Dice are a great way to teach students about probability. The different combinations they offer are the perfect grounds for many SAT questions. For instance, your teen might need to answer a question such as, “What’s the probability that the total of two rolled dice will be 9?”
Here’s a quick game that will help your student figure out and remember the difference between rolling Snake Eyes and Lucky Number Seven!
What You Need:
- A pair of dice, two different colors (I’ll use red and blue for examples)
- A piece of paper
- Some M&M’s or another little treat
What You Do:
- Tell your teen that you’re going to learn all about dice and probability.
- Ask him how many different ways there are to roll 2 dice. Remind him that there are 6 options on both sides. Together, you can determine that there are 6 x 6 = 36 possible rolls.
- Ask him how many ways there are to roll a total of “2” using two dice. After thinking, he should conclude that there’s only one way: 1 + 1
- Ask him how many ways there are to roll a total of “7.” He should come up with 6 ways: 1 + 6, 6 + 1, 2 + 5, 5 + 2, 3 + 4, 4 + 3.
- Time to figure out all of the rolls. Have him fill out the last two columns of the following chart. He has already figured out “2” and “7,” and he can do the rest the same way.
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Total to Roll
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Ways to Get the Total
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Probability of that Roll
|
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2
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1
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1 /36
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3
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/ 36
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|
4
|
|
/ 36
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5
|
|
/ 36
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|
6
|
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/ 36
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7
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6
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6 /36 = 1/6
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8
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/ 36
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9
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/ 36
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10
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/ 36
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11
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/ 36
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12
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/ 36
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- When he’s done, the chart should look like this:
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Total to Roll
|
Ways to Get the Total
|
Probability of that Roll
|
|
2
|
1
|
1 / 36
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|
3
|
2
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2 / 36 = 1/18
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4
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3
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3 / 36 = 1/12
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5
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4
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4 / 36 = 1/9
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6
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5
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5 / 36
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7
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6
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6 / 36 = 1/6
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8
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5
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5 / 36
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9
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4
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4 / 36 = 1/9
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10
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3
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3 / 36 = 1/12
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11
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2
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2 / 36 = 1/18
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12
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1
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1 / 36
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- Here’s a dice challenge for him. First, tell him the roll you want him to try and get. Then, give him two opportunities to win a reward (like a small piece of candy.) He can win an award if he rolls what you asked him to get. And, he can win another award for guessing the correct probability of rolling what you’ve asked of him. Good luck!
- Roll a total of “9” (1/9)
- Roll a total of “11” (1/18)
- Roll a total of 8” (5/36)
- Roll a total of “12” (1/36)
- Roll a total of “5” (1/9)
- Roll a “7” or an “11” (6/36 + 2/36 = 8/36 = 2/9)
- Roll a “2” or “6” (1/36 + 5/36 = 6/36 = 1/6 )
- Roll a “2” or a “6” or a “7” or an “11” (1/36 + 5/36 + 6/36 + 2/36 = 14/36 = 7/18)
- You can make up your own as you go
Extension:
Tell your teen, if he doesn't already know, that the game “Craps” is all about rolling two dice over and over. Ask himif he could figure out why “7,” “2,” and “12” are the most important rolls. If you know more about the game, it’s a great way to teach probability.
By Cindy Donaldson
Cindy Donaldson, BS Mathematics, taught Math, Business, and Computer Science at Menlo-Atherton High School for seven years. She has also worked as a tutor for SAT and SAT II test preparation. She is the mother of two young daughters.
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