Jennefer SimmonsGrade Level:6th– 8thTopic: ProbabilityLearning Objective: Students will demonstrate anunderstanding of the concept of probability by solvingprobability problems in various formats, providingrationale for their methods, and by creating their ownexercises that deal with probability.------------------------------------------------------------------- 1. First, visit http://dictionary.reference.com/ Enter the term “probability” in the search box located at the top of the screen. Look at the definitions listed for the term. Click over to the “Thesaurus” tab, located above the definitions. a. From reading through the definitions and synonyms of “probability,” see if you can provide a definition in your own words as to what you think it is: _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ b. Next, tell me how you think “probability” might be applied to math, using your previous experiences. (There is no right answer here; just give me your best guess.) _____________________________________________________ _______________________________________________________________ _______________________________________________________________ 2. To complete the next activity, you should visit the website (http://www.mathsisfun.com/data/probability.html); be sure to read through the entire page to get a better feeling for the concept of probability. Once you’ve read the page in its entirety, answer the following questions. a. What are the odds of rolling a 4 on a six-sided dice? ____________________ b. In your own words define the following. i. Experiment: ______________________________________________ ii. Event: ___________________________________________________ iii. Sample Space: ____________________________________________ iv. Sample Point: _____________________________________________ c. Use your newly acquired vocabulary words to explain your answer to 2a. Break down your reasoning to shed light on how you arrived at your answer: _______________________________________________________________
_______________________________________________________________ _______________________________________________________________3. Watch the video titled “Simple Probability at the URL below and answer the questions that follow. http://www.khanacademy.org/math/probability/v/simple- probability a. The narrator uses the term “possible outcomes.” Of the vocabulary you have learnt so far, which one is the most similar to this new idea? ______________ b. Using the example provided in the video, tell me what the probability of picking a blue marble is. __________________________________________ 4. When you visit the following website: http://www.cut-the- knot.org/probability.shtml you will find a list of many probability problems near the bottom of the page. Choose one of the following problems to analyze. You do not need to solve these problems yourself, but you should summarize and explain the solution in your own words. a. Stick Broken Into Three Pieces (Interactive Triangle Problem):_______________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________________________________ b. The Careless Mailing Clerk ________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ c. Three Pancakes (In this problem, 3 solutions are offered. Describe the one that makes the most sense to you.) ______________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________
5. For the next activity, you will complete one problem of each type found at the following website:http://www.pearsonschool.com/live/images/custom/envisionmath_ca/games/pond.htmlThis should make for a total of 6 kinds of problems that you will have to complete. Asyou play the games, answer the following questions. a. For the “describing chances” sets, explain how you know an event is i. Impossible: ____________________________________________ ______________________________________________________ ii. Certain: _______________________________________________ ______________________________________________________ iii. More Likely: __________________________________________ ______________________________________________________ iv. Less Likely: ___________________________________________ ______________________________________________________ v. Equally Likely: _________________________________________ ______________________________________________________ b. For the “finding probabilities,” lay out the steps you took in determining the answers. _______________________________________________________ _______________________________________________________________ _______________________________________________________________ c. After the “showing probabilities” set, you should have some practice creating a desired probability. In the space below, please represent the probability of 1/5 circles. You can use any other shapes you prefer to create your own unique sample space.6. Explore Probability Circus at http://www.hbschool.com/activity/probability_circus/ After completing a few exercises, explain what two things you need to know in order to determine probability. a. ______________________________________ b. ______________________________________
7. At this URL,http://www.cyberbee.com/probability/graph3.htmlcomplete numbers 1- 4. The M&Ms will be provided to you. In order to simplify this problem, there is space below to record the number of each color of M&M below. There is also a blank circle, which you will use to create the circle graph for question # 4. a. Record the number found in your bag. Convert into a percentage. (Hint: You will need to know the total number of M&Ms in order to convert.) i. Green: _______________________________________ = _______ % ii. Blue:_________________________________________ = _______ % iii. Red: _________________________________________ = _______ % iv. Brown: _______________________________________ = _______ % v. Yellow: ______________________________________ = _______ % vi. Orange: ______________________________________ = _______ % b. Transfer the information you have just recorded into the graph provided below. Be sure to provide a key, so that those interpreting the graph will be able to understand it. KEY8. Read the webpage found at: http://mste.illinois.edu/reese/birthday/After reading through the information, enter the number of people in our class (25) in the textbox. Press the “Calculate” button a few times and focus on the experimental probability. Once you have gotten a feel for this, use the “Run 100 Trials” Button. a. Record the experimental probability after i. 1 trial: ______________________ ii. 2 trials: _____________________ iii. 100 trials:____________________ iv. 300 trials: ____________________ v. 500 trials: ____________________ b. Describe what happens the more trials you conduct: _____________________ _______________________________________________________________ _______________________________________________________________
9. For this next exercise, you will create your own probability experiment. Your problem doesn’t have to be complicated, but you should demonstrate your knowledge of the sample space, the sample point, and the difference between an event and an experiment. At this URL, http://jmathpage.com/JIMSProbabilitypage.html you can find spinners and dice to assist you in your task. Each simulation will guide you through and allow for the creation of your own experiment. Record the details of your experiment below: a. Of the 27 available simulations, I used: _____________________________ b. The sample space was: ____________________________________________ _______________________________________________________________ c. The experimental probability was: ___________________________________ _______________________________________________________________10. For your final activity, you will visit a webpage (http://www.studyzone.org/mtestprep/math8/g/intro probquiz.cfm) that contains a probability quiz. You will not need to complete the entire quiz. Choose one of the questions and solve it using any spare space on the page. Then, explain why/how you arrived at your answer: _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________ _________________________________________
Answer Key1a. Answers will vary.1b. Answers will vary.2a. 1/62bi. An action where the result is uncertain.2bii. The result of a single experiment.2biii. All the possible outcomes of an experiment.2biv. One possible outcome of an experiment.2bv. Answer should include the terms: experiment, event, sample space, sample point. No one answer forthis question.3a. Sample space.3b. 1/84a. b. c. Answers will vary. Only one must be completed.5ai. The outcome described is not contained within the set.5aii. The outcome described is the only one contained within the set.5aiii. The outcome described comprises the majority of the set.5aiv. The outcome described comprises the minority of the set.5av. The outcome described comprises half of the set.5b. No two answers will be the same. However, answers should involve at least the student counting thetotal possible outcomes as well as the desired outcome.5c. Answers will vary. Image should be representative of 1/5 circles.6.Sample space & sample point.7ai. – vi. Answers will vary by M&M bag.7b. Graphs will vary based on information in part a.8a. Answers will vary.8b. The general trend should be that experimental probability will not increase as much the more trialsyou conduct. For example, probability between 1 trial and 100 is quite significant; between 100 and 200is not as significant. However, answers will likely vary as many different observations can be made.9a.- c. Answers will vary greatly. Students should address each question based on the simulation theychoose.10.Answers will vary based on which question students choose to explore in detail.