Monday, March 16, 2020

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!

Thursday, July 12, 2018

Donuts, Lattes & more

It was a hot summer day. My cooperating teacher had handed me the keys to the classroom the day before and said he’d be around eventually to check on me. On my way in to work, I stopped by the local donut shop and ordered 2 boxes of donuts, the classic cake kind with rainbow sprinkles and varying colors of frosting. I arrived at the portable building, used the key to open the door, turned on the lights and switched on the air conditioning to mitigate both the heat and musty smell that seemed to be embedded in every surface of the room. I carefully cut each donut into pieces, laid out paper towels on each student desk and tried to steady my hands and nerves until the students all arrived. 
Welcome to my first day of teaching.

“It smells good in here,” said the first student to walk in.

“Are you going to have us clean our desks today?” said another.

“I hope you have the chocolate ones in the there,” said one student who spied the boxes of donuts.

“Are you trying to bribe us to behave?”

“Wait until the teacher finds out!”

I thought I was doing okay, until that last statement filled the air. Any illusion I had that these students viewed me as their teacher was gone. Just because I had the key and was the only one old enough to vote in the room didn’t mean I was a teacher to these students. 

Take a breath. Take another one, I thought to myself.

Once the room filled and the bell rang, I wrung my hands together one last time and said, “I love donuts.” 

My confession that caused a few students to chuckle.

“The other day, I bought a donut with sprinkles and I felt like it just wasn’t right. There just weren’t enough sprinkles on the donut. It looked like some kid had come by and licked half of them off, or the sprinkle shaker was clogged, or the baker was in a hurry and only gave them one shake of sprinkles instead of 3.”

I took another deep breath, “So I began counting sprinkles.”

“Man, you must be lonely.” Said one kid quickly.

“Maybe,” I replied. “Mostly, I’m curious. You’ll learn that about me. I wanted to know just how many sprinkles were on that donut. But I have to tell you, it was hard to count all the sprinkles. You end up going in circles around the donut, and I couldn’t remember where I began and where to stop…I was going cross-eyed over sprinkles. And I thought, there has to be a better way.”

We had a conversation about what we could do to make it easier to count. For some reason, most of the students were ready to offer ideas. It could have been the smell of donuts, or the hope that there was a reward for good answers, or maybe it was just curiosity…their own or mine. We spent the day counting sprinkles and looking for relationships between the size of donut piece of number of sprinkles. We mapped rates, and looked for patterns, and tried to make conjectures and test them. Did chocolate frosted donuts have more sprinkles than the vanilla frosting? It sure looked like it, but was ‘looking like it’ good enough? What evidence would convince you?

The day was long. Not the longest of my career, but I remember sore feet, feeling like I was losing my voice, and wondering if I had the strength to go back for another day. I got back to my parents’ house, where I was staying until my first paycheck came through (#newteacherreality), and my dad asked about my first day of teaching. I smiled. The donuts and sprinkles worked.  He started to laugh.

“What do donuts have to do with math?”

“How are they not math?” I asked back with incredulity. I tried to explain it to my dad then, as I have on numerous occasions since. Sometimes I think he gets it -- I see math everywhere. I’m like the math version of Cole Sear in Sixth Sense…but instead of seeing dead people, I see math. Is that more creepy, or less? Hmm.

Math is all around us. It’s in the numbers we see, the things we count, the shapes, lines and curves we notice, patterns, structures, artwork and symmetry. I could go on.

But I recently realized that my children don’t see math everywhere. Actually, I don’t think most people do.

My son reads every sign he sees when we’re driving. He’s in the stage where he can decode words, and it’s a revelation to him that these signs that were in plain sight for years now have meaning. He can’t stop reading them. Similarly, my daughter is learning her letters and is particularly fond of the letter S. She will shout when she sees an S in a sign, on a package at the store, or sees one as a shape in the clouds. In the same way that these naturally playful games help build early reading and literacy skills, I want to be building my children’s mathematical skills.


“This is for you. Somewhere inside you is a child who used to play with numbers, patterns and shapes. Reconnecting with your inner mathematician will improve your teaching and benefit your students, and it will also benefit you.” 

Zager, T. (2017). Becoming the math teacher you wish you’d had: ideas and strategies from vibrant classrooms. Portland, ME: Stenhouse. (p. 39)
 
So this summer, I’m trying to up my game, for my children and perhaps for you. There’s an opportunity to learn to see math everywhere, for you and for your children.


Check out the #mathphoto18 prompts on Twitter or view some of the submissions at https://mathphoto18.wordpress.com. Each week, there is a challenge to find something mathematical in the world around you. Just like my daughter looks for “S”s, the first week of #mathphoto18 was about looking for lines. You’d be surprised just how many lines you encounter every day! Take a photo, tweet and tag it, and check out what others have found. 

You might be surprised, but just by reading this post or checking out the photos, you are more likely to see math all around you --it's actually a scientific principle


Want to up your game? I’ve found almost as much joy in not finding what the prompt is than in finding the prompt. For instance, last week was #primes…I can’t tell you how many things I counted that ended in not being a prime. While there was always a slight ting of disappointment in not fulfilling the challenge, I realized that I had a lot of curiosity around #howmany different things there were. I’ve never counted so many things in a week before. Ever. I counted chairs, lights, nail hole patterns, plants, doors, windows, people… Sometimes seeing the actual thing has to be equally important to looking for it and recognizing that I didn’t see it. Knowing whether or not it is mathematics means I’m enhancing my decision-making skills, and that’s just as important. Add a fun hashtag, like #arrayfail and enjoy realizing you didn't find what you were looking for.

This summer, you have an opportunity to record the math you see, too. Join the #mathphoto18 challenge. Talk to your kids about what you see, and what you wonder. 


Recently, my parents kindly offered to watch my two little ones so that I could get a breather in. I stopped by Peet’s coffee and ordered an almond-milk latte, and was treated to this beauty:


And do you know what I did? I counted the leaves. I saw 17. #prime #odd


Do you know what my dad said?






Nope, not far at all.


Cultivate your curiosity, find joy and beauty around you and share it with others.