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Bell Work

Use data and probability to predict the outcome of a hidden spinner in this classroom experiment. Analyze experimental and theoretical probabilities.

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Bell Work

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  1. Bell Work Cronnelly

  2. Have you ever tried to predict which football team will win a big game?  If so, you probably did not just pick the team with the coolest colors or the neatest mascot.  You may have based your pick on statistics about win‑loss records, player injuries, and other data.  Knowing what has happened in the past can sometimes help you predict what will happen in the future.  In this lesson, you will use data to make predictions. Cronnelly

  3. As you work with your team to uncover a mystery spinner, keep the questions below in mind. • What is the probability or likelihood? • What do we expect to happen? • How does the actual event compare to our prediction? • What can we know for sure? Cronnelly

  4. 1-63. THE MYSTERY SPINNER        • Your teacher has a hidden spinner.  Your challenge is to perform an experiment that will allow you to predict what the spinner looks like without ever seeing it.  • Your Task: Your teacher will spin the spinner and announce each result.  During the experiment, you will consider several questions about the results and about the hidden spinner.  However, you will not be allowed to see it.  Using the information you get, work with your team to figure out what the spinner looks like.  When you think you know what it looks like, draw a diagram of the spinner. Cronnelly

  5. 1-64. Use the data you collected in problem 1-63 to answer the following questions. a. Based on your data, how can you describe the likelihood of landing on each part of the spinner?  How does the spinner that your team drew represent these likelihoods?  Be prepared to share your ideas with the class. b. Use your data to write the experimental probability of each of the following results as a fraction, a decimal, and a percent. i.The spinner lands on purple.  ii.The spinner lands on green or orange.  Cronnelly

  6. 1-64 cont. c. If your teacher were to spin the spinner 15 more times, how might this change your answers for part (b)? d. Do you know for sure that the spinner you drew in problem 1-63 looks exactly like your teacher’s?  Are you certain that the portions that you drew for each color are the same size as the portions on your teacher’s spinner?  Why or why not?  Cronnelly

  7. 1-65. Now your teacher will reveal the mystery spinner. • How does your team’s spinner compare to the actual spinner?  Discuss the similarities and differences.  • Do your spinner and your teacher’s spinner show the same likelihood for each section being spun?  Explain why or why not.  Cronnelly

  8. 1-66. One way to compare your spinner and your teacher’s spinner is to calculate the theoretical probability for each colored section of your teacher’s spinner. • What are some reasons the experimental probability and the theoretical probability for any section of the spinner could be different?   • b. Estimate the theoretical probability for getting each color on your teacher’s spinner.  • c. How do the experimental probabilities (based on your class data) and the theoretical probabilities (based on the actual spinner) compare?  How do you think they would compare if there were twice as many spins made?  What about three times as many spins?  Cronnelly

  9. 1-66 cont. • d. If you were to spin the spinner the number of times listed below, how many times would you expect it to land on orange?  Explain how you found your answers. • i. 6 times • ii. 48 times • e. Approximately how many times would you expect to land on orange if you were to spin 100 times?  Cronnelly

  10. 1-67. Rachel and her little sister Christie often argue about who should wash the dishes at their house.  Rachel suggests that they flip coins to solve their argument. • “Flipping a coin is fair, since heads and tails each have an equal chance of happening.  Each one has a probability of  Rachel says.  “If the coin shows heads, then I do the dishes.  If it shows tails, then you do them.” • a. Is this system fair?  That is, does each girl have an equal likelihood of washing the dishes each day?  What is the theoretical probability for heads?  For tails?  Cronnelly

  11. 1-67 cont. • b. Rachel and Christie flip a coin every evening for the first week.  Christie has washed the dishes four times, and Rachel has washed the dishes three times.  Christie tells Rachel that the system is not fair, because Christie has done the dishes more often than Rachel.  Is Christie right?  • c. After the second week of coin flipping, Christie has washed the dishes ten times and Rachel has washed the dishes four times.  Now Christie is really upset at Rachel because she has washed the dishes so many times.  • In light of this new information, do you think the system is fair or not fair?  What would you recommend to Christie?  Discuss your ideas with your team and be prepared to discuss this with the class. Cronnelly

  12. Practice Describe the situation below using the vocabulary words: certain, likely, neither likely nor unlikely, unlikely, or impossible.1. What is the likelihood of pulling a blue marble out of a bag of green marbles?2. What is the likelihood that there are students in your classroom that will be at school each day this year?3. What is the likelihood of landing on an odd number when the spinner is labeled with numbers 1 – 10?4. What is the likelihood that the students in your school like chocolate ice cream?5. What is the likelihood that your teacher will be at school tomorrow? Cronnelly

  13. Practice Independent Practice Time Cronnelly

  14. Exit Ticket 1) Sawyer has a deck of cards numbered 1 – 9. What is the probability of selecting a 3, 4, 5, or 6?A) 1 B) C) D) 2)What is the probability of landing on an even number on the spinner below?A) B) C) D) 3) What word would be used to describe the probability of spinning and landing on a space with red on it?A) impossible B) unlikely C) likely D) certain4) What word would be used to describe the probability of spinning and landing on a space with yellow on it?A) neither likely nor unlikely B) unlikely C) likely D) certain Cronnelly

  15. EXIT TICKET 1-70. Imagine that you have a bag containing 10 marbles of different colors.  You have drawn a marble, recorded its color, and replaced it fifty times, with the following results: 9 purple, 16 orange, 6 yellow, and 19 green marbles.  Make a prediction for how many marbles of each color are in the bag.  Show all of your work or explain your reasoning. 1) Sawyer has a deck of cards numbered 1 – 9. What is the probability of selecting a 3, 4, 5, or 6?A) 1 B) C) D) 2)What is the probability of landing on an even number on the spinner below?A) B) C) D)

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