"Remove One" - Probability Game

A Probability Game for Middle School Math

Remove One is my favorite probability game and one of my all-time favorite math games! It's a great way to teach probability and the students love it.

I've been using the Remove One probability game nearly every year since I was introduced to it through a program called the Mathline Middle School Math Project, sponsored by PBS (back in 1997?). I was involved in the program through my graduate studies at Allentown College of Saint Francis DeSales (now DeSales University).

​Anyway, this year, my student teacher is teaching our probability lessons; so she is the one who taught this lesson.

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How This Probability Game Works:

This is how the lesson works:
1. Students use a piece of paper as their "game board" and number the paper from 12-2 (or 2-12).

• They place 15 chips next to the numbers.
• They are told they can place one chip next to every number and then place the extras next to any number they want. Or, they can leave some numbers with no chips and put several on others.
• Usually, they place the chips like those in the picture to the right.

2. Once students have their chips set up, the teacher rolls 2 dice and finds the sum of the numbers that are rolled.
3. If students have a chip next to that sum, the students may remove ONE chip from their paper (thus the name of the game -Remove One).
4. Play continues, with the teacher rolling the dice and the students removing one chip each time the corresponding sum is rolled.
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The "winner" is the student who removes all of the chips first.

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Playing Remove One a Second Time:

Without much class discussion about the first game, we play the game a second time. Normally, I just ask students to make some quiet observations to themselves before placing their chips again.

​Students typically notice that the sums of 6, 7, and 8 are rolled the most often and that 2 and 12 are usually rolled the least often, so they arrange their chips differently.

Discussion After Playing the Game a Second Time:

After the second game, we have a discussion about all of the possible outcomes (sums) one can get when rolling 2 dice.

We also discuss how many ways there are to roll each of those outcomes, and what the probability is of rolling each sum. We find this probability in fraction form, and then often convert them to decimals and percents.

After this discussion, we play the game for a third time, and students' "game boards" look a bit different!

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Observations During the Game:

This year, since I was observing rather than teaching, I was better able to hear some of the students' quiet comments to each other...  

• "There's a better chance of getting a seven." 
• "I'm not going to put any on 2, because it still hasn't come up."

When I started discussing this lesson with my student teacher, I searched for the lesson online, just in case it was around, and I found it right away. Click HERE to see the full lesson plan from PBS.

Have you played this probability game?
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What other probability games or activities do your students enjoy?

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Resources to help teach and practice probability concepts:

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