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# High or Low: A Game of Probability

Tom DeRosa | Teaching

The premise of the game High or Low is to guess whether the next card is higher or lower than the last one dealt. That’s basically it (minus the obvious). The only element we’re going to add to the game is that students will figure out the exact probability that the next card will be higher, lower or the same suit.

**Introduction/Guided Practice:**
Explain that you’ll be using a regular deck of cards to help students understand some challenging probability problems. Show them the graphic organizer and how to fill it in by “playing” a few sample rounds. Click through for a rough example of what a filled in organizer might look like.

While you’re modeling how to play and use the organizer, that’s the best opportunity to review the structure of a regular deck of cards, as that’s essential knowledge they’ll need to play.

I wouldn’t try to sell this to your students as a super fun game so much as a different way to practice problems (better than say, doing problems out of a textbook). They might get into the guessing element, but I don’t think it will be as engrossing as my Deal or No Deal probability game. Students definitely don’t like it when you tell them something is fun when it’s not, but they do appreciate the novelty of using cards and just doing classwork differently in general.

**Collaborative Practice:**

Split your class into small groups, giving each one no more than 10 regular playing cards. Each group would have a different set of cards and probabilities to figure out, which eliminates the problem of students copying answers. That element plus the “game” itself should keep most students focused and invested in the activity. They’ll be filling out the organizer and then considering the reflection questions as well.

**Wrap-Up:**

At the end of the game there’s a few reflection questions you might talk about together. Students will probably think this game is pretty easy at the beginning—how hard can it be to guess correctly high or low? I think their results will probably skew towards an even number of correct and incorrect guesses.

You could also give them an exit slip like: “How could we change this game to make it easier? …harder?” A game of Red or Black?, for example, would elicit some interesting answers.

**Things to Consider:**

Do you want students to leave probabilities as fractions, simplified fractions, or change them to percents as well? The latter would take a bit more time and might require you to give 1 or 2 less cards to each group. How long do you want this activity to take? As is, it should fill a 45-55 minute period, allowing for opening and closing procedures and transitions. If you want to spend less time on this, give students only 4 or 5 cards. You can spend the rest of your class period on similar probability problems from your usual resources or whatever you’d like.

This should be taught after you’ve introduced the basics of probability in other ways, as it involves the idea of independent and dependent probability (replacement).

Every time I post something about probability, some people like to start an argument over the Monty Hall Problem. I think you could argue either way, but the point of this activity is to provide practice on finding probability in a way similar to typical standardized test questions, and that’s all. Let’s leave that debate for another time.

If you want to add an additional challenge, you can use this activity as a segue to talk about compound probability!

Materials to Download:

High or Low card game graphic organizer Rough example of filled-in graphic organizer