Suggested Activities

1
Suggested Activities

• Unit 4 Probability

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Remove OneInvestigating 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

4
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.

5
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.
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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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.

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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?

14
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
• Rewrite the fractions so that they have a common
  denominator (18).
• How many total people did Matt observe sitting in
  his section?
• If Matt took a photo of each person with his
  BlackBerry and then randomly selected two photos
• 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.