Suggested Activities

Unit 4: Probability

Remove One:Investigating ProbabilityA game adapted from PBS Mathline

(http://www.pbs.org/teachers/mathline)

Before We Begin…

On the sheet provided, Place a total of 10 open circles next to any of

the numbers listed You may choose to scatter them any way you’d

like, i.e.,

12 11 10

. .

2

NCTM Standards

In grades 6-8, all students should:

understand and use appropriate terminology to describe complementary and mutually exclusive events;

use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations;

compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models.

Objectives

Students will develop winning game strategies based on probable outcomes of events.

Students will also define the terms sample space, theoretical probability, and experimental probability.

Schema Activator (Warm-Up!)

Turn and Talk.

How would you define probability?

Let’s Play!

1. Two number cubes will be rolled.

2. The sum of the number cubes will be called.

3. If you have an open circle next to that number, cross one of them off.

4. The first player to eliminate all open circles from their board wins!

Drawing Conclusions

What did you notice about the frequency of the numbers called?

Which sums appeared to occur most often? Least often?

Why might this be the case?

What kind of graph/distribution would likely be produced if you were to graph the sums that were rolled? Explain.

Vocabulary

Theoretical Probability: the likelihood that an event will occur

Experimental Probability: the ratio of the number of times the event actually occurs to the total number of trials

Sample Space: the set of all possible outcomes of an experiment

Sample Space

Sample Space

The probability of rolling a sum of 12 is 1 out of 36 or 2.8% since there is only one way to roll that sum (6 and 6).

The probability of rolling a sum of 11 is 2 out of 36 or 5.6% since there are two ways to roll that sum (5 and 6 and 6 and 5).

We can use technology to assist us in calculating the remaining probabilities.

Let’s Try It Again!

Using what you now know about probability, design a game board on the back of your handout that

will increase your chances of eliminating your circles more

quickly, resulting in a win!

Pulling it all together…

What strategy did you used to place the circles on your game board the second time around?

What advice would you give to your peers about developing a winning game strategy for Remove One?

Extensions for the Classroom

To differentiate, teachers may choose to assign students the task of designing a “winning” game board assuming that number cube subtraction replaces number cube addition.

Software can be used to simulate the rolling of two dice, while simultaneously keeping track of the sums. This will allow students to experience what could

happen when dice are rolled a large number of times and how close to the theoretical probability the outcomes can be. (http://www.pbs.org/teachers/mathline)

Schema ActivatorSchema Activator Matt went to the Jingle Jam concert this weekend and

made the following observations about the people sitting in his section:◦ 1/6 of the people were wearing red shirts◦ 4/18 of the people were wearing green shirts◦ 4/9 of the people were wearing Ed Hardy shoes◦ 1/6 of the people were wearing baseball caps1.Rewrite the fractions so that they have a common

denominator (18).2.How many total people did Matt observe sitting in

his section?3.If Matt took a photo of each person with his

BlackBerry and then randomly selected two photos

1. What’s the probability that the first photo he selects is of someone wearing red and the second photo is of someone wearing Ed Hardy shoes? Assume that his BlackBerry deletes photos from his album after viewing them.