Title of Activity: Probability for two the sum of two six - sided die

Grade Level: 5 +

Name Dr. Robert Sweetland

Concept Assessment Information

Concepts

Supporting Information

Misconceptions

Assessment

1. The probability of a certain sum of two die is equal to the total number sum combinations for each possible sum out of the total number of all possible sums.
2. The probability of a specific outcome is equal to the total number of ways to achieve the same outcome out of all the total number of different outcomes possible.
3. The probability of an outcome is the number of specific outcomes out of the total number of all possible outcomes of one event.

Each die has six sides.

Each die is the same.

Each side has an equal chance of being rolled.

Each die is fair.

The sums of the die are: 2, 3, 4, 5, 6, 7, 8, 9, 110, 11, 12.

There is one way for the dice to have a sum of 2, two for 3...six for 7 five for 8... For a total of 36.

I can cause a certain number to be rolled (blowing, throw hard, throw a certain way...).

It is magic.

Diagnostic: What number(s) do you think will be the most likely to be rolled? The least likely?

Summative: What is the probability for all possible rolls? How do you know?

Generative: Have students predict the probability for certain sums if dice with a different amount of sides than six were rolled and summed.

Spinners with unequal partitions and or different colors of sections and the probability of getting pairs of colors.

1. Theoretical probability is found by generating all the possible outcomes or combinations of events.
2. Theoretical probability doesn't usually match the experimental probability

Theory is an idea used to explain or predict an event.

Experiment is a test made to try to understand something.

The only way to figure probability is to crunch numbers.

Have students explain how to find the experimental probability and theoretical probability of each of the following.

1. Ask students how to display data. If students do not know how to arrange data have them chart the number of rolls for each sum 2 - 12 (2 - 12 horizontal axis, # rolls vertical axis). Data could also include the addends for each sum.
2. Students put their data on the board.
3. Ask questions like the following to see how they interpret the data.
4. What pattern do you see from the data?
5. What sum turned up most?
6. What are the odds of each sum turning up?
7. Analyze the data by having students explain the pattern. It may be necessary to list every pair of addends for each sum 2 - 12 theoretical probability.
8. Have students communicate the pattern and compare the experimental probability with the theoretical probability.

Ask questions such as:

1. What sum would you predict would turn up most if you did it again?
2. What would happen for dice with different amounts of sides?
3. What would happen with spinners that have different sized areas of colors on different spinners?