Expected Value-Activities 1-3

Activity 1(will probably take 2 periods)

1.    Show the children a coin and discuss what the possibilities are if the coin is flipped. Discuss the term “expected value” and “trials”. Have the students predict the outcomes if you flip the coin 10 times, 20 times, 30 times, 50 times. They should write their predictions in their math journal.
2.    Break students into groups of 2.   Give each group a coin and a worksheet for the coin toss. They should record whether they get heads or tails for each flip of the coin. After 10 times, they will record the total of tails and heads. Then, they should do the same for 20 times, 30 times, and 50 times. In their journals, they should compare their predictions with what actually happened.
3.   Put 2 groups together (4 students in a group) and have the students combine their results for 50 flips. Are the results getting closer to the expected value of .5 .
4. List the results for 50 trials, obtained by all groups, on the board.
Have the students put these in their journal and find the totals for heads and the totals for tails.   Are the results getting closer to the expected value. What does that tell you about more trials.

Activity 2

1.    Repeat the coin flips from activity 1, using the program auto coin on the calculator. Put the results into math journals and compare the results to the results from Activity 1. Also in math journals, have students discuss whether this was easier or harder than actually flipping the coins? Why?
2.   Lead a discussion on expected value and the importance of being able to do many trials.

Activity3
1.   Divide the children into different groups of 2. Discuss what the expected results would be for each number on a dice. (1/6 or .17, in this case out of 36 rolls one might expect, 6 of each number. Give each group a dice and have them predict, in their journals, how many times each number would come up, if you rolled the dice 36 times.
2. Have the children take turns and roll the dice, keeping a tally of how many of each number were rolled.
3.   Students should compare their predictions with what really happened and write in their journals.
4.   Then, write down everyone’s results and have the students total them. Lead a discussion on whether or not the expected results are more nearly met with a larger number of trials.

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created by Nelda Baker
Magdalena, NM
Last updated July 30, 2002 08:52 AM -0600