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Wentzville School District Curriculum Development Template Stage 1 – Desired Results Unit 9 - Probability Unit Title: Probability Course: Integrated 7 Brief Summary of Unit: Students will learn to determine probabilities of both simple and compound events, and why the theoretically calculated probability does not always equal the actual experimental probability. Textbook Correlation: Glencoe Math Course 2 Chapter 9 EXCEPT 9-6 (including all labs) Time Frame: 3.5 weeks WSD Overarching Essential Question Students will consider… ● ● ● ● ● ● ● ● ● ● ● ● How do I use the language of math (i.e. symbols, words) to make sense of/solve a problem? How does the math I am learning in the classroom relate to the real-world? What does a good problem solver do? What should I do if I get stuck solving a problem? How do I effectively communicate about math with others in verbal form? In written form? How do I explain my thinking to others, in written form? In verbal form? How do I construct an effective (mathematical) argument? How reliable are predictions? Why are patterns important to discover, use, and generalize in math? How do I create a mathematical model? How do I decide which is the best mathematical tool to use to solve a problem? How do I effectively represent quantities and relationships through mathematical notation? WSD Overarching Enduring Understandings Students will understand that… ● ● ● ● ● ● ● ● ● Mathematical skills and understandings are used to solve real-world problems. Problem solvers examine and critique arguments of others to determine validity. Mathematical models can be used to interpret and predict the behavior of real world phenomena. Recognizing the predictable patterns in mathematics allows the creation of functional relationships. Varieties of mathematical tools are used to analyze and solve problems and explore concepts. Estimating the answer to a problem helps predict and evaluate the reasonableness of a solution. Clear and precise notation and mathematical vocabulary enables effective communication and comprehension. Level of accuracy is determined based on the context/situation. Using prior knowledge of mathematical ideas can help discover more efficient problem solving ● ● How accurate do I need to be? When is estimating the best solution to a problem? ● strategies. Concrete understandings in math lead to more abstract understanding of math. Transfer Students will be able to independently use their learning to… ● ● Make predictions about given situations. Mathematically determine the chances of a favorable outcome. Meaning Essential Questions Understandings How can you predict the outcome of future events? Why (experimentally) do you not always get what you (theoretically) should? How can finding the probability of a simulation help form inferences about real-world events? How can you determine if an event is fair or unfair? What is the best method for finding the probability of simple and compound events? Probability of a chance event is a number between 0 and 1, written as a fraction, decimal, and/or percent. What should happen (theoretical probability) is not always what does happen (experimental probability). Probabilities of simple events can be combined to form the probability of a compound event. Lists, tables, tree diagrams, and simulations can be used to represent compound events in order to draw inferences about the event. Probability experiments can be used to determine if an event’s outcome is fair or unfair. Acquisition Key Knowledge complementary events compound event dependent events Key Skills Use informal descriptions to describe the probability of events experimental probability fair Fundamental Counting Principle independent events outcome permutation probability random relative frequency sample space simple event simulation theoretical probability tree diagram uniform probability model unfair Find and interpret the probability of a simple event. Use an experiment to determine relative frequency. Find and compare experimental and theoretical probabilities. Use experimental and theoretical probabilities to decide whether a game is fair or unfair. Find probabilities of compound events. Perform probability simulations to model realworld situations involving uncertainty. Use a simulation to generate frequencies for a compound event. Use multiplication to count outcomes and find probabilities. Explore the probability of independent and dependent events. Find the probability of independent and dependent events. Use a list, table, tree diagram, or the Fundamental Counting Principle to find out how many items are in the sample space of a compound event Use a simulation to discover the experimental probability of an event and compare it to the theoretical probability of the same event (M&M lab). Design a simulation to represent an event and use it to find the probabilities of various outcomes. Standards Alignment MISSOURI LEARNING STANDARDS Investigate chance processes and develop, use and evaluate probability models. (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) 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. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. (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. a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? Investigate chance processes and develop, use and evaluate probability models. (7.SP.8) Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a. 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. b. 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. c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning. SHOW-ME STANDARDS Goals: 1.1, 1.4, 1.5, 1.6, 1.7, 1.8 2.2, 2.3, 2.7 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8 4.1, 4.4, 4.5, 4.6 Performance: Math 1, 3, 5