.  I added the obvious questions:

How many eyes do you see?  How do you see them?

AND I shared my pic with my 4-year-old nephews.  They thought it was fabulous.  We had a great lunch time conversation about how many eyes do you see and how you do you see them?  The result:  smeared peanut butter from their peanut butter sandwiches on my iPhone!!  Totally love those guys–so into math conversations at lunch that they strayed from the awesome pb and j sandwiches their dad made.  Go Jack!  Go Josh!

AND also appreciative of my photos were my colleagues who teach first grade.  We started our grade level work session with an estimation question (idea “borrowed” from Andrew Stadel at estimation180.com).

How many eyeballs are in the jar?

Awhile ago, I bought several bags of eyeballs.  They do not work so well as counters.  Since they are round, rolling objects, it is really difficult to use them as counters.  They do what comes natural to round, rolling objects, they roll all over the place.  Round eyeballs do not play well with ten frames; they roll right off the ten frames and onto the floor.  So, if you are working with a small group of kiddos–both the eyeballs and kids are now rolling around.

So, thanks Chris for a perfect solution.  I can now use these fabulous counters that had, until about 10 days ago, just been sitting quietly in a plastic container on a shelf in my garage.  Now, they are the object of LOTS of math conversations with kids who crack up at my current favorite questions to ask–how many eyes do you see and how do you see them?

As you can tell from the fact that it is Sunday–and almost time for the second mission from the leaders of the Exploring the MathTwitterBlogosphere project–I am struggling with my post.  Glad whomever is in charge of Mission #2 did not post at 5:02 am today!!

I am a teacher on assignment.  My contract is a half-time (50%) position, so I work 92.5 days a year.  (I do other stuff the other half of my time with other groups of fabulous educators.)  It’s a great deal.  I work with great people–people who are learners and who are truly committed to making their classrooms an awesome place; a place where learning happens every day, where kids are asked to explore their assumptions, values, and beliefs about math, where opportunities exist every day for kids to build confidence, to reason, and to communicate their thinking.  However, I don’t have my own classroom.

This year, I have the great fortune to spend a lot of time in Tami’s classroom.  (She blogs at shouldbequiltin’.)  She lets me hang-out in her 2 math lab classes.  As the organizers and designers of the instructional sequence for the kids in her classes, we have chosen to focus our collaboration and planning for these 2 classes on providing an environment that supports kids building their confidence as learners, as people, as mathematicians.  One way we do this is to include opportunities for mathematical discourse in the learning we organize every single day.  We believe that it is essential for the kids learn to advocate for themselves, to ask questions, to become invested in their learning, to identify what they can do, and to figure out where their understanding starts to break down.  Hard stuff for kids who have not felt particularly confident as learners or as mathematicians.

So…we started out our year with a planning and organizing conversation that included everyone from our 2 middle schools involved with math lab.  We talked about what we didn’t want our classes to be like and what we did want for the kids who spend time with us each day.

As a learning team, we decided that we wanted to change how the  instructional sequence was designed and organized, it should match our philosophy about learning and what we know is good for kids.  We are about kids having enough opportunities to make connections, to see how topics, ideas, and concepts are related, and to build perseverance.  We are not about marching through worksheets and workbook pages from the intervention materials the publisher of our textbook series provide, teaching the same content the same way with a different set of exercises.  We are about using the quality resources shared by colleagues from the MathTwitterBlogosphere and from other high-quality sources. We are about offering our students awesome, quality, interesting tasks to investigate, talk about, reason through, get frustrated about, and make sense of, all in support of them building confidence as learners and in their math skills.

We include number talks (Number Talks by Sherry Parrish), counting circles (Number Sense Routines by Jessica Shumway), and/or estimation tasks (estimation180 by Andrew Stadel) as starting points for the day’s work.  The rest of class is dedicated to kids working on tasks that relate to and support the content they are learning in their math classes, or building concepts that will support the next big topic they will work on in math class, and/or pursuing tasks that explore essential understanding and big concepts in math.

All of this is a very LONG response to the prompt that asked each of us to discuss what is one thing that happens in our math classes.  The bottom line-we believe that our students are mathematicians and we have set up our classes to ensure that they believe that as well.

## Introduction to Exactly 20

This post might be slightly out of order with the post Exactly 20 already up and out, but it wasn’t out of order the day we were working on the task.  After we tried Exactly 20 ourselves, we talked about what support or scaffolding we might need to put in place so that the kids can play the game independently and, as they play, are also working on using strategies efficiently and building computational fluency.

So, this was our idea for an introduction to Exactly 20.

We wanted to create some pre-determined sets of cards to use as the basis for a whole class conversation.  We selected a set of 4 cards to see what combinations were possible.  Then, we checked to see if we could use make 10 as a strategy and if we used the pair as 2 of our 3 cards, would the 3 cards result in a sum closest to 20 or a sum that was close to 20.

Here is the set of cards we started with:  4, 7, 3, 7.

The set has a pair cards that make 10, the 3 and the 7, and when the second 7 is added to the 10, results in 17, a sum pretty close to 20:  7 + 3 + 7.  But…there is a second set of cards that results in a sum of 18: 7 + 7 + 4.  You can use doubles to find the sum. You can also use a make 10 strategy, if you split the 4 into a 3 + 1, and then, add the 3 + 7 to make 10 and then add the 7 and the 1, you get a sum of 18.  You are using make 10, but it is not as obvious as 3 + 7 that make 10.  We were looking for an obvious pair that made 10 for the first set.  So, we replaced one of the 7s with a 5.  The next set we tried was 4, 5, 2, 7.  It did not contain an obvious pair that makes 10.  What were we thinking!!!  The third set was the charm:  4, 3, 2, 7.  It made for great conversation as we found that we had to generalize a bit:  look at the three largest to see if they resulted in a sum that was 20 or less, and then check to see if we had an obvious pair that would let us use the make 10 strategy.  As you can guess, we needed to do some adjusting to some of the sets of cards we chose.

We found three sets that fit our criteria:  close to 20 or 20 exactly and an obvious pair that let kids use make 10. We then decided we wanted to stretch kids a bit and include, in the last 2 sets, some combinations that obviously made 10, to which a third card could be added, but would not have the sum closest to 20 or exactly 20.  We wanted to see what the kids would notice; who would use the make 10 strategy and who might would find other combinations of cards that would actually be closer to 20.

Our final list:

We used this as a whole class lesson, with some partner conversation and partner work, to introduce the game Exactly 20 and to provide additional opportunities for kids to use the strategies we had been working on.  Our ultimate goal:  we want the kids to be so good at this game that it can be sent home for homework:  teach someone at your house how to play Exactly 20.