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Alliance Class April 17, 2012 Probability

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Agenda Development of Probability Concepts How Likely Is It? Exploring the vocabulary of probability What are the chances of seeing an elephant a the zoo? Exploring the meaning of the probability of event A occurring What’s in the Bag? Experimental probability vs. theoretical probability

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WALT Use the terms certain, likely, unlikely, and impossible correctly Associate the chances of occurrence of an event with a position on a probability scale Become familiar with the process of randomly choosing an item from a data set Compare fractions by comparing empirical probabilities (expressed as fractions) and associate larger (smaller) fractions with events being more likely (less likely) to occur

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CCSSM 7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

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Why is Probability Important? Everyday we make probabilistic decisions: Buy a Lottery ticket Walk outside in a storm Fly on an airplane Buy stocks Medical results

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Vocabulary What are some events that you would list as Impossible for you to perform.

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What are some events that you would list as Certain that you could perform? “In this world nothing can be said to be certain, except death and taxes.” BENJAMIN FRANKLIN, letter to Jean Baptiste Le Roy, Nov. 13, 1789

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What are some events that you would list that are between impossible and certain for you to perform?

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Chance Events Classify each of these chance events as being impossible to occur, unlikely to occur, neither unlikely nor likely to occur, likely to occur, or certain to occur. a. Our class will watch TV tonight during class. b. You will use a computer sometime during school tomorrow. c. Governor Walker will get recalled in the June election. d. The Brewers will win the Central Division in baseball this year. e. You will go to the movies during the next month. f. We will go outside for break tonight. g. If you were to put the names of all the students in our class in a hat and draw one name, a boy’s name will be chosen. h. If I have a bag of 10 blue cubes and one red cube and draw one cube, the red cube will be drawn.

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ImpossibleUnlikelyNeither Unlikely nor Likely LikelyCertain

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Probability Scale

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Directions: Think about each of the following events. Decide where each event would be located on the scale. Place the letter for each event below on the appropriate place on the scale. A. The next roll of a fair number cube will be a 2. B. You will be successful in four of your next 10 free throw shots. C. You will meet a dinosaur on your way home from school. D. You will read at least three books this month. E. A coin will come up heads five times in a row. F. A word chosen randomly from this sentence has four letters. G. It will be sunny tomorrow. H. You will eat something the color blue today. I. A spinner with 10 equal parts numbered 1 through 10 will come up a prime number in the next spin. J. You will have math homework tonight. K. If the names of all the teachers at our school are in a hat, my name will be picked.

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CCSSM 7.SP.6 Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

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A Trip to the Zoo “If an animal were to be chosen at random from a bag of zoo animals, which type of animal would be the most likely or least likely to be chosen?”

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Collecting the Data Name of AnimalTallyFrequencyRelative Frequency

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Graph Bar Graph

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Analyze 1. If one “animal” is drawn at random from your zoo, which animal is the most likely? Least likely? 2. What is the probability that: a. The animal is an elephant? b. The animal is an elephant or a lion? c. The animal is an elephant and a lion?

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Collecting Class Data Name of AnimalTallyFrequencyRelative Frequency

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Analyze 1. If one “animal” is drawn at random from your zoo, which animal is the most likely? Least likely? 2. What is the probability that: a. The animal is an elephant? b. The animal is an elephant or a lion? c. The animal is an elephant and a lion?

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Connection to Science Using the class data, ask what the probability is of randomly choosing: 1.An animal with four feet? 2.An animal with claws? Hooves? 3. An animal with knees? 4.A meat-eating animal? A pure carnivorous animal? 5.An animal that eats vegetation? A pure herbivorous animal? 6. An animal that eats both meat and vegetation? A pure omnivorous animal?

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Extensions Venn diagram

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CCSSM 7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

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What’s in the bag?

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Randomly select 20 cubes from the bag. Record your selection on the recording sheet. After each selection replace the cube. Selection NumberOutcome 1 2 3

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Organize your data What do you think is the percent of each of the following colors in your bag? Red Blue Brown

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Summary 7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.6 Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. 7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

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Homework Probability Worksheet (Due May 1) Read “6-8 Statistics and Probability pp. 7 - 10 Make note of the vocabulary and concepts that you are unsure of Complete video of your class poster presentations (remember to include the student that your are doing your reflection on). Bring camera and video on May 1 st. Chris will help with the editing. May 8 th you will share your edited video with our class Final reflection on the poster project (Due May 1 st ) Your reflection should include: What struggles did your students have pertaining to the construction of the poster? Reflection on the whole poster project – including the strengths and weaknesses of the project How does the poster project fit into the CCSS Mathematical Practices? Resource Binder project (Due May 8 th ) Final exam May 15th

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