A Probability Lesson 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 during my graduate studies. It was a lesson in a program called the Mathline Middle School Math Project, sponsored by PBS, back around 1997.
I used this game in 6th grade math for many years, but it could definitely be used in 7th and 8th; 5th graders may do well with it also.
Anyway, this year my student teacher is teaching our 6th grade probability lessons; so she is the one who taught this lesson.
How to Play the Remove One Probability Game
This is how this probability game works:
1. Students use a piece of paper as their “game board” and number the paper from 12-2 (or 2-12).
2. Next, students place 15 chips (or any type of marker) next to the numbers, in any configuration they want.
- They can place one marker next to every number and then place the additional 4 markers next to any number they want. This means they have some numbers with one marker and 4 with two markers.
- Or, they can leave some numbers with no markers and put several on others – whatever they choose.
- Usually, the first time they play, they place the markers like those in the picture to the right.
3. Once students have their game boards set up, the teacher (or designated student) rolls 2 dice.
4. Then, students find the sum of the numbers that are rolled.
5. IF students have a marker next to that sum, they may remove ONE marker from their game board (thus the name of the game – Remove ONE).
6. Play continues, with the teacher rolling the dice and the students removing one chip each time the corresponding sum is rolled.
In the image above, one chip was removed from the 9 (there were two chips at 9 in the previous picture)
The “winner” is the student who removes all of the chips first.
Playing This Probability Game the 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 markers on their game boards again.
Students typically notice that the sums of 6, 7, and 8 were rolled the most often and that 2 and 12 were rolled the least often. So, they arrange their chips differently. (Sometimes 2 and 12 aren’t the least, but they usually are.)
Discussion After Playing the Second Game
After the second game, we have a discussion about all of the possible outcomes (sums) one can get when rolling 2 dice.
We discuss how many ways there are to roll each of those outcomes, and what the probability is of rolling each sum.
Then 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!
Observations During the Remove One 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.”
6th grade math students LOVE this probability game and always get more excited as we progress to the 2nd and 3rd games, because they begin to understand that there’s a greater probability of some numbers being rolled. They realize they can use some strategy to place their markers, and the games get more and more suspenseful as they wait for the last marker on their page to have it’s number rolled!
When my student teacher and I were planning for probability and I started discussing this lesson, I searched for it online, just in case it was still around, and I found it right away. Click HERE to see the full lesson plan from PBS.
Have you played this probability game?
What other probability games or activities do your students enjoy?
If you’d like another great strategy game, check out The Factor Game – this one is great for reviewing factors and developing strategy.