Monday, March 30, 2015

WODB Part 2 Creation Day

This post is student work after day one which I wrote about here. We quickly reviewed the criteria for a good WODB and the big content ideas in the course.

For each of the samples I have shown a picture of each groups final work, a picture of their reasons for each image not belonging and for some groups a picture of all their doodles (brain storming). Some samples have a commentary from our debrief from our lesson study. Lastly this is everything-not hiding anything here folks. If you teach grade 10 applied students in Ontario you know how hard  this work is. We do everything can to engage these students. We try our best.

I think if I was going to do this again I would wait until later in the course when students had a little more depth of knowledge in some areas. Day 1 was amazing. I knew making a WODB would be a challenge. Enjoy.

Sample A

This group basically gave the same image four times - mathematically correct, just subtle differences. Not much math going on.
Sample B

This group focused on linear and quadratic relations. Not much math. Did use a little vocabulary.
Sample C

This group tackled similar triangles and orientation of the shapes. I liked their doodles before they settled on Similar triangles. Felt like they got the idea of WODB.
Sample D

 This group was two english as a second language learners. They really struggled with this activity.

Sample E


This group struggled :(
Sample F

This group spent forever doing quadratics on the graphing calculators. Not much in terms of understanding or clarity.
Sample G


This group tackled knowing the opposite label in Trigonometry (celebrate the small stuff) BUT they knocked it out of the park when it comes to a WODB. I loved the amount of brainstorming they did before they settled. This one made me smile.
Sample H
 Sum of squares - not much understanding.

 Sample I

This is actually a very good example using visual patterns but hard to see as they did it in pencil. The top right did not have the fourth image drawn as they ran out of room. Too bad needed it to establish quadratic relation. Tackled linear and quadratic relations. As you can see by their doodles they played around with this for a while.
Sample J
 This group clearly remembered the day we did visual patterns and used some. No connection to the mathematics however.

Sample K


Lots of brainstorming here but really did not get the idea of WODB. Let us just pick 4 different ideas from the course and say they don't belong because they are each different.
Sample L

Sample M

This group argued, yelled at each other, you name it. Finally they decided on a visual pattern and did a good job. Understood WODB and gave good reasons why. Linear and quadratic patterns :)
Sample N

This group understood WODB. Similar triangles and sum of squares.
Sample O

This group was too busy talking about anything but a WODB.
That is it that is all. Tomorrow everyone does all of these in class. Analyse data. Get it on the board. Rank em all. Winner takes all.

WODB Part 1

If you hang out in the #MTBoS (Math Twitter Blogosphere) you no doubt have came across Christopher Danielson who does #TMWYK (Talk Math With Your Kids) amongst many other great things.

Mr. Danielson was compelled to create a better children's shape book with the premise of Which One Doesn't Belong (WODB) that was designed to not have an answer key. All 4 pictures or shapes can be argued as to the one that does not belong. I love this idea. It promotes thinking, critiquing, justifying and communicating amongst other things. All skills that I love seeing students do in my math classes.

Mary Bourassa has grabbed the bull (by the horns) and created a website WODB.ca. Kudos to her for taking this on. You can follow on twitter @WODBmath.

So I hymed and hawed (whatever that is) about how I could pull this off in my class. Most people in #MTBoS seem to be planning to use this as a class starter. I wanted to do more with it. Here is an overview of what I came up with (actually I lesson studied this with a few colleagues):

Day 1 (this post-WODB Part 1)
Introduce students to the idea of WODB. Look at some old examples and videos. Talk about Danielson's complaint about typical examples. Look at some examples from his book. Look at the example from the avatar for WODB.ca.

Once students got the idea of WODB, do an activity that would have them chose top left, bottom left, top right, bottom right for 10 different examples individually. Then they would analyze the data for one of them. We would get it all on the board. Then as a class we co-created the criteria for what makes a good WODB. Finally, based on the criteria, have students individually rank the ten chosen samples from best to worst. Analyze that data.

Day 2 ( Next day WODB Part 2)
Groups of three, students will create a WODB using the course content. This will be difficult.

Day 3 (Vote day based on the criteria WODB Part 3)
Students will do all other groups WODB. Then they will analyze results for their WODB.
Data on the board. Then rank from best to worst individually ( can include your groups). Winner takes all.

So here is what happened day 1 ( I teach two sections of this course so I did this twice):

Students came in and I asked if any of them had seen or remembered anything about Sesame street. Much conversation about different characters and different things they remembered. I prompted if any of them remember any games they played and we got to "which one doesn't belong" or "one of these things is not like the others".

I showed this video and stopped it as soon as the image came up (about the 12 second mark). Of course I picked this video- something about circles for me. This led to lots of discussion about which one did not belong.

"Top right because it is the smallest one."


"Bottom right because it is the thickest chalk."

And so it began. Students volunteering a variety of reasons for which one did not belong.

Eventually I got this.

"Of the three panels the middle panel does not belong because there are no circles drawn on it."

hmmmm student has a point

and then of course the student who blew our minds and did the meta-cognitive.

"Hold on sir, they all belong. See we have an argument for all of them not belonging. This means they all belong to the category of not belonging." Of course the entire class erupted into cheers and I acknowledged this student's deep thinking.

I diverted to this website quickly.
We hit the play button and got this.
"Really sir?"
Perfect-they thought this one sucked.
Me: "Why don't you like this one?"
Students: "It is so obvious."
Yes it is!!!
Me: "Anyone want to take a shot at picking a different one for some reason."
Student: "Could we use primary colours?"
Me: "Not quite-red and yellow are primary but yellow and orange are not."
I divert to this image from WODB.ca
I tell students to not say a word. I get them all to stand up. I instruct: "Front left corner of room for top left. Front right corner for top right. Back left corner for bottom left. Back right corner for bottom right."
While students are moving and I interact with them about the reasons why they chose (pretty evenly distributed and multiple reasons for each one) the one they did I am walking around the room placing stacks of slips (chose and reason slips), an envelope and a WODB image and placing them on the ten pods of three desks that I have set up around my room.
We discuss whether this "Which One Doesn't Belong" is a good one. It is mentioned that there are people in every corner. It is mentioned that there were more than one reason for each one. This is important - the seed is planted.
Before anyone leaves a corner I instruct about the next part.
"Absolutely no talking. There are ten images at ten different pods. Pick a starting point (1 or 2 start at each pod). Work your way around the room and pick the first one you see as not belonging and explain why on one of your slips. Fold the slip and put it in the envelope. When your done go back to the one you started at. Go for it."
This was awesome-not a word-total engagement.
Here are the ten WODB's. These are from the WODB website, except #4 which I scammed from a Dan Meyer tweet. Thanks to all for posting to the site.

Once students got back to their starting pod I had them analyse the data and the reasons for the one they started on. Here is the results for both classes combined (first number am and second number pm, third number total from both classes):

Here are some sample responses as to why students picked certain images.
For Image # 10.
Top Left         - only one that goes through three quadrants
                       - only one that goes through the negative x axis
Bottom Left    - only one under the x axis
                       - least slanted
Top Right        - line goes through the x axis and y axis at the same point
Bottom Right   - line goes down instead of up
For Image # 3.

Top Left         - smallest upper number
                       - only one with denominator double digits and numerator single digit
                       - biggest difference
Bottom Left    - smallest sum when added
Top Right        - largest sum when added
                        - only one with denominator and numerator double digits
Bottom Right  - doesn't have a two
                        - highest percentage
For Image #7.
Top Left         - widest
                       - goes through all boxes
                       - only mirror one
Bottom Left    - opens up
Top Right       - no x intercepts
                       - shortest
Bottom Right  - just touches the x axis
For Image #4.
Top Left         - Best Bond
Bottom Left   
Top Right       - sexiest
                       - newest Bond
                       - plain background
                       - most attractive
Bottom Right - it is a cat
At this point I posted all the images on the front board along with all the data of how many people chose each. I asked so what makes a good WODB? This is what we came up:

Then based on this criteria I asked students to rank the ten images from best to worst. Here is the raw data with averages (far right side bottom) and final rankings (far left side bottom).
I enjoyed the first day of this. I think the students understand WODB. Next up create one based on the course content - challenging!