unit title: 1 grade level: statistics ii grades 11-12 ... ii curriculum.pdf · unit title: 1 grade...
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Unit Title: 1 Grade Level: Statistics II grades 11-12
Timeframe: 20 days
Essential Questions
How can probabilities be estimated? How can probability distributions be used to make predictions in real-life situations?
Standards
Standards/Cumulative Progress Indicators (Taught and Assessed) CCSS: HS.S.MD.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. HS.S.MD.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. HS.S.MD.3: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes HS.S.MD.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. HS.S.MD.5.A: Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant. HS.S.MD.5.B: Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. HS.S.MD.7: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). HS.S.MD.6. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). 21st Century Skills Standard and Progress Indicators: Critical thinking and problem-solving, communication and media fluency.
Instructional Plan Reflection
Pre-assessment
Unit Pretest- Teacher created
SLO - WALT Student Strategies Formative Assessment
Activities and Resources Reflection
Define a random variable for a quantity of interest by assigning a numerical
• Inquiry-based Learning • Cooperative Learning
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized
http://www.shmoop.com/common-core-standards/ccss-hs-s-md-1.html
Teacher will create using: http://electronicportfolios.com/reflection.html
value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
• Project-based Learning • Peer Led Team Learning • Think-pair-Share
Teacher feedback based on rubric
Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://www.shmoop.com/common-core-standards/ccss-hs-s-md-2.html
Teacher will create using: http://electronicportfolios.com/reflection.html
Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://www.shmoop.com/common-core-standards/ccss-hs-s-md-3.html http://www.shmoop.com/common-core-standards/ccss-hs-s-md-4.html
Teacher will create using: http://electronicportfolios.com/reflection.html
Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://www.shmoop.com/common-core-standards/ccss-hs-s-md-5.html
Teacher will create using: http://electronicportfolios.com/reflection.html
Find the expected payoff for a game of chance
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://www.shmoop.com/common-core-standards/ccss-hs-s-md-5a.html
Teacher will create using: http://electronicportfolios.com/reflection.html
Benchmark Assessment:
Teacher created quiz
Evaluate and compare strategies on the basis of expected values.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://www.shmoop.com/common-core-standards/ccss-hs-s-md-5b.html
Teacher will create using: http://electronicportfolios.com/reflection.html
Analyze decisions and strategies using probability concepts
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://www.shmoop.com/common-core-standards/ccss-hs-s-md-7.html
Teacher will create using: http://electronicportfolios.com/reflection.html
Use probabilities to make fair decisions (e.g., drawing by lots,
• Inquiry-based Learning • Cooperative
*Graphic Organizer *Exit Slip *Peer Assessment
http://www.shmoop.com/common-core-standards/ccss-hs-s-md-6.html
Teacher will create using: http://electronicportfolios.com/reflection.html
using a random number generator).
Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Individualized Teacher feedback based on rubric
Benchmark Assessment:
Summative Written Assessments
Unit Benchmark Test
Summative Performance Assessment
Students will create a game of chance and determine the expected payouts.
Unit Title: 2 Grade Level: Statistics II grades 11-12
Timeframe: 20 days
Essential Questions
How can a sample be used to provide information about a population? How can probabilities be used to estimate an unknown mean with some margin of error?
Standards
Standards/Cumulative Progress Indicators (Taught and Assessed) CCSS: HS.S.IC.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. HS.S.IC.1: Understand statistics as a process of making inferences about population parameters based on a random sample from that population. HS.S.IC.6: Evaluate reports based on data. HS.S.ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots). HS.S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. HS.S.ID.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
HS.S.ID.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. 21st Century Skills Standard and Progress Indicators: Critical thinking and problem-solving, communication and media fluency.
Instructional Plan
Reflection
Pre-assessment
Unit Pretest- Teacher created
SLO - WALT Student Strategies
Formative Assessment
Activities and Resources Reflection
Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://www.shmoop.com/common-core-standards/ccss-hs-s-ic-5.html
Teacher will create using: http://electronicportfolios.com/reflection.html
To describe the behavior of sample means using the Center Limit Theorem
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://www.jerrydallal.com/lhsp/meandist.htm http://bolt.mph.ufl.edu/6050-6052/unit-3b/module-9/
Teacher will create using: http://electronicportfolios.com/reflection.html
To create confidence intervals and test hypothesis about proportions.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
https://onlinecourses.science.psu.edu/stat200/node/53 https://onlinecourses.science.psu.edu/stat200/node/53
Teacher will create using: http://electronicportfolios.com/reflection.html
To use statistical inference to compare the means of two independent groups.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://sites.nicholas.duke.edu/statsreview/means/ https://onlinecourses.science.psu.edu/stat500/node/55
Teacher will create using: http://electronicportfolios.com/reflection.html
Teacher created quiz
Benchmark Assessment:
Evaluate reports based on data
• Inquiry-based Learning • Cooperative Learning • Project-
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized
http://www.shmoop.com/common-core-standards/ccss-hs-s-ic-6.html
Teacher will create using: http://electronicportfolios.com/reflection.html
based Learning • Peer Led Team Learning • Think-pair-Share
Teacher feedback based on rubric
Summative Written
Assessments
Unit Benchmark
Test
Summative Performance Assessment
Students will conduct a survey or
experiment and analyze the
results.
Unit Title: 3 Grade Level: Statistics II grades 11-12
Timeframe: 15 days
Essential Questions
How can probabilities be used to estimate an unknown proportion with some margin of error? How does sample size affect margin of error? How can we verify or refute a claim about a proportion?
Standards
Standards/Cumulative Progress Indicators (Taught and Assessed) CCSS: HS.S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard
deviation) of two or more different data sets. HS.S.ID.4: Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. HS.S.IC.1: Understand statistics as a process of making inferences about population parameters based on a random sample from that population. HS.S.IC.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. HS.S.IC.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. HS.S.IC.6: Evaluate reports based on data. 21st Century Skills Standard and Progress Indicators: Critical thinking and problem-solving, communication and media fluency.
Instructional Plan
Reflection
Pre-assessment
Unit Pretest- Teacher created
SLO - WALT Student Strategies
Formative Assessment
Activities and Resources Reflection
Construct and interpret a confidence interval to compare two proportions
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://www.kean.edu/~fosborne/bstat/06d2pop.html http://stattrek.com/estimation/difference-in-proportions.aspx?Tutorial=AP
Teacher will create using: http://electronicportfolios.com/reflection.html
Perform a significance test to compare two proportions
• Inquiry-based Learning • Cooperative Learning
*Graphic Organizer *Exit Slip *Peer Assessment *Individualize
http://stattrek.com/hypothesis-test/difference-in-proportions.aspx https://onlinecourses.science.psu.edu/stat414/node/268
Teacher will create using: http://electronicportfolios.com/reflection.html
• Project-based Learning • Peer Led Team Learning • Think-pair-Share
d Teacher feedback based on rubric
Construct and interpret a confidence interval to compare two means
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://onlinestatbook.com/2/estimation/difference_means.html http://stattrek.com/estimation/difference-in-means.aspx?Tutorial=AP
Teacher will create using: http://electronicportfolios.com/reflection.html
Perform a significance test to compare two means
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://onlinestatbook.com/2/tests_of_means/difference_means.html http://stattrek.com/hypothesis-test/difference-in-means.aspx?Tutorial=AP
Teacher will create using: http://electronicportfolios.com/reflection.html
Determine when it is appropriate to use two-
• Inquiry-based Learning •
*Graphic Organizer *Exit Slip *Peer
http://math.arizona.edu/~jwatkins/T_ttest.pdf http://www.statstutor.ac.uk/resources/uploaded/paired-t-test.pdf
Teacher will create using: http://electronicportfolios.com/reflection.html
sample t-procedures versus paired t procedures
Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
Assessment *Individualized Teacher feedback based on rubric
Summative Written
Assessments
Unit Benchmark
Test
Summative Performanc
e Assessment
Students will conduct a survey or experiment and analyze the results.
Unit Title: 4 Grade Level: Statistics II grades 11-12
Timeframe: 15 days
Essential Questions
How can we verify that two variables are independent? How does one distinguish among the various tests of significance? What makes an argument statistically convincing?
Standards
Standards/Cumulative Progress Indicators (Taught and Assessed) CCSS: HS.S.IC.1: Understand statistics as a process of making inferences about population parameters based on a random sample from that population. HS.S.IC.2: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with a probability 0.5. Would a result of 5 tails in a row cause you to question the model? HS.S.IC.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 21st Century Skills Standard and Progress Indicators: Critical thinking and problem-solving, communication and media fluency.
Instructional Plan
Reflection
Pre-assessment
Unit Pretest- Teacher created
SLO - WALT Student Strategies
Formative Assessment
Activities and Resources Reflection
State appropriate hypotheses and compute expected counts for a chi-square test for goodness of fit.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://stattrek.com/chi-square-test/goodness-of-fit.aspx http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_HypothesisTesting-ChiSquare/BS704_HypothesisTesting-ChiSquare_print.html
Teacher will create using: http://electronicportfolios.com/reflection.html
Calculate the chi-square
• Inquiry-based
*Graphic Organizer
http://stattrek.com/chi-square-test/goodness-of-fit.aspx?Tutorial=AP
Teacher will create using: http://electronicportfolios.com/reflection.html
statistic, degrees of freedom, and P-value for a chi-square test for goodness of fit
Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://www.stat.yale.edu/Courses/1997-98/101/chigf.htm
Perform a chi-square test for goodness of fit
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
https://www.khanacademy.org/math/probability/statistics-inferential/chi-square/v/pearson-s-chi-square-test-goodness-of-fit http://stattrek.com/chi-square-test/goodness-of-fit.aspx?Tutorial=AP
Teacher will create using: http://electronicportfolios.com/reflection.html
Compare conditional distributions for data in a two-way table
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
https://www.youtube.com/watch?v=ByywCuLHDwI http://stattrek.com/statistics/two-way-table.aspx?Tutorial=AP
Teacher will create using: http://electronicportfolios.com/reflection.html
Choose the appropriate chi-square test
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://stattrek.com/chi-square-test/independence.aspx?Tutorial=AP http://www.ling.upenn.edu/~clight/chisquared.htm
Teacher will create using: http://electronicportfolios.com/reflection.html
Conduct a follow-up analysis when the results of a chi-square test are statistically significant.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://pareonline.net/getvn.asp?v=20&n=8 http://www.upa.pdx.edu/IOA/newsom/pa551/lectur13.htm
Teacher will create using: http://electronicportfolios.com/reflection.html
Summative Written
Assessments
Unit Benchmark
Test
Summative
Performance Assessment
Students will conduct a survey or
experiment and analyze the results.
Unit Title: 5 Grade Level: Statistics II grades 11-12
Timeframe: 15 days
Essential Questions
How can we test the slope of a correlation? How do we use a model to make a statistical inference? Is all data created equal?
Standards
Standards/Cumulative Progress Indicators (Taught and Assessed) CCSS: HS.S.IC.1: Understand statistics as a process of making inferences about population parameters based on a random sample from that population. HS.S.IC.2: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with a probability 0.5. Would a result of 5 tails in a row cause you to question the model? HS.S.IC.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. HS.S.IC.4: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. HS.S.IC.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. 21st Century Skills Standard and Progress Indicators: Critical thinking and problem-solving, communication and media fluency.
Instructional Plan
Reflection
Pre-assessment
Unit Pretest- Teacher created
SLO - WALT Student Strategi
es
Formative Assessme
nt
Activities and Resources Reflection
Check the conditions for performing inference about the slope of the population regression line.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
https://www.stat.berkeley.edu/~thornton/STAT20/lec18slides4.pdf http://math.arizona.edu/~ghystad/chapter17.pdf
Teacher will create using: http://electronicportfolios.com/reflection.html
Construct and interpret a confidence interval for the slope of the population regression line.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://stattrek.com/regression/slope-confidence-interval.aspx?Tutorial=AP https://www.youtube.com/watch?v=_ly1nmVuB00
Teacher will create using: http://electronicportfolios.com/reflection.html
• Peer Led Team Learning • Think-pair-Share
Perform a significance test about the slope of the population regression line.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://stattrek.com/regression/slope-test.aspx?Tutorial=AP https://www.youtube.com/watch?v=q_ma0FtFp04
Teacher will create using: http://electronicportfolios.com/reflection.html
Use transformations involving powers and roots to find a power model that describes the relationship between two
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://pmwestapstatistics.wikispaces.com/file/view/Section12.2Print.pdf https://www.coursehero.com/file/8363374/Transforming-to-Achieve-Linearity/
Teacher will create using: http://electronicportfolios.com/reflection.html
variables. Team Learning • Think-pair-Share
Use transformations involving logarithms to find a power model that describes the relationship between two variables.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning • Think-pair-Share
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://pmwestapstatistics.wikispaces.com/file/view/Section12.2Print.pdf http://faculty.harford.edu/faculty/dschwank/Stat216/lectures/textbook_4th_ed.pdf/4.5_nonlinear_regression.pdf
Teacher will create using: http://electronicportfolios.com/reflection.html
Determine which of several transformations does a better job of producing a linear relationship.
• Inquiry-based Learning • Cooperative Learning • Project-based Learning • Peer Led Team Learning
*Graphic Organizer *Exit Slip *Peer Assessment *Individualized Teacher feedback based on rubric
http://stattrek.com/regression/linear-transformation.aspx?Tutorial=AP https://www.pearsonhighered.com/assets/hip/us/hip_us_pearsonhighered/samplechapter/0205019676.pdf
Teacher will create using: http://electronicportfolios.com/reflection.html
• Think-pair-Share
Summative Written
Assessments
Unit Benchmark
Test
Summative Performan
ce Assessmen
t
Students will
conduct a survey or
experiment and analyze the results.