The big Monopoly battle is coming near its end, and the iron and racecar are battling for Monopoly supremacy.

Both players own properties on the next block, and have some spaces they’d like to avoid. For the car, here are the spaces he’d like to avoid.

And for the iron, there are a few spaces to avoid.

Since there some houses and hotels on some of the spaces, they are worth different amounts. Below, here is how much each player will have to pay if they land on the “bad” spaces.

So, here’s the question: which player is in “worse” shape? Which player should be more worried about their upcoming turn?

Let this stew with your classes, and would enjoy hearing some class reflections. The big reveal will come in a few days.

A recent problem I reviewed from the Mathematics Assessment Project (MAP) caused me to refelct upon the coverage of probability in our classrooms. The website provides sample tasks and assessment tools for schools and districts as they adjust curriculums to match the Common Core. In the standards, probability begins to take center stage in grade 7:

Probability is treated like the ugly step-sister in many math courses: ignored, shoved to the side. Look at standardized testing results, including AP Statistics, and you will find that probability standards often produce weak results. The isolated fashion with which we treat probability is certainly not helping. Let’s develop strategies to not only re-think probability, but to encourage communication of ideas and develop understanding.

I have taught probability at many levels: as an 8th grade teacher, as an AP Statistics teacher (and reader) and as the author of a Prob/Stat course delivered to 9th grade students. This year, I taught my first college course in Statistics, where the problems with probability persist. The picture below is from my college Stat 1 class, which you can also see on the great site Math Mistakes, by Mike Pershan. Visit and provide your input:

Here are two activities I hope you can use in your classrooms to help fight the probability battle.

“WHICH IS MORE LIKELY” OPENER:

The Core Standards provide a framework for our students base knowledge of probability:

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Before we can start diving into formulas and fractions with probability, we need students to understand, and be able to express, whether an event is likely or not likely. For simple events, like flipping a coin or drawing a card, this can be an easy discussion, but what happens when we start talking about complex events, like flipping multiple coins, tossing 2 dice, or choosing a random car from a parking lot? Download my Probability Opener, which asks students to assess events and compare their probabilities. Answers are provided. The events start off innocently enough, but soon meander into more complex tasks, where students are asked to identify the more likely outcome:

You roll the dice and move your piece in the game of Monopoly…

A: You end up on Boardwalk

B: You end up in Jail

This is also a great activity if you have a classroom clicker system, or for Poll Everywhere if cell phones are allowed.

SPINNER BINGO

This activity is an adaptation of a Spinner Bingo problem from the Mathematics Assessment Project site I mentioned at the top of the post. Visit the MAP site for not only the task, but a rubric and samples of student work.

The problem presents a scenario where students are asked to assess a spinner game, and bingo cards created for the game. Read the files given on your own, but here is a quick summary:

3×3 bingo cards are filled out, using non-repeating numbers from 1-16.

Two spinners with 8 equal spaces numbered 1-8, are spun, and the sum computed.

Players mark off their bingo cards if the sum appears on their card.

This is a nice scenario, so let’s adapt it and use it as our unit opener. Having students play a game, and develop and justify a strategy, is a great way to get started. Here is a lesson guide I have written to help you get started. Also, the site Unpractical Math provides a virtual spinner applet you can use. It’s often easier to just dive in and play, so here is a brief video demo of the game and how you can play it in your classroom:

Please let me know if you use either of these activities, and would appreciate your feedback. Thanks.

Now is a good time to reflect upon the past year, and think about all of the professional growth I have made through the people whose ideas I have shared and experienced through the twitter-sphere and blog-o-sphere (are these actual words?), and to send thanks from all of the new math friends I have made. I took a look back at all of my posts from the previous year, and here are 5 great activities you can use tomorrow is your classroom. Share them, adapt them, expand upon them…it’s all good. Just pay it forward and share your best works, or leave a comment /contact me and let me know if you use them! Enjoy.

Conic Sections Drawing Project – this was the most popular post of the year. For algebra 2 or pre-calc, this project just got better with the Desmos online calculator, which is my favorite new tool of the past year.

Tall Tales for Probability – Featuring the poker chip drawing game, and examples from the Amazing Race and craps. Probability should be fun. Make it so!

Let’s Play Plinko! – I have used Plinko as an introduction for binomial distributions for years, but in this presentation from last summer’s Siemens STEM Academy, tech tools like PollEverywhere and Google Drive are used to increase interaction.

Composite Functions and ESP – Use this activity with middle-schools and see if they can develop the pattern. For high school, have students write and justify their own ESP puzzles. Also features Doceri, another favorite new tool of mine, for iPad.