Wentzville School District Honors Algebra II

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1 Wentzville School District Honors Algebra II Unit 7 - Statistics Unit Title: Statistics Course: Honors Algebra II Brief Summary of Unit: Students will investigate the methods and purposes of sampling, data analysis and appropriate representations of data. Students will examine characteristics of the normal curve and use to find appropriate data values and probabilities. Students will use data from samples to make inferences about the parameters of populations and draw conclusions. Textbook Correlation: Glencoe Algebra II Chapter (not 11.4 or hypothesis testing in 11.6) Timeframe: 3 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 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

2 relationships through mathematical notation? How accurate do I need to be? When is estimating the best solution to a problem? help discover more efficient problem solving strategies. Concrete understandings in math lead to more abstract understanding of math. Transfer Transfer Goal Students will be able to independently use their learning to use discretion when faced with meaningful statistics and consider the validity of those statistics when making informed decisions. Meaning Essential Questions Students will consider Understandings Students will understand that How can I obtain a reasonable estimation of a population parameter without completing a census? What are reasonable outcomes of a simulation? What types of sampling methods are best in what situations? Why is making an inference about a population better than counting and describing every member of the population? What information can be obtained from a sample survey or observational study? How can the results of an experiment be used? How can statistics be misleading? Sampling and simulation can be used to estimate parameters and possible outcomes. Inferences are a mathematical way to predict population characteristics without having to account for every member of a population. Data can be collected in a variety of ways, but causation can only be determined through a wellcontrolled experiment. Inferences about populations can be made by using information from a smaller sample If a distribution is roughly unimodal and symmetrical, than a normal distribution can be used to approximate the percentage of values that are found within an interval. In what instances would someone want to use misleading statistics?

3 How can statistics be used to evaluate reports based on data? When can I approximate the percentage of values that are between two values in the distribution? When is it necessary to standardize (use z-scores) to approximate population percentages? How do the mean and standard deviation affect the distribution used to approximate population percentages? When and how can the properties of a normal distribution be used to find probabilities? Acquisition Key Knowledge Students will know Sample Census Population expected value random variable (discrete and continuous) confidence interval Bias margin of error (maximum error of estimate) for large samples box and whisker plot probability distributions theoretical probability distribution frequency table relative frequency table histogram Empirical rule Density curve Bell curve Sample Survey Experiment Observational Study Statistic (mean, standard deviation, variance, median, mode) Parameter (mean, standard deviation, median, mode) Key Skills Students will be able to. Design a survey by clearly stating the objective, identifying the population and choosing unbiased survey questions. Analyze experiments to determine validity of the results. Differentiate between a sample survey, an observational study, and an experiment. Analyze reports and data representations to determine if there are misleading statistics or explain why the statistics are sound. Summarize data graphically, in a table or in another manner by hand and/or using technology such as spreadsheets or graphing calculators. Use graphic representations to describe and compare distributions of different data sets. Describe a distribution using its mean and standard deviation. Calculate the weighted mean by finding the expected value and explain the meaning in context of the problem. Calculate mean, standard deviation, variance, median, and mode to describe the distribution of data sets. Identify important properties of a normal distribution density curve (bell curve). (The

4 Probability Simulation Theoretical and empirical probabilities positively skewed distribution Negatively skewed distribution symmetric distribution normal distribution standard normal distribution z-scores (z-values) Inferential Statistics empirical rule) Determine if a normal distribution is appropriate Calculate a z-score for a data value. Read a standard normal probability table (zdistribution table***more than one type of table can be used) Construct a model (density curve) to illustrate the problem. Estimate population percentages (area under the normal curve) using the z-distribution table and/or technology such as spreadsheets or graphing calculators. Determine the parameter of interest in a given scenario and what statistic can be used to estimate it. Use data from a sample survey to calculate the margin of error in order to provide an interval estimate of a population mean. Standards Alignment MISSOURI LEARNING STANDARDS S.IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. 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 probability 0.5. Would a result of 5 tails in a row cause you to question the model? S.IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 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. S.IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. S.IC.6 Evaluate reports based on data. 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.

5 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. Goal 1: 1, 4, 5, 6, 7, 8 Goal 2: 2, 3, 7 Goal 3: 1, 2, 3, 4, 5, 6, 7, 8 Goal 4: 1, 4, 5, 6 Show Me-Standards Mathematics: 1, 3