Alexander, Who Used to Be Rich Last Sunday by Judith Viorst

Mathematical Strand:

Probability

Topic:

Students will figure out the probability that the penny's sixth toss will be heads also. Students will also figure the probability of having six coin tosses in a row all end on the same side.

Grade level:

6-8

Lesson Created by:

Stacy Aschenbrenner Bergman Elementary, Manhattan, KS

Lesson Description

Materials

• Book-Alexander, Who Used to Be Rich Last Sunday by Judith Viorst
  

1. Launching the lesson

1. Read the story.
   

1. Developing the lesson

1. Pose the following problem. Alexander's brother Anthony is showing off that he has money and Alexander does not. While they were waiting for the bus to pick them up for school, Anthony flipped a coin to pass the time. He was amazed to see that it turned up heads five times in a row. Alexander was looking over Anthony's shoulder. "I'll bet you a quarter against your penny that the next one has to be tails," said Alexander. "You mean if it comes up heads I win a quarter and if it comes up tails you when one cent?" Anthony asked. "That's right," Alexander replied. "That's how sure I am that it won't be heads again."
   
2. Challenge the students to figure out the probability that Anthony's sixth toss will be heads also.
   
3. Give the kids pennies and let them experiment. Also stress that they could probably figure this out without actually doing it.
   
4. After the kids have experimented and tried to come up with answer let them share their answers.
   

3. Closure/Discussion/Elaboration

1. Discuss the answer. (The probability that Anthony's sixth flip will be heads is 1 in 2. Despite what many people think, the number of times coins have been flipped doesn't matter. Any coin you flip has a 1 in 2 chance of ending up on one side or the other.)
   
2. Then challenge the students to figure the probability of having six coin tosses in a row all end up on the same side. (It is unusual for this to happen, however, the probability of having six coin tosses in a row all end up on the same side is 1 in 64 (½ x ½ x ½ x ½ x ½ x ½ =1/64)