Simplified Probability Bingo

I teach an Algebra 1 course and the other day we were studying experimental and theoretical probability. I saw a Probability Bingo activity on Dave Ferris’s and Sarah Hagan’s blogs and wanted to try it. The problem was I saw it the day of the lesson and didn’t really have a bunch of prep time. In fact, I had about 15 minutes. (I changed my previous plans at the last moment.)

What do teachers do? We adapt at the last second. Here’s what I did and it took about 10 minutes of prep.

I colored several pieces of paper in different colors.

I also created 2×2 squares in Word and printed them out on 1/3 sheets of paper. During the lesson, I put all of the colored paper in a small cup. I told the students I was going to pull out two pieces or paper, one at a time. I asked the students to predict what I was going to pull out by filling in their tables by putting two colors in each corner of the table.

I proceeded to pull out the pieces of paper from the cup. If the combination they wrote down was pulled from the cup, they crossed it out. The first student to have their  2×2 grid entirely crossed out wins.

We played twice. Afterwards, we discussed the probabilities of choosing each combination of colors. They then dived into some practice problems on probability. It was great because the formal “learning” about probability took place after I had them engaged in the activity and not the other way around.

I found that the students thoroughly enjoyed the activity. It was a simple game and they didn’t even care what they won (which was nothing). They just wanted their colors pulled from the cup. Plus, it was an awesome hook into basic probability….especially since it only took 10 minutes of actual prep time. Next time, I may try and go with full-blown bingo.




Classroom Economy

I have been meaning to write about a rewards/management system that I use in my classroom for the last couple of years. It’s math money. I have heard of other teachers that use fictitious money in their classroom, but mine has interesting and meaningful twist: students pay taxes and file tax returns for all the money they earn. I cannot remember who I got the idea from, but I remember it was an elementary or middle school teacher. If I can find who it was, I will post the link.

A few years ago, I had one of my (now) former students create some $1, $5, and $10 math money “bills” that I use for currency. He created it in Photoshop (they’re somewhat elaborate) and gave me the files. The little I actually know about Photoshop allows me to update them from year to year.

The students earn money for lots of things. It’s all about positive reinforcement. I especially prize participating in class and collaboration – and will usually pay students for these things. Attendance, homework, hard work, Student of the Week, exam scores, etc….these are also things that will earn a student some dinero. We also have various paid positions that students must be elected to (attendance taker, runner, etc.), each of which receive a weekly salary.

Students spend their money during auctions every two weeks. I auction off candy, dollar store items, homework passes, positive calls home, among other things. We even have 50/50 raffles every now and then. The possibilities here are endless, plus its where all the fun is! It’s crazy, students love to compete to be the highest bidder and spend their money.

As students earn their money, I keep a simple tally of how much they earn. Other than Student of the Week payments, all income is taxed. Students can choose to withhold income as they earn it – they simply give it back to me (i.e. the government). Each class elects a treasurer that will take my tallies and enter them into our class database (Google spreadsheet), which sums all taxed and untaxed money each student earns. At the end each marking period I take this spreadsheet and mail merge it into individual W-2’s for each student, which I print and give to them.

I have created a tax form that students complete on tax day. We literally spend an entire day doing taxes. They ask questions, get confused, and eventually learn (like most people who do their own taxes). Students itemize their deductions and compute their taxes using our tax rate table. I used to have adjustable tax rates, but it got too complicated. Deductions include high exam scores, donating to a class pencil fund, seeing me for extra help after school, and other “good” deeds. After they submit their income tax forms, the treasurer examines them to ensure there are no discrepancies. Some students will receive a tax refund while most others will owe taxes.

The whole process really does mock the tax-filing process. I like to think that after students take part in this process six times every year, they have a pretty good understanding of how the IRS does its thing. It’s also an effective way to promote positive behavior in my class. Using money in my classroom has afforded me loads of flexibility in terms of classroom management and allowed me to mimic the real world in countless ways. Plus, its just plain fun.


Inspiring and Humbling

Me, Mike, and Mike on a early morning TMC14 bike ride

It’s been a few days since Twitter Math Camp 2014 and here I find myself reflecting on the whole shindig. If I had to sum it up in one word…I wouldn’t. I would choose two words instead: inspiring and humbling.

I chose those words carefully. During those three and a half days, I was surrounded by folks with amazing ideas. I mean these people are doing AWESOME things with their kids. Because of this, I have nothing but admiration for the other 149 attendees of the conference. At the same time, I realized (yet again) how much I do not know about teaching. I am hungry to learn and gobble up everything I can (be selfish as Lisa put it), but there will always, always, always be more to learn. For this fact, I am deeply humbled by all of the knowledge and expertise I was able interact with at TMC14.

I could on and on about all the ideas I took from TMC14, as this was the absolute best professional development experience I have participated in. I’ll try and simplify some of the tools/resources/sessions/ideas that immediately stand out to me (in no particular order):

  • Plickers – amazing app that essentially allows you to use paper and your mobile device’s cam to poll your audience…just like a set of clickers (response system) would.
  •  60 Formative Assessment Strategies in 60 Minutes – awesome ideas. Check them out, very practical.
  • Steve Leinward’s idea that student’s are poisoned for life when teachers introduce a concept in an ineffective way. Powerful stuff.
  • Justin Lanier’s recommendations of How Children Learn and How Children Fail by John Holt.
  • The concepts of “Make a one/zero” and “Use a one/zero” when simplifying expressions and solving equations (instead of traditional methods). I forget who it was that told me about them, but thank you.
  • Malke Rosenfeld and Chris and the Math In Your Feet sessions. I will never see dancing in a non-mathematical way again. Step, slide, turn! See it action here (1 of 6). #bluetapelounge
  • Not using numeric grades for students. Instead, use stickers and stamps to assign grades. From Andrew Mazarakis. It sounds odd, but removing numbers from the grading system could be useful.
  • Absolute value blackjack from Anthony Rossetti. Just plain fun. Even for high schoolers.
  • Just how awesome Eli Luberoff and the Desmos team is. They are a company truly all about education. How refreshing.
  • Nik Doran and his push for Hinge Questions. I’ve never thought about multiple-choice questions in this very bottom-up, diagnostic way.

I’ve actually thought about this post since we left TMC14, wondering what it would look like. Also, given that it’s my inaugural post, I guess that had something to do with it as well. Part inspirational and part humbling. And now that its done, I’m glad. Reflection is essential to us all. I’m eager to travel on this journey. I cannot guarantee much along the way….but I do guarantee more questions than answers.


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