COIN TOSS AND PROBABILITY

intended for 5th or 6th grade

Materials: quarters, pencil, paper, ruler (9)

Objective: This activity is designed to activity involve all students in the cognitive exploration of probability and allow them to demonstrate personal strategies and graph constructing skills. (intended for 5th or 6th grade) (8)

Prerequisite knowledge includes the understanding that probability is an experiment which includes a set of possible outcomes in a given event and weighted averages directly affect the probability outcome.

Students must also understand that a quarter yields two possibilities (heads or tails) and one has a 50/50 chance of getting heads or tails. (2)

Procedure: (6)

1. The teacher reviews probability definition and shows a quarter to the class, pointing out that there is a 50% chance of getting heads when flipping a coin. She demonstrates this by flipping the coin. An equation is introduced:

weight * probability= expected value (8)

2. The teacher presents an experiment or problem. " If I said I would give you 100$ if the quarter lands on heads, would you take the chance and flip the coin or take 20$ and walk away? Let's explore the probability that you will get the 100$ and what might be the best way to approach this situation." (10) (15)

3.The class is then divided into groups of three and each group is given a quarter to work with. (this can be adjusted according to classroom needs)

4. The teacher explains procedure and expectations: (11)

a. What is the best strategy? Come up with your own strategy, commit to it , and tell why on a piece of paper. (1)

Possible strategies: A student may choose to take the 20$ each time, A student may choose to bet each time in an attempt to get the 100$, A student may alternate taking the risk or taking 20$. (7)

b. Each person in the group will take turns flipping the coin and recording their results. They will flip the coin 50 times each. At the end, each student will count the amount of money earned and record it on their paper.

c. Then the groups will combine their earnings.

d. Would you change your strategy and why?

5. The students will construct an individual graph and a group graph to show the results of their experiments.

6. The teacher may then choose to increase the amount of money offered not to bet and the class repeats the previous procedure using a new strategy. (12)

note: 50$ is the magic value where it is better to just take the money instead of betting.

7. Class Discussion: Who won the most money? So what was the best strategy to use? Let's apply this to our equation:

Weight (100) * Probability (.5) = Expected value (50)

note: The ones who bet every time will have more money. This is counter intuitive because the risk taking is actually better.

The teacher also posts the results on the chalk board:

Bets non bets Total for group

group 1

group 2

group 3

(3,4,5,7,13,14)Results: I actually tried this lesson with three seventh graders from my church. They were excited to try it. I had two boys and one girl. (Darren, Evan, and Lisa)

Darren chose to take the risk and hope to get heads each time.

Evan wanted to bet 25 times and take the 20$ the other 25 trials.

Lisa chose to bet only 10 times and took the 20$ the other 40 trials.

Darren ended up with the most money as expected.

Lisa: 20$ * 40 = 800$ + 1 successful bet = 900$

Evan: 20$ * 25 = 500$ + 9 successful bets = 1,400$

Darren: 100$ * 43 = 4,300$

Bets Non-Bets Total $$

Darren Evan Lisa

At the end of our experimentations, Lisa stated that she would change her strategy if we were to do this again. Darren was pretty confident that his strategy would always keep him on top. It would be interesting to know what he would do if I were to only offer him 40$ for betting. Obviously the odds would be different and he would loose if he kept his original strategy to always bet.

I found this activity not only held their attention , but also made them think independently. It will be great to try out in a classroom.