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

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?  

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.

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.

• 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!”

• 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!