Undressing Tables, Naked Numbers and Modeling

I had the 2nd grade names and the information I needed, so I created this table and asked the students WDYN?

Screen Shot 2014-11-04 at 9.09.16 AM

Immediately students recognized the names of their 5 classmates and the perplexity session began! Lots of different ideas and “noticings” were floating around the room:

  • They all have different numbers but some people have the same numbers
  • Trent doesn’t have any numbers less than 10
  • Trent also has the biggest number of “what-evers!”
  • My names not up there?!
  • No number is greater than 25

When asked WDYW it was unanimous…What’s all the information on the chart for?  

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I stole the idea from Dan when he discussed Edmonton’s water consumption during the gold medal hockey game of the 2010 Winter Olympics.  Dan took the graph, stripped away the labels which left it more open for conversation.  Steve Leinwand might be the GodFather of approaching lessons this way. He discusses the idea of undressing the data in Accessible Mathematics.

After a really great conversation with students about the data on the label-less graph, I threw all their notice and wonderings into a context by adding labels.  I had never tried discussing data and numbers out of context before but when we talk about multiple entry points and making math accessible…this was a home run.

Screen Shot 2014-11-04 at 8.23.57 AM

The WDYWs went far better than I could expected but full credit goes to the “No Name” table.  It allowed students the time necessary to digest and discuss numbers through observation and comparison.

Side note: When students were discussing the table something really cool happened which I have never noticed or looked-for before.  While listening to students, I noticed that when they compared only Marcus’s minutes to each other they focused on the digits. But once they began comparing Marcus’s times to Isabella’s times (or any other student) they shifted from focusing on digits to focusing on the whole number (I like this way more). I’m still trying to understand if this is something I can purposefully control.

Their WDYWs:

  • Who ate the fastest on each day?
  • Who was timing them and why?
  • Were they all eating the same lunch? (we made sure all students got lunch from school)
  • Who was the fastest eater last week?  *main question based on student votes*

I was amazed to see the variety of ways that students used mathematics to model who was the fastest eater last week.  Students worked in pairs and here’s some of the highlights from student thinking:

  • 3 groups immediately said Dartavious because he had 8 minutes on Friday and mentioned it was the fastest time for the entire week. But then we discuss the other days and times and they wanted to change.

Screen Shot 2014-11-04 at 8.26.36 AM

  • 1 group said Ja’Nay because she had 2 times under 10 minutes.
  • Using Educreations, 2 groups added up the total number of minutes spent eating lunch and determined that Trent was the fastest because he had the fewest minutes overall.  Loved this thinking because although they didn’t average out the minutes per day (6th grade standard), the result is still the same.

All of the aforementioned responses I was expecting but with students I have learned to expect the unexpected.

A pair of girls were quiet as ninjas as they worked on the front board until one said “Mr. Fletchers, we’re done!”

Screen Shot 2014-11-04 at 8.47.58 AM

Who uses a yellow expo marker?!? These two little gems of 2nd graders…that’s who!

  • Me: Wow!  This looks really interesting.  What is it?
  • Girls: We bunched the numbers together to find out who was the fastest eater. (We had a small conversation as to why they bunched the numbers the way they did)
  • Me: Ok I get it.  And when you bunched the numbers what did you figure out?
  • Girls: Dartavious and Marcus have too many big numbers so they’re slow.  Then we compared Isabella’s and Trent’s numbers. Trent’s 12, 11, 11 are way faster than the 15, 14, 14 so Trent is faster than Isabella.
  • Me: Ok and what about Ja’Nay and Trent?
  • Girls: She was tricky, but they each have 10, 12 and 24 so those numbers don’t count. But Trent has two 11s left which is faster than Ja’Nay’s 9 and 16.  So that means that Trent was the fastest eater last week than Ja’Nay.

Boom!

Reasoning, conjectures and modeling…oh my!  It’s time I start undressing more tables!

About gfletchy

K-8 math consumer trying to listen and learn each day. Stay thirsty my friends!
This entry was posted in Making Math Accessible, Measurement and Data, Modeling, Patient Problem Solving, Teaching in a Context and tagged , . Bookmark the permalink.

3 Responses to Undressing Tables, Naked Numbers and Modeling

  1. Joe Schwartz says:

    Brilliant idea. I am totally stealing this. Did you give them the context all at once? What would happen if you first gave them the days of the week part. What might the numbers mean then? After that maybe the unit-minutes. What might take these kids that amount of time to do each day? Then finally the title. I love this because it scales up to every grade level.

  2. gfletchy says:

    Great point Joe! I definitely could have “Milked the Data” more and been more patient when releasing/giving it to students. Even when I’m “less helpful” I appreciate your reminder to slow down!
    Reminds of your post that “Had Me at Hello!” http://exit10a.blogspot.com/2014/01/what-would-happen-if-we-took-problem.html
    Love your critical eye my friend!
    Cheers!

  3. Christy says:

    I did this with a bar graph with my students. First it was just bars and numbers, then I added colors as the categories. They eventually figured out it was about shoe color. Everyone had a title, categories, and numbers on their bar graphs the next day! Love extending it with numbers and the connections your students made! I will have to try that!

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