The Power of Incomplete WODBs

Yesterday I posted the following WODB:


I asked “How would you finish this WODB?” and I appreciate the responses I have received.


These are all great answers, and I would tell my students the same when offered.  The one thing I would do is to remind them what makes a good WODB problem and challenge them to create another response with that in mind.

So, what is the Power of WODB? What makes a good WODB problem? The ability to pick any picture and come up with AT LEAST one description of why that one isn’t linked to the other three.  It may be easy to fill in a reason the last image we pick isn’t related to the three posted, but it also needs to support choosing one of the three.  This is something that my students struggle with at first, then they really start examining the problem from a variety of perspectives- many times more than what they engage in with a “complete” WODB.

So, as we typically do in class, reflect on the Tweets I received on the possible missing part.  Do they provide us with a good WODB problem that allows any of the four to be correct? I know my thoughts, I am really interested in yours.

Day 3: About that “Finding Answers” Thing

My first week or two: introducing my students to the awesomesauce called #MTBoS and showing students examples of what will come this year.  Today- WODB, Would You Rather and Open Middle.

I started with Would You Rather…


Install and maintain a hand dryer or a paper towl dispenser in a public washroom?

Whichever option you choose, justify your reasoning with mathematics.

This was especially fun since most of my students walked in, saw this on the SMARTBoard and looked at me like. “Wha?”  Once I talked about the site and we looked at the text, (yes I know- that’s a very hard thing for students to do), they really got into this problem.  I will warn you, beware the conversations that can spawn with this problem- there were many redirects to get focused back on the original question.  The biggest hang-up for students this year was the “justify your reasoning with mathematics.”  They could tell me many practical or preferential reasons, but connecting those to mathematics was a stretch for them.  It definitely was a great activity to introduce my students to, I know they are thinking differently about things and can’t wait to hear their reasoning on the next “Would You Rather?”

We then transitioned into Open Middle.  I started with something I knew students would feel comfortable with:

Directions: Make the smallest (or largest) sum by filling in the boxes using the whole numbers 1-9 no more than one time each

Note: I didn’t have them consider the negative possibilities
I first asked students to find the largest sum.  This activity went very well, students grasped the task very quickly and immediately I hear things like “My sum is 156.”  Another student would say they had something larger, and things took off from there.  Students like the challenge of this problem, finding a maximum or minimum, but they couldn’t tell me what knowledge this problem gave me about their mathematical skills.  Many didn’t think of place value- they just did it.  There was a conversation about the combinations of numbers that resulted in the same sum, and sadly students couldn’t put a name to that property.  Good thing: students know commutative property.  Bad thing: they can’t use the formal verbiage for it.  Needless to say, the second question of finding the smallest sum went very quick- they are fast learners.  Every student in class preferred this question over being assigned a traditional assignment.  Open Middle will be revisited often this year.
The last task of the day is WODB.  I really like these problems because I learn something from every class.  Today was no exception.  When I put this WODB on the board:
 I once again was surprised by my students.  One student said that 16 doesn’t belong because it had the most factors.  Another student told me 43 because you can make an equation out of the other 3.  Once again WODB brings up great thinking that you might not recognize in the classroom.  WODB allows you to bring a lot of mathematical vocabulary into the classroom, especially the geometric figures.  One thing that drove my students crazy, there wasn’t ONE correct answer- there were many!
I like all of these activities because they take away from the answer finding that usually occurs in class.  My students were surprised that I was allowing them to express ideas that were different than their neighbors but were still correct.  What?  There isn’t only ONE answer you are looking for?  Is this math class?  What is going on?  After a few minutes of talking about math thinking and the multiple ways we can look at solve problems, they started to come around.  The conversations were great, it was good to see students get fired up to share their ideas, they were comfortable with having a different opinion or view.  I am seeing sparks in the eyes when they look at problems, they are going beyond answer finding, yes it will be a good year.