No really, which one doesn't belong?

dedicated to all the parents of teens and preteens

I'm guessing in the last 24 hours of being home from school, that your teenager has begun at least one argument. Teens seem to love to argue. My favorite part of teaching teenagers math was always the logic and deductive reasoning section just for this reason. It's one way that they make sense of the world: does that always work, is there an exception to the rule, could there be another way?

One way to embrace this, and to sneak some math and art learning in along the way, is through a structure called "Which One Doesn't Belong?". Here's an example:

In the shape above, which corner doesn't belong?

Don't skip too far ahead too fast. Did you find a corner that doesn't belong?

     Which one?

           Why doesn't it belong?

Can you find another corner that doesn't belong? Does it have more than one reason it doesn't belong with the others? If you can come up with more than one reason, is one of the reasons more convincing than the other(s)?

One of the fun parts about these is they are designed so that each corner has at least one reason it doesn't belong with the rest. You can find more these here and here.

Want to make sure this is hitting at the math your 4th through 6th grader needs? Try mixing Fraction Talks with a Which One Doesn't Belong:

Want to push your middle schooler into argument overdrive? Have them create their own "Which One Doesn't Belong" (WODB).

To begin, I recommend starting with an incomplete set. There are some incomplete sets here, or you can take any one of the WODB examples and cover up a corner and challenge yourself to come up with an alternative for the covered corner. It's not as easy as it looks -- be sure that your newly created corner still allows each corner to have at least one reason it doesn't belong. (There's a blog post here for more help on this.)

What becomes nearly essential is organizing your thinking. One way to do that might be to consider creating a chart like this one to help you keep track of the characteristic and the corner that matches it. Here's an example filled out for the "Shape 55" we looked at above in this post.

Once you figure out how to complete a set, you're ready to create your own. This is a great place to think outside the box and use the things around you to figure out if you can come up with a set of four things where each one has at least one reason it doesn't belong. Check out how some folks have experimented in using photography and the world around them to create their own WODB. You can grab items around the house, look at the environment around you or use images found online.

Trying to make your final product look nice? I've seen folks use many online tools and phone apps to organize the photos into the same 2 by 2 grid as the ones Ive shared in this post. Check out these tools and apps if you need some help: Pic Collage, Diptic, Layout, Fotor, PS Express, Pic Stitch, Pic Play Post, and Google Slides.

Want to Amp Up the Arts & Math in steAM? Check out a few more resources for the work and how to ensure you're giving math and the arts a top spot in your work here.

Share what you create by posting it on Twitter with the tags #WODB and #SDCOEmath. I can't wait to see how argumentative your teens can get!