Dice Roll! What are the chances?

 Hi All,

I enjoy probability games. I think kids do too. Dice, spinners, and cards, all of these figure importantly in many board games. 

Dice Roll explores some of the probability around a pair of dice. 

1. Partner students and give them a copy of the Dice Roll Record Sheet, a pair of dice, and a pencil. The link is here: https://drive.google.com/file/d/1kxOcSpD3t90OFMKK01eht2FbZlI5CFUq/view?usp=sharing

 

2. Explain that we are going to investigate which numbers come up most frequently when rolling dice. Give students an opportunity to predict which sum they think will come up most often. Students should take turns rolling the dice as many times as possible for twenty minutes. As they roll they should record the sum of each roll on the record sheet using tally marks.

3. After the allotted time, have players tally the totals for each sum and write down the sum (or sums) that came up the most.

4. Have students think about why this sum came up the most and write down their thinking.

5. Now, have students use a new record sheet and write down all of the possible combinations of numbers on the dice that would yield each sum. For example, to get a sum of "2" there is only one combination using dice and that is 1 + 1. To get a sum of 3, there are two ways; 2 + 1 and 1 + 2. Work through each sum. Remember, dice only have numbers 1 through 6 on them, so you can't get a sum of 9 by adding 8 + 1 because there is no 8 on dice.

 

6. After completing the sums chart, players will learn that there are 6 combinations to make the sum of 7, the most of any sums.

7. It's interesting to note how there are mathematical patterns that emerge with these results. The combinations when layed out on the Record Sheet form a triangle as do the tally marks on the chart as you work.

8. There is 1 way to make 2, 2 ways to make 3, 3 ways to make 4, etc. Another interesting pattern.

9. Notice in my example results, because of the randomness of dice, my sum of 6, where there are 5 combinations came up only once. This is a good reason why you have to roll a lot to get reliable results. Talk to students about this. For example, if you only rolled 5 times and the sum of 4 came up 3 out of 5 times, would you be able to reliably say that 4 is the sum "most likely" to come up? No, of course not. Lots of trials are key to getting reliable conclusions.

10. Use probability language when describing results and possibilities. Write up a chart of probability words and phrases like: possible, impossible, likely, unlikely, most likely, least likely, and certain. Encourage students to use these words as they talk and write about their work.

11. You could get into fractions if you want to talk about things like a 1 in 6 chance of a number coming up on a die or 1/6.

12. LOTS to learn with this little investigation!

All the best,

Bob

PS - This idea appeared in Reteaching Math: Data and Probability (Scholastic), a book I wrote with Mary Ann McMahon Nester.