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Posts tagged ‘Christopher Danielson’

Which One Doesn’t Belong (again)

This is a good week.

No.This is a GREAT week.

A colleague and I have the privilege of spending four days with four groups of teachers: Day 1 with TK and Kindergarten, Day 2 with grades 1 and 2, Day 3 with grades 3, 4, and 5, and Day 4 with MS math teachers (grades 6 – 8). Pretty nice.

The opening task of each day is Which One Doesn’t Belong? It’s a pretty nice way to start the day. We show a photo, similar to this one we used with grades 1 and 2.

Screen Shot 2015-07-28 at 8.06.14 PM

We ask everyone to take a moment to think about and prepare a response to the following questions:

  1. Which domino doesn’t belong? Why?
  2. Find a second or third reason why the domino doesn’t belong?
  3. Find a reason why each of the dominoes would not belong.

Then, everyone has the opportunity to share their ideas in small groups. After a bit, the entire group chats about the reasons why each domino does not belong.

Some more good stuff happens as teachers make their own WODB that can they use next week–which for us in this part of Southern California–is the FIRST week of school. The conversations really gets going: ideas are shared, drawing, planning, arguing, advocating for ideas. Pretty nice.



We do a Gallery Walk. After, the groups retrieve their posters, review the reasons that were noted on their posters, and make any revisions they want to based on the feedback shared during the gallery walk.


The best part happens now. We talk about how Which One Doesn’t Belong? is good for kids. We talk about how this is a great opportunity for kids to share ideas, to listen to each other, to talk with each other, to build language skills, and develop ideas about reasoning. We talk and laugh and think. PERFECTION!

Our conversation moves on to discussing the Standards of Mathematical Practice, specifically SMP #3: Create viable arguments and critique the reasoning of others. On Monday, we had the usual teacher talk about how WODB supports Standard of Mathematical Practice #3. On Tuesday, we had a different conversation because Christopher Danielson posted this statement on Twitter:


Tuesday’s conversation was different. More serious. More focused on our responsibility to help our students develop good habits to use while they work on interesting and perplexing questions, scenarios, tasks, and problems.

Thank you, Christopher, on behalf of our kiddos.

Which One Doesn’t Belong?

Summer Math Camp = Five Days +  Educators + a Focus on Learning

We spent quite a bit of time considering the underpinnings of the frame for the five-day program. After considerable deliberation, we determined the structures we would use to engage the campers in thinking about teaching and learning would be exactly what we want classrooms to be built upon:

  • Building Community
  • Promoting Conversation
  • Encouraging Exploration

We then moved to the next step in our planning: THE HOW?

How do we accomplish this? How do we make it a transparent component of the five days? How do we start camp? The how was following by and connected to the what. What opening task would we choose and how will it support our underlying structures?

The Question: What do you choose to be the opening task?

The Answer: Which One Doesn’t Belong?

We started with this image from Christopher Danielson’s book, Which One Doesn’t Belong? and asked everyone to take a moment to consider which shape doesn’t belong and why.

Screen Shot 2015-07-17 at 8.40.48 AM

The educators then thought about these two statements:

  1. Provide more than one reason that the shape you chose might not belong
  2. Offer a reason why each of the shapes might not belong

We asked that they ensure that each person in their group had enough time to ponder, notice, and formulate ideas prior to engaging in a group conversation.

The Result: LOTS of conversation

We then showed the next image, from the website Which One Doesn’t Belong.Screen Shot 2015-07-17 at 9.19.36 AM

After the table conversations were concluded and a brief whole group discussion was had, chart paper and markers were distributed, and directions to create a WODB that your students could discuss in the opening week of school were posted. The groups set to work creating their posters.

The energy and the conversations the groups generated were amazing. We heard consideration about number size, entry points for all kids, WODB as a formative assessment tool for the Standards for Mathematical Practice, specifically practice #3, and all kinds of important stuff.

After the charts were finished, they were posted around the room.


Each camper grabbed some post-it notes, selected a chart that was interesting, and off they went on a gallery walk. We used the following protocol for the gallery walk.

  • Take a moment and individually think about the options displayed on each chart
  • Decide which one doesn’t belong
  • When all members of your group are ready, share ideas and explanations
  • Select one of the ideas and the explanation and record it on the wrong side of a post-it note, and attach it to the chart

A side note: If the ideas are written on the wrong side of the post-it note, groups are not influenced by the ideas already shared. If a group wants to check out what others have written, they can always check after posting their idea. The team that developed the chart will have a larger set of original ideas, not just variations on a theme.


At the end of the gallery walk, the team retrieved their chart, discussed the information on the post-it notes, and made revisions, as needed.

The Opening Task debrief encompassed the following topics:

  • general thoughts
  • feedback from the gallery walk
  • instructional moves that were used
  • the critical idea of providing an entry point for a task
  • inclusion of all kiddos into the conversation

What I learned:

  1. It is really hard to resist the question “which one doesn’t belong?” even at 8:15 am on a lovely summer morning.
  2. Gallery walks need to be purposefully structured. When organized as such, they become a strong instructional tool that promote mathematical conversations.
  3. When the teacher participates, students emulate the academic modeling.
  4. The closing structure of the opening task needed to be stronger, more focused on the learning and the learner. It needed something similar to the question written by Nicora Placa her blog post on Bridging the Gap.

Doing mathematics: Write a about the activity from the perspective of a learner. Think about the learning processes. What helped you as a learner? What helped you sort out the mathematics?

Over the course of the next two weeks, I’ll be using a similar version of the opening task with a few groups. I am interested in how the use of a different closing reflection might impact the learning and the learners.


  1. Talking Math With Your Kids–a blog hosted by Christopher Danielson
  2. Which One Doesn’t Belong–a blog hosted by Mary Bourassa
  3. Bridging The Gap–a blog hosted by Nicora Placa


Our grade 8 team has been working together for about 4 years.  We have a pretty good system in place, and by all measures, our kids have been doing just fine.  Our district has always provided time for us to collaborate and to learn; through lesson study, data teams, or just by giving us time to work together. With all of the opportunities we have for serious conversations about learning and teaching, we started asking questions.  It was when we started asking questions that “got under the kids’ thinking” that we began to see things differently, and we realized that we had some serious work to do.  (The quotation refers to Cathy Fosnot’s eloquent description of what happens when you ask kids to talk about their thinking.  She shared this during her presentations at the 2013 CMC-South Math Conference in Palm Springs, CA.)

Based on what we learned by asking our kids questions about their mathematical thinking, we decided this year we would focus explicitly on our own learning.  We began the year by reading the Standards for Mathematical Content and the Standards for Mathematical Practice.  Then, we selected Functions as our first unit of study.  Our first few conversations were centered around an idea we read about on blogs and tweets shared via the MTBoS (–what are the 4 big ideas of functions?  Our first draft list looks like this:

The Big Ideas of Function (take one)

  • Functions describe a situation in which 1 quantity is determined by another
  • How are 2 quantities related
  • Use Functions to model relationships between quantities
  • Interpreting graphs and relationships

Our first draft list was based on reading the content standards, side-by-side, with the Progressions Documents from The Institute of Mathematics and Education.  We also used documents and resources from the functions class organized by Christopher Danielson, at Overthinking My Teaching.  We are slowly making our way through some of the resources he shared–an article written by Shlomo Vinner entitled The Function Concept as a Prototype for Problems in Mathematics Learning, the work of the School Mathematics Study Group on functions, and tasks from Mathalicious and Connected Mathematics.  Each time we meet, we bring other resources and documents into the conversation.

We want to give a shout out to Fawn Nguyen for creating the site visual  It has been a great resource for us as we investigate the big ideas of functions.

It’s an interesting and crazy journey.  We are learning about and deepening our understanding of the same ideas, at about the same time our students are investigating the ideas.  Makes for some challenging and frustrating days, and for some really fabulous days–all of which are providing amazing aha moments for our kids and for us.

We meet tomorrow afternoon to do some more work.