| Code |
Description |
| MA.912.DP.6.1: | Define a random variable for a quantity of interest by assigning a numerical value to each individual outcome in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. |
| MA.912.DP.6.2: | Develop a probability distribution for a discrete random variable using theoretical probabilities. Find the expected value and interpret it as the mean of the discrete distribution. |
| MA.912.DP.6.3: | Develop a probability distribution for a discrete random variable using empirical probabilities. Find the expected value and interpret it as the mean of the discrete distribution. |
| MA.912.DP.6.4: | Given a binomial distribution, calculate and interpret the expected value. Solve real-world problems involving binomial distributions.Clarifications:
Clarification 1: Instruction focuses on the connection between binomial distributions and coin tossing and the connection to one-question surveys in which the question has two possible responses. |
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| MA.912.DP.6.5: | Solve real-world problems involving geometric distributions.Clarifications:
Clarification 1: Instruction focuses on the connection between geometric distributions and tossing a coin until the first heads appears and the connection to making repeated attempts at a task until it is successfully completed. |
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| MA.912.DP.6.6: | Solve real-world problems involving Poisson distributions.Clarifications:
Clarification 1: Instruction focuses on the connection between Poisson distributions and tossing a coin a large number of times for which the probability of heads is very small and the connection to the number of accidents occurring among a large number of people. |
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| MA.912.DP.6.7: | Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values and standard deviations. Evaluate and compare strategies on the basis of the calculated expected values and standard deviations.Clarifications:
Clarification 1: Instruction includes the relationship between expected values and standard deviations on one hand and the rewards and risks on the other hand.Clarification 2: Instruction includes reducing risk through diversification. |
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| MA.912.DP.6.8: | Apply probabilities to make fair decisions, such as drawing from lots or using a random number generator. |
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| In terms of soccer: Nike or Adidas?: | In this lesson, students calculate and interpret the standard deviation for two data sets. They will measure the air pressure for two types of soccer balls. This lesson can be used as a hands-on activity or completed without measuring using sample data. |
| If The Shoe Fits – A "Normal" Cinderella Story: | Using a normal distribution manipulative and a calculator, students will explore the normal distribution curve to determine the area between each standard deviation from the mean using the empirical rule. Students will use the mean and standard deviation to predict outcomes in real-world situations and finally answer the age old question: What size was Cinderella's glass slipper? |
| The Cereal Prize Estimation: | How many boxes of cereal would you have to purchase to win all six prizes?
This lesson uses class data collected through simulations to allow students to answer this question. Students simulate purchasing cereal boxes and create a t-confidence interval with their data to determine how many boxes they can expect to buy. |
| Sweet Statistics - A Candy Journey: | Students will sort pieces of candy by color and then calculate statistical information such as mean, median, mode, interquartile range, and standard deviation. They will also create an Excel spreadsheet with the candy data to generate pie charts and column charts. Finally, they will compare experimental data to theoretical data and explain the differences between the two. This is intended to be an exercise for an Algebra 1 class. Students will need at least 2 class periods to sort their candy, make the statistical calculations, and create the charts in Excel. |
| Proposed Budgets: | In this Model Eliciting Activity (MEA), students will analyze federal budget data to propose strategic allocations using mathematical skills like expected value calculations and data normalization to justify their recommendations.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx |
| Winner! Winner! - Expected Values: | County Fairs and Carnivals are wonderful. The smell of the food, the thrill of the rides, and the chance to win prizes make for a perfect combination.
In this Model Eliciting Activity, MEA Winner! Winner! is an activity about the Carnival coming to town with seven (7) exciting games: Rolling Dice, Bottle Bowling, Fishbowl, Weigh in on That! Pin the Wing, Colors, and Spin It! Student groups must look at the cost, rules, and awarded prizes in order to give the best rank order for these games. The groups will be expected to give details on the procedures they used to develop their ranking order. Furthermore, students will be expected to calculate the expected values of the Rolling Dice game and interpret the results in context.
All of a sudden more information is collected about these Carnival Games and now the savvy students must use this information to either revise or rewrite their procedures. Then, when the students are ready to attack this new dilemma, they will encounter Andy, a Carnival Lover, who has had a thrilling time but now discovers his funds are running low. Which games will the students select for Andy and why?
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx. |
| Phalangelpodscribitis? - Analysis with Probability: | In this Model Eliciting Activity, MEA students will be presented with seven (7) medications that will help cure an individual of Phalangelpodscribitis (a fictitious ailment). Students will be given the effectiveness of each medication, the cost to patients with and without insurance, and the possible side effects of each. Each team will be tasked with ranking these medications for a client to help decide the pros and cons of the medications that should be used in treating Phalangelpodscribitis (PPS).
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx |
Vetted resources students can use to learn the concepts and skills in this topic.
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