This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.
S.MI: : Making Inferences & Justifying Conclusion
1.1: : Surveys, Experiments, & Observational Data
1.1.1: : Students make inferences and justify conclusions from sample surveys, experiments, and observational studies.
S.MI.1: : Estimate a population mean or proportion from a sample survey; develop a margin of error through the use of simulation models for random sampling.
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
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S.MI.2: : Calculate the standardized test statistic and p-value for a test about a population proportion and a population mean; determine if the sample data provides convincing evidence against a parameter claim.
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
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Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population.
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S.MI.3: : Compare two treatment groups in an experiment and determine if the difference in parameters is significant by calculating the standardized test statistics and p-value.
Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population.
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S.RP: : Conditional Probability & Rules of Probability
2.2: : Independence & Conditional Probability
2.2.1: : Students understand and use independence and conditional probability to interpret data.
S.RP.3: : Determine if two events, A and B, are independent when given the probabilities of A and B.
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events.
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S.RP.4: : Calculate and use conditional probabilities to determine if events are independent.
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events.
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S.RP.7: : Explain conditional probability and independence using everyday language in a variety of real-world contexts.
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events.
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S.RP.8: : Find the conditional probability of A given B, P(A|B), and interpret the answer in terms of the model, including two-way frequency tables and Venn diagrams.
Theoretical and Experimental Probability
Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes.
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S.RP.11: : Apply the general Multiplication Rule, P(A and B) = P(A)P(B|A) = P(B)P(A|)B and interpret the answer.
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events.
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S.RP.12: : Compute the probability of compound events and solve problems using combinations, permutations, Venn Diagrams, and Tree Diagrams.
Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle.
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3.1.1: : Students calculate and use expected values of random variables to solve problems.
S.PMD.1: : Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
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S.PMD.2: : Calculate the expected value for a discrete random variable; describe the expected value as the mean or typical value of the probability distribution in context.
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
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S.PMD.3: : Create a probability distribution of a discrete random variable using theoretical probabilities and use the probability distribution to calculate the probability of an event.
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
5 Minute Preview
S.PMD.4: : Create a probability distribution for a discrete random variable using experimental or observational data; calculate the expected value.
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
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3.2.1: : Students evaluate outcomes of decisions using probability.
S.PMD.6: : Analyze the costs and benefits of possible outcomes of making a decision by assigning probabilities to particular payoff values of a discrete random variable and calculate expected values.
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
5 Minute Preview
4.1.1: : Students explore best practices of collecting data while identifying possible sources of bias in data collection methods.
S.CD.2: : Use randomization strategies to ensure random selection processes are fair.
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
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Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling.
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Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population.
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S.DD: : Displaying & Describing Distributions of Data
5.1: : Data Representation
5.1.1: : Students represent raw data in tabular and graphical form to describe features of the data and summarize trends.
S.DD.2: : Determine if there is an association between two quantitative variables using the correlation coefficient and scatter plots.
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line.
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Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line.
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Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line.
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Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
