Once your students have done a number of Which One Doesn't Belong, they should be able to create their own. I described what I do with my calculus classes here, but thought I should take the time to outline my creating process.
Thanks to Chris Hunter, both when I am vetting or creating a WODB, I use a table like this where there are 4 criteria/characteristics labelled along the top.
I consider it a strong WODB if 3 of the items share a characteristic that is not present in the 4th. For example:
The criteria used for Shape 5 could be:
I find that working through one like this with students is a really important step for them to understand that "It's the only one that's pink" is not the depth that we are looking for (unless you are looking at colours!).
I also strongly encourage you to do some Incomplete Sets before your students create their own. Here is an example:
I love that there are many different options for the missing number here. And students (may) quickly see how helpful the table is to ensure a strong WODB.
What have I missed? Let me know in the comments!
We started the day by looking at the remaining visual patterns from yesterday. Participants shared their strategies and we talked about finding the simplified rule IN the pattern as explained by Hedge in her recent blog post here. There were really interesting strategies used for the last pattern - the one that I had really gotten stuck on this semester. I showed them my (Dave Lanovaz's) clever solution, which I blogged about here.
I wanted to get everyone up and moving so we did the "Don't Lose Your Marbles" activity next. I don't think I have blogged about this one, so I will try to describe it in more detail. I do this activity on day 1 of grade 10 academic. It allows me to observe students working in groups and really gives me a feel for the class without them even realizing it. They also talk about math and help each other recall some of what they learned in grade 9. Each group has to determine a relationship between the height of a ramp and the distance a marble will travel after going down the ramp. Here is the handout I give.
Although the relationship is actually quadratic, my students use a linear model which works well for the relatively small data that is collected. Also, my MPM2D students have only modelled linear data so they don't have anything else in their toolkit (you could throw this wide open in Algebra II). I tell them that there will be a competition at the end (with a prize!) where they will need to determine the height of a ramp that will allow the marble to travel a particular distance (I use masking tape to put a start line and finish line on the floor - they measure the distance).
It is really interesting to watch students collect data. Some will do repeated trials and average the results, others are not nearly as meticulous. The ironic part is that most school floors are nowhere near level so attending to precision while collecting data in this activity does not guarantee a win at the end. However, I really like this activity for the math it pulls out and for the opportunity to learn about my students.
The next activity we did involved looking at this picture:
Just as I do with my students, I asked what questions they had. The participants in my class came up with a good list which I wrote on the board. They included "How big is it?", "How old is it?", "How many creatures live in it?", "How many houses could be built from it?", and so on. Great! My students do this in groups on big whiteboards and then go around the classroom to see what questions other groups came up with and together, we choose the "best" question that we can answer. This question is usually something that requires finding the volume (how big is it? how many chairs/houses/toothpicks can you make from it?). I gave them some information to help them find an answer:
What happened next in today's class was awesome! Some chose to look at the shape as a cylinder, or more specifically, as three cylinders. Others looked at it as a cone. It is actually more of a truncated cone, or frustum. I have seen all this before. What I hadn't seen that was so cool was someone who did an exponential regression on the diameter vs. height data (or was it radius? - someone will have to help me out with that question). This is what it looked like:
Wow! A perfect fit! (I had no idea.) They then used calculus - volume of revolution (which is why I think we need radius, not diameter) to calculate the volume. How cool is that?!? Clearly, I don't teach teach volumes of revolutions of solids, but it was exciting for me to learn a new way of solving this. We did look at the "actual" answer on the website, but I think that as with my students, that was secondary to the work they had done. I have blogged about this, minus the calculus part, here and here.
We spent the last part of our class time on a Desmos activity:
All of the Desmos activities can be found at teacher.desmos.com and they are really well done. They allow students to go at their own pace and the teacher can see what each student is doing the whole way through. This lets you know who might need a little individual help as they work through the activity and when you might need to stop the whole class and work through a common error. If you have not checked out these activities yet, you need to do that!
I will be attending some CWiC sessions this afternoon and doing one of my own on Which One Doesn't Belong? I have blogged about WODB? a number of times... announcing the website and incomplete sets may be the most useful links to provide here. Oh, and the website itself is wodb.ca.
I am extremely happy at how well received the Which One Doesn't Belong? website has been. I announced it here and wrote about how I planned to use it in my calculus classes here (I will blog about how it went eventually). Others have also contributed in fantastic ways. You can keep up with submissions to the site and blog posts related to WODB? by following @wodbmath on Twitter. Last week Chris Hunter and I presented at Global Math Department's weekly meeting. I learned a lot from Chris and through that process comes a new page on the site: Incomplete Sets.
The idea is that students would have to logically determine what is present or absent in each of the objects shown, and find a way of completing the set. This can act as a stepping stone between students finding which one doesn't belong and creating their own set. Chris showed a great way of organizing characteristics that would look something like this for the above set:
Since seeing Chris do it this way, I have used this type of table to sort through submissions to the site. I love how logical it is and how it makes it obvious whether you have a solid set - one where each group of 3 objects have something in common that the 4th does not.
Here are two more that I made:
I should specify that when I made these I had characteristics for all four objects, but only showed three. I love that there could be multiple correct answers and that students need to be able to justify their reasoning.
I hope you will join me in creating new complete and incomplete sets! Please use the submission form here and let us all know how you are using these with your students. I have an ever-growing list of other improvements/additions to the website. Please let me know what you would like to see by leaving a comment. Thanks for all the support!
Today is Monday so our warm up was a counting circle. We started at 47 and counted down by 3.
When we got to student B we stopped and I asked what number we would be at when we reached student C. Some counted down 7 times to get to 8 and then others shared their strategy of multiplying the number of students to get from B to C (7 students) by 4 (because we were counting down by 4) and subtracting the result from the number that student B said. I hope that exposing students who would count down for each student to an alternate strategy will help them add this to their tool kit.
Next up, Which One Doesn't Belong? I showed them the logo first and asked them which one they thought didn't belong.
The first student said the bottom left because it was pink. The next student said the top right because it was a circle, not a square. The next one said the bottom right because the font was white and the top right also because the font is different. I wanted to make sure they understood that there was a reason for each one to not belong.
Then I showed them their task.
We talked about using volume and surface area as criteria and looked at the volumes of the prisms shown:
They told me that using a cylinder would be a bad idea as both the surface area and volume involve pi which means that it would be impossible to get either surface area of volume to match that of a prims. They said that they could use triangular prisms. I mentioned that they could draw pictures if they chose to use triangular prisms. And then I let them go.
Well, the Monday morning after March break was perhaps not the best time to give a wide-open task. We did solidify understanding of volume. When they had created one rectangular prism with a particular volume at least one member of each group understood that to get another with the same volume they needed to take the same number of blocks and arrange them differently. That was good. Some groups calculated surface area and found that they were all different. Several groups came up with 3 prisms with equal volume but struggled to move forward from there. One group was doing odd shapes and could have matched volume and surface area. Here are some examples:
One group did come up with a proper WODB? set, but I didn't get a picture. This is the "almost there" picture which I will replace with a good one when I recreate it:
I believe this activity could be really good but I would scaffold it more next time. I would have groups randomly choose volume or surface area and work with that as a required criteria. I will work on a handout to go with this where they can list the criteria they are choosing and show their attempts - more of the record of their learning and progress. I also continue to learn how to better serve their needs and bring out the e.
Four days ago I wrote this blog post about using Which One Doesn't Belong? as an activity for my calculus classes. I have had a lot of positive feedback about it and along the way Pam Wilson tweeted this:
and that also got a good response. So I decided to take this on. It's a good thing that I'm on March break as this has taken a few (!) more hours than I normally have "free" during the week.
<insert drum roll>
Announcing the Which One Doesn't Belong? website at http://wodb.ca/
I really hope that many of you will contribute to the site (some of my children already have!) as that is the only way it will grow. I plan on having my students create their own and will add them - please do the same with your students.
You can also follow @WODB?Math on Twitter.
2015-03-20 - Update
In order to help you use and create WODB?, here are some links.
To help you create:
WODB? Template (SMART Notebook)
Graph software that I use (produces very clean graphs)
To help you use (especially if your students have trouble with right & left):
WODB? ABCD Template (SMART Notebook)
WODB? ABCD Template - white background (.jpg)
WODB? ABCD Template - blue background (.jpg)
Please let me know if there is anything else that would be helpful. Also - I am happy to format submissions if you just send in content.
