Notice Wonder Meets Numberless Word Problem

Saturday, November 21, 2015 / 16 comments
First, let me tell you how much I love Twitter for the #MTBoS.  This connection has allowed me to collaborate with the great, Kristin Gray, all the way in Delaware from California!  That in itself is pretty awesome!

Kristin Gray (A.K.A. @mathminds) recently tweeted that she was going to begin working on planning a first grade lesson and posted a blog a few days ago about 1st Grade Story Problems.

After all of the discussion about the lesson that she was going to do (and a little peer pressure) I decided to scrap my lesson on time for the day and give the lesson a shot.  It was the last day of school before Thanksgiving break anyway. ;)  (I told my student teacher that this was a "Do as I say, not as I do" situation.)

I had an hour and twenty minutes for math... which wasn't enough.
We began with a number talk.  We rotate number talks and estimation routines daily in class.  I planned the dots purposefully hoping a few strategies/properties might surface.  There was a lot that could happen here: associative property, commutative property, making tens strategy, doubles strategy, or at least counting on.  In Student Centered Mathematics, Van de Walle said that the making tens strategy is perhaps the most important addition strategy, it builds a foundation for working with larger numbers.    What I was hoping for most was that the students would see the 2, 6 and 8 and make a ten with the two and the eight.  This strategy would be very helpful in the following math lesson.

The number talk helped set the stage for the following math lesson.
We began with the same very open "Notice/Wonder" as Kristin Gray.
My kids are familiar with "Notice/Wonder" and I can tell that they know where we are headed before we even begin.  Not sure if I really like that or not...  I really liked how open Kristin's class was during the "Notice/Wonder."
We did one more notice/wonder.
(Yay!  I had my first stab at numberless word problems!)  
What I love most about what came out here is the discussion about the word "some" lead by  Carson.
After some rich discussion, we moved on to the task.
I projected the question for the class and left it up for them to refer back to while they were working.  What I was hoping for was that they would use some of the strategies they have been learning in number talks and apply it on their own.  Here are a few samples.
Many kids were showing the making ten strategy in some way in their work.  I noticed that the kids who used 120 chart were marking the digits 4, 6 and 13.  They still got to 23, but they weren't marking 6 more from 4 or 13 more from 4 or 6, they were just circling the numbers that were associated with the problem.  We had mentioned once in a missing addend problem that we could put a box for a missing number, or maybe we could write "n" because it's the first letter in number and that would represent the missing number.  I see River playing with that idea here.  She said she had all n's first because when we did the first "notice/wonder" sessions we didn't know what any of the numbers were.  I can see in her work that she is also trying to prove that she went back into the context of the story problem.  We talk about this often.  Some of my typical questions I ask kids when they are finishing up their work are, "Does it make sense?  If someone else sits down and looks at your work will they be able to understand it?  Did you go back into the context?  Where is the proof? Can you show your thinking another way?  What equation could you write that would represent your work?"
After students were finished, we did an "Around the World." I asked students to stand up behind their chair with their white board marker.  When I said, "Around the World" students switched seats with anyone in the room.  Then they had about 2 minutes of quiet time to look at the work where they were sitting.  Then, they table talked about the work where they were sitting.  They had to explain the work of their classmate.  If it was wrong, they had to explain why.  They had to explain how/if it connected to the story problem.  Then, they left a little star, happy face or a question mark before I called out "Boomerang" and they went back to their seats. I had many representations to choose from for the "Connect" (5 Practices) portion of the lesson.  We moved from concrete to representational to abstract.  Something else I was happy about in this lesson was that it exposed a limitation of the part-part-whole mat.  First graders, at least mine, are overly reliant on this tool.  This was a good time to talk about why this tool might not be the best one to use and how a tape diagram or number line might work better.  I noticed that a couple kids were off by one on their answer to the problem.  In talking to each of them it was due to a counting error on the 120 chart. While students were working with their tools I had a decent amount of time to walk around and talk to them about what they were doing and take a quick inventory of which students got the correct answer and who was using strategies.  I have an inclusive class this year.  I highlighted my identified special needs students.

We ran out of time for an exit ticket before recess, but I had them do it when they returned.  These were a few that I found interesting.
We have just finished a unit on place value last week so it was
neat to see this student using some of those concepts here.

It was cool to see this student choose numbers that make a ten.

Wow!  He was showing off using larger numbers, although they are easier to
add together. I like how he composed and decomposed the numbers.
This is from one of my struggling students.  He
chose smaller, safer numbers, but he was applying properties
of addition. :)

I can see ideas about place value surfacing here.

Thank you, Kristin, for a wonderful lesson that showed so much student thinking! It was so fun working with you!  Click the link to read how Kristin's lesson went:


  1. Jamie,
    I learn more from reading your blog about teaching primary math than anywhere else. Have you done a post yet about Math Talks - what is it? How do you set it up? How do you facilitate discussion? Something really basic, for a novice like me who doesn't know anything about them? I'd love that if you could write it!
    Thank you friend!

    1. Hi Michelle!
      I sent you a couple things about Math Talks. The ten second answer about discourse is start with number talks. Use kids' work to fuel the discussion. Have kids explain other student's work. Ask good questions. Empower kids to ask their own questions. Also, incorporate math into writing.

    2. Great question Michelle and Jamie answered so well. I would be happy to chat with you about this awesome strategy as well! In our district, we have been using them in 6-8 for six years and they can transform class discussions. The K-5 buildings are now doing them more which makes me happy! :)

  2. Thank you Kristin, Jamie and Brian Bushart for inspiring me to take the plunge on a numberless word problem. Your blogs gave me such insight into the how and why that I felt comfortable giving it a try this morning when I had a last second opportunity to teach a Grade 2 subtraction word problem lesson. Students shared that they most enjoyed being able to choose "just right" numbers for themselves (I love the literacy connection). They said that the most challenging part was selecting numbers that "made sense" in the context of the problem. I loved that for some students, this was very important to them. This gives insight into their depth of understanding of the problem (background knowledge) as well as their number sense and estimation skills. My biggest regret is not having enough time for students to share and hear each other's reasons for the numbers they selected, the models they used, and their computational strategies. However, I was able to connect with many students individually and their worksheets shed light on their strategies. I feel a huge sense of success in witnessing so many Standards for Mathematical Practice at play in this one short 30 minute lesson and in seeing so much engagement and interest on the part of the students. So much potential here. Thank you again.
    Lauren Giordano

    1. Hi Lauren!
      I'm so glad you took the plunge! It's new to me too! I feel you on the time issue. I use the 5 Practices daily and sometimes we run out of time or steam by the time we get to the "Connect" portion of the lesson which is the most important. When that happens it is a good idea to either collect student work or take pictures of student work to use at the beginning of the next lesson. What a great launch for the next day's lesson where you might build on the ideas learned in the lesson from the previous day!

  3. I am thinking of trying this in a grade 2 class. I wanted to model with the open ended one and do the notice and wonder and then have them solve the problem. I may differentiate by giving my low group a total number. Do you have any more sample problems?

    1. Really, you can take any word problem and take out the numbers and put in the word some to reason with before you give them numbers. What standard will you be working on?

  4. I am hoping to share the idea of Numberless Word Problems with my teachers when we come back from break. Thanks for sharing.

  5. Thanks for the link! I am definitely going to try s numberless word problem when we go back in Janaury. What other resources would you suggest? Currently doing math talks and number talks. Looking to do more notice and note. Any other suggestions?

    1. What grade do you teach? Have you checked out www.estimation180.Com ?
      If you are in K-2 I have primary measurement tasks I can give you the link to. Have you used WODB?

  6. Hello! This post was recommended for MTBoS 2015: a collection of people's favorite blog posts of the year. We would like to publish an edited volume of the posts and use the money raised toward a scholarship for TMC. Please let us know by responding via email to whether or not you grant us permission to include your post. Thank you, Tina and Lani.

  7. I just read this again as I work with a middle school teacher on story problems. This is so informative and helpful. This time reading I'm loving how your exit ticket was the kids basically creating their own problem. I have not thought to do that before (well I don't teach math but still...ha!) I also love how you're tracking information not just about if the problem is correct, but what strategies are being applied. Your math mind blows my mind Dunk!
    Anyways, thanks again for your expertise and I wish you lived in CHICAGO!!! xo bff :-)

  8. You guys are so amazing. I'm a SPED resource/inclusion teaching assistant and I've spread the love throughout our K-5 campus about numberless word problems. It's so awesome to see their thinking.

  9. I enjoyed the numberless word problems and the notice and wonder. I plan to implement it on our campus


Powered by Blogger.
Back to Top