The Writing Process–in Math??

Yep, you read correctly.  We’ve been learning the writing process–mainly in regards to our work in Writers’ Workshop–but also in math!

A few years ago, when our school started working with Cathy Fosnot and Mathematics in the City, I learned about how many parallels there are between communicating in mathematics and communicating in most any other setting.  At the time it was kind of mind-blowing to think about how mathematicians revise and edit their work just like authors.  After hearing more, and thinking it through, and then trying it with kids, it made sense.

So…as with many other things I learned about with older kids, and protocols that I know work well with any age, we’re talking about the writing process in mathematics again.  In 2nd grade. 🙂

The first unit we worked through this year was about place value, and was related in many ways to money; this made sense to kiddos and helped them think through how to “trade” 1s for 10s, 10s for 100s and just how to make groups in different ways to “make” a number.

One day they were challenged to consider this story:

Screenshot 2015-10-08 20.37.03-minWith their elbow partner they were supposed to figure our the answer to that question: If Jerry has $1000 to share, with how many people could he share a $10 bill?

Kiddos worked for almost 2 math periods to figure out their answer (which was really the answer to the question of how many 10s are in 1000) and clearly share their thinking on a poster.  For many, the answer of how many people was easy, the way to share their ideas not so much.

As a means of helping them know when they were “finished,” we discussed these parameters for their work:

Screenshot 2015-10-08 18.51.45-minAfter we had our posters finished, we were ready for our gallery walk.  During a Gallery Walk, students put their posters out for other mathematicians to read and comment upon–with the goal of helping deepen mathematical thinking and help create more meaningful representations.  It works much like a writing celebration, which is a great connection because all of our kiddos know how to do that. 🙂

Before we were ready to start commenting on others’ work, we needed a review of how to make effective, meaningful notes on our friends’ work.  We sat for a quick refresher using this flipchart:

Screenshot 2015-10-08 18.51.56-minThen we practiced recognizing helpful comments that followed the guidelines.  I gave examples and non-examples, and then we modified the ones we have given a thumbs-down (which mean they were not specific, kind or math-related).

After that, we were off to work in our gallery walk.

IMG_5395-min IMG_5396-min IMG_5397-min IMG_5398-min

We did pretty great with our first walk of the year, and I’m sure kiddos brought their kindergarten and first grade knowledge with them to help as they shared their thoughts with other groups.  I was impressed with how questions were used and kids were specific with what parts didn’t make sense or that they thought others could improve upon.

After adding comments, partners were given a few minutes to review what others had shared.  In order to debrief and think about how to use this to help us next time, partners had to share out with the larger group one thing they would do to revise their poster to make it better (and ideally we’d have taken time to actually revise them, but we ran out of time!).  Next time we are ready for a math congress and gallery walk, we’ll definitely come back to this moment and remember what we learned. 🙂

Fractions with Fosnot and Flex Time

Remember last year when I told you all about Feast Week?  Well, it’s that time of year again, for fractions at least, but not–it seems–for Feast Week.  Instead, we’ve begun using some AMAZING new resources from Cathy Fosnot, that have helped our mathematicians think of fraction parts in a whole new way.

My favorite part of math right now is the addition of Fraction Flex Time (man, it seems like we need to add a cute name to every thing fraction related…).  After we finished the investigations in our Fosnot unit (which included figuring out the Best Buys, Oatmeal Problems and Gas Tank problems), our team sat down to figure out how to divvy up our kiddos between the 7 teachers we have (Yes, I said SEVEN!! Isn’t that FABULOUS!! ??), based on the information we’d gathered during our first few weeks of study.  We made the groups small and intentional, and we planned for intense teaching and practice.

Although the pacing and strategies are a little different based on the groups’ need, the goal is the same (based on our district rubric):

Screen Shot 2013-11-19 at 9.03.25 PMJust like I shared in my post about our visit from Kara Imm from Mathematics in the City, number strings have become our new best friend.  I mean, honestly, before this year I really didn’t spend much time on them, but now I am not sure I can go a day in math without one–they just have such HUGE bang for their buck.  Just the other day we spent 45 minutes doing a number string together.  It sounds like a long time, maybe, but in that 45 minutes (during which my small group of friends was TOTALLY ENGAGED!), we were able to touch on the clock model, common denominators, reducing fractions, equivalent fractions, improper fractions and mixed numbers.  So cool!

I have heard such positive feedback from my class since we’ve been doing flex time. Most mention that they love the small numbers, the focused nature of the lessons and the time they get to spend with the teacher.  I agree, friends, I’m loving all those things, too!

My favorite thing from our lessons lately  is all of the “lightbulb moments” that I can actually see happen.  It’s so great to see that look of AHA! on a kiddo’s face, and how often these moments even have a sound.  All of the “ahs” I’ve heard lately have definitely made my days.

What do you think about fractions?  How do you think you would react to Fraction Flex Time?  Do you think you’d like it?  Please leave your feedback. 🙂

 

What’s All This “Box Factory” Business?–Part 1

You may have heard me or my students mention the Box Factory lately, and wondered what in the world we were talking about.  Let me tell you about this fabulous math work we’ve been doing lately.
In 5th grade, we have a unit on 3D geometry, focused around finding volume of different kinds of rectangular prisms and figuring out a formula for how to do this (l x w x h or b x h).  This year we incorporated a unit by Cathy Fosnot, which created a context for this learning.  Enter the “Box Factory.”

The basic premise of the investigation is that kids work in a box factory and have to figure out certain things related to volume and surface area (although these things are not specifically named until later in the unit).  There were three parts, and kids worked small groups to investigate the answers to these questions:
1.  If the box factory wanted to create boxes that held 24 items, how many different boxes could they create?  What would the dimensions be of those boxes? Which box would be the cheapest one to produce? There were 16 possible answers to this question, and the students used cubes, graph paper, equations, drawings, or whatever necessary to figure it out.  They had to then create a poster to show their strategies and explain their thinking to show to the other groups.

2. How much cardboard would you need to cover each of these boxes? This one extended the conversation into surface area, and invited students to now look at the outside of the box, instead of just the inside.  Most groups figured out that if they used the formula (2 x L) + (2 x W) + (2 x H) to determine how much cardboard they’d need.  The cheapest boxes to make would be ones that are closest to the shape of a cube, as opposed to a long, skinny box.

3.  If the factory created three sizes of cube-shaped boxes–2 x 2 x 2, 3 x 3 x 3, and 4 x 4 x4, how many units could each hold?  If it costs 12 cents per unit, how much would each box cost?  This one looked at the inside again, and added another layer of multiplication (with money) to figure out the final answers.

 

All throughout this investigation (which goes for about 10 days), the focus is on kids discovering strategies for volume, rather than just giving it to them.  Through the posters they create and the Math Congress conversations we share, they are also working on sharing and representing their thinking.  They are learning how to make their representations clear and concise so that other people can understand exactly what they did.

This poster-sharing part is not new to me in Math Workshop.  But Fosnot’s unit added a layer I’ve never thought of before in math–revision.  Much like when mathematicians publish proofs (and like we’d just spent time on in Writer’s Workshop!), students were able to get feedback from others on what worked, what was confusing, what they should add or take away.  They they had the opportunity to revise and edit their posters before they shared.  With each new poster they created, they added new ways of showing their thinking clearly.   They did this by discussing with their group, and then leaving suggestions on post-its.  We used the “Plus-delta” model to share something we liked and something we’d change:

 

So by the third time around, we were pretty great at showing thinking on our posters.  Even though you didn’t see all the steps, you can still appreciate the clarity and organization of these:

 

 

 

 

 

 

Have you ever done a Cathy Fosnot unit before?  How have you used revision and feedback in math to clarify thinking? What strategies do you use for teaching volume? We’d love to hear about it!