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Suggested Activities Unit 4: Probability

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Remove One: Investigating Probability A game adapted from PBS Mathline (http://www.pbs.org/teachers/mathline)

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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 youd like, i.e., 12 11 10. 2

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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.

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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.

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Schema Activator (Warm-Up!) Turn and Talk. How would you define probability?

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Lets Play! 1. Two number cubes will be rolled.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!

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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.

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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

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Sample Space

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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.technology

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Lets 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!

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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?

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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)

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Schema 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 caps 1.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.Whats 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.

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Lesson 10.4. Imagine that you are sitting near the rapids on the bank of a rushing river. Salmon are attempting to swim upstream. They must jump out.

Lesson 10.4. Imagine that you are sitting near the rapids on the bank of a rushing river. Salmon are attempting to swim upstream. They must jump out.

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