Understand solving equations as a process of Standard 22 reasoning and explain the reasoning. Represent and solve equations and inequalities Standard 23 graphically. Analyze functions using different representations. Standard 24 Trigonometry of General Triangles and Trigonometric Functions Apply trigonometry to general triangles. Standards 25-27 Extend the domain of trigonometric functions Standards 28-29 using the unit circle. Model periodic phenomena with trigonometric Standard 30 functions. Mathematical Modeling Create equations that describe numbers or Standards 31-34 relationships. Interpret functions that arise in applications in Standards 35-37 terms of a context. Analyze functions using different representations. Standards 38-40 Build a function that models a relationship Standard 41 between two quantities. Build new functions from existing functions. Standards 42-43 Construct and compare linear, quadratic, and Standard 44 exponential models and solve problems. Visualize relationships between two dimensional Standard 45 and three-dimensional objects. Apply geometric concepts in modeling situations. Standards 46-48 Inferences and Conclusions from Data Cluster Summarize, represent, and interpret data on single count or measurement variable. M.3HS.1(*) 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. Instructional Note: While students may have heard of the normal distribution, it is unlikely that they will have prior experience using it to make specific estimates. Build on students’ understanding of data distributions to help them see how the normal distribution uses area to make estimates of frequencies (which can be expressed as probabilities). Emphasize that only some data are well described by a normal distribution. Cluster Understand and evaluate random processes underlying statistical experiments. M.3HS.2(*) Understand that statistics allows inferences to be made about population parameters based on a random sample from that population. M.3HS.3(*) Decide if a specified model is consistent with results from a given data-generating process, for example, using simulation. (e.g., 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?) Instructional Note: Include comparing theoretical and empirical results to evaluate the effectiveness of a treatment.
Understand solving equations as a process of reasoning and explain the reasoning. Standard 22 Represent and solve equations and inequalities graphically. Standard 23 Analyze functions using different representations. Standard 24 Trigonometry of General Triangles and Trigonometric Functions Apply trigonometry to general triangles. Standards 25-27 Extend the domain of trigonometric functions using the unit circle. Standards 28-29 Model periodic phenomena with trigonometric functions. Standard 30 Mathematical Modeling Create equations that describe numbers or relationships. Standards 31-34 Interpret functions that arise in applications in terms of a context. Standards 35-37 Analyze functions using different representations. Standards 38-40 Build a function that models a relationship between two quantities. Standard 41 Build new functions from existing functions. Standards 42-43 Construct and compare linear, quadratic, and exponential models and solve problems. Standard 44 Visualize relationships between two dimensional and three-dimensional objects. Standard 45 Apply geometric concepts in modeling situations. Standards 46-48 Inferences and Conclusions from Data Cluster Summarize, represent, and interpret data on single count or measurement variable. M.3HS.1(*) 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. Instructional Note: While students may have heard of the normal distribution, it is unlikely that they will have prior experience using it to make specific estimates. Build on students’ understanding of data distributions to help them see how the normal distribution uses area to make estimates of frequencies (which can be expressed as probabilities). Emphasize that only some data are well described by a normal distribution. Cluster Understand and evaluate random processes underlying statistical experiments. M.3HS.2(*) Understand that statistics allows inferences to be made about population parameters based on a random sample from that population. M.3HS.3(*) Decide if a specified model is consistent with results from a given data-generating process, for example, using simulation. (e.g., 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?) Instructional Note: Include comparing theoretical and empirical results to evaluate the effectiveness of a treatment.
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