Probability Openers – Separating the Possible from the Plausible

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:

Investigate chance processes and develop, use, and evaluate probability models.

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:

Conditional

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.

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