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Roselle School District Grade 7 Pre-Algebra Honors Curriculum Unit 10 Essential Question(s) How can you use probabilities to make predictions? How can probabilities be calculated? How does understanding probability affect the choices you make? Enduring Understanding(s) Probabilistic thinking develops notions of chance. Understanding and utilizing probability can be very helpful in predicting future events. Common Core Standards, 2010 S&P 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. S&P 6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. S&P 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. S&P 7a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. S&P 7b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. S&P 8a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. S&P 8b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event. S&P 8c. Design and use a simulation to generate frequencies for compound events. W.7.2. Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content. Learning Expectations Activities/Resources Student Strategies Formative Assessments Technology Infusion/ Resources Explain that the probability of an event is the measure of how likely it is that the vent will occur is a number between 0 and 1 Explain that a probability near 1 indicates an unlikely event, a probability around ½ indicates an event is neither likely nor unlikely, and a probability near 1 indicates that an event is likely Have students create a list of events that have a probability of zero and a different list of events that have a probability of one. Interpret probabilities as ratios, percents, and decimals. ___ Watch the Brainpop video and take the quiz receiving a score of at least 9 out of 10 http://www.brainpop.com/math/probability/independentanddependent events/preview.weml http://www.brainpop.com/math/dataanalysis/statistics/preview.weml Play and analyze probability-based games, and discuss the concepts of fairness and expected value. Have students turn to a partner and compare their lists. Have a few student volunteers put an event from their list on the Smart Board Students will watch the video “Probability with Ben and Jerry” on Youtube: http://www.youtube.com/watch?v=hUIvyKqamjg Probability Activity Menu Directions: Choose a variety of activities from the menu below. The activities must total at least 10 points. Place a checkmark next to each box to show which activities you will complete. 2 Points ___ Complete the Worksheet ( No work = No credit) Watch the Brainpop video and take the quiz receiving a score of at least 9 out of 10 http://www.brainpop.com/math/probability/compoundevents/prev iew.weml http://www.brainpop.com/math/probability/gametheory/preview. weml 5 Points ___ Create a cartoon explaining probability and how to find the probability of independent and dependent events and compound events, using paper and colored pencils or online at: http://www.makebeliefscomix.com/Comix/ or Small group instruction Individualized instruction Choice activities Chunking information Rephrasing of questions Working with partner Do now Quiz Test Oral questioning Homework http://www.b rainpop.com/ math/probabil ity/compound events/previe w.weml http://www.b rainpop.com/ math/probabil ity/gametheor y/preview.we ml http://www.b rainpop.com/ math/probabil ity/independe ntanddepende ntevents/prev iew.weml http://www.b rainpop.com/ math/dataanal ysis/statistics /preview.wem l http://www.y outube.com/ watch?v=hUI vyKqamjg http://www.readwritethink.org/files/resources/interactives/comic/ index.html ___ Create a worksheet with a separate answer key, including definitions and sample problems for simple probability, compound probability, independent and dependent events using real-world scenarios in word problem format ___ Create a poster explaining probability and how to find the probability of independent and dependent events and compound events with sample problems and solutions included on the poster 8 Points (Individual or Group) ___ Create video for other students explaining what probability is, how to solve problems related to simple and compound probability, probability of independent and dependent events with specific examples for each of the topics mentioned above ___ Create a Google Site or Power Point that students could use to help review for a test on probability showing how to solve problems related to simple and compound probability, independent and dependent events with an instructional video clip included, sample problems with solutions and an original problem of each type with a separate answer key ___ Create a Probability Brochure that students could use to help review for a test on probability showing how to solve problems related to simple and compound probability, independent and dependent events with an instructional video clip included, sample problems with solutions and an original problem of each type with a separate answer key The probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs, just like with simple events Design and use a simulation to generate frequencies for compound events Show visual representations of sample spaces for compound events (Use organized lists, use tables, use tree diagrams) Show a mathematical algorithm for determining the probability of compound events Conduct an actual experiment and record the results From the results, predict the approximate relative frequency given the probability Students will conduct a simulation to determine the number of times Ashante will take out a ball and a truck that are the same color given the following scenario: Ashante’s toy chest contains a blue, a red, a yellow, a brown and an orange ball. It also has a blue and a white truck. Ashante takes out a ball and a truck without looking. If Ashante does this 35 times, about how many times can she expect to take out a ball and a truck of the same color? Use a number cube and a coin to do a simulation. Assign a number to each ball and a heads or tails to each truck. Make a table to display your results. Experimental Scenario: TaNaiyah takes a 3-item true or false test. She guesses each of the answers. How many correct answers can she expect to get? Before conducting the simulation, make predictions as to the probability of the events. Now, toss a coin three times, once for each item on the test. Do this simulation 25 times and display your results in a bar graph. Experimental Scenario: Each Thursday, a radio station randomly plays new releases 50% of the time. What is the probability that 6 of the next 10 songs will be new releases on any given Thursday? Use a coin to simulate playing a new release. Let heads represent a new release and tails represent a song that is not a new release. Create a table in which you record the data you collect over five trials. For each trial, toss the coint 10 times to represent playing the song 10 times. In how many trials did heads appear 6 or more times? Find the experimental probability that 6 of the next 10 songs on any given Thursday will be new releases based upon the data you collected from your simulation. Why is tossing a coin a good way to simulate the situation? What other methods could you use to simulate this situation? Which methods are best? Explain your reasoning. Small group instruction Individualized instruction Peer tutoring Chunking information Rephrasing of questions Exit ticket Journal entry Do now Quiz Test Oral questioning Homework Conduct an experiment that shows probability that is not uniform Develop probabilities from that experiment Explain why the actual results of an experiment might not match the probability Determine the probability of an event by assigning equal probability to all outcomes Use that probability to determine an estimate of an extrapolated situation Probability & Wheel of Fortune: Probing Question: Why are contestants on Wheel of Fortune always given R, S, T, L, N, and E as their first letter guesses in the bonus round? Performance Task I: Scenario: Studies have been done on use of the English language that indicates that the most commonly used consonants are R, S, T, N, and L and the most commonly used vowel is E. Select an adequate number of paragraphs from a variety of sources or use the paragraphs given to you by your teacher and count the occurrences of these letters and organize your data in a chart or table using Excel or Microsoft Word and graph your data using the most appropriate display of data. Compare and contrast the results of your data collection experiment with the claims of the studies. Based on your conclusions, critique whether the consonants R, S, T, N, and L and the vowel E is a reasonable approach when appearing on Wheel of Fortune and present your findings to the class. Performance Task II: (Optional Lesson) Probing Question: What other three consonants and what vowel should you select if you were a contestant on Wheel of Fortune in the bonus round? In the bonus round you are allowed to pick three more consonants and one vowel. Using the same paragraphs as before, analyze the letter frequency of the paragraphs and decide what three consonants you should pick and what vowel if you made it to the bonus round of Wheel of Fortune from the data you’ve collected. Compare your data with another group’s data and present your findings to the class. (Performance-Based Curriculum: From Knowing to Showing pg. 50) Summative Assessment Task Small group instruction Individualized instruction Peer tutoring Chunking information Rephrasing of questions Working with partner Exit ticket Journal entry Do now Quiz Test Oral questioning Homework