Students use probability to make better decisions based on knowledge than on intuition alone, and use the normal distribution to understand outcomes of random processes repeated over time.
This unit focuses on standards in the Conditional Probability and the Rules of Probability and Making Inferences and Justifying Conclusions parts of the Statistics and Probability standards. The portion of the unit focused on probability focuses on experimental and conditional probability in an experimental context, emphasizing applications to medical testing. Probability helps us to reason about phenomena in the world and make decisions with better knowledge than relying on intuition alone. An emphasis on conditional probability helps students to reason about cause and effect and serves as an introduction to principles of experimental analysis.
The portion of the unit focused on making inferences emphasizes normal distributions and understanding the outcomes of random processes when they are repeated over time. Finally, students use distributions to make inferences about populations based on samples and apply an understanding of variability to reason about the relationship between samples and populations.
This unit is slightly abbreviated to allow our teachers time to teach the next unit, Limits and Continuity, that prepares students for calculus. Each portion of this unit addresses most but not all of the standards in their respective strands, so if teachers have extra time in the year we suggest adding lessons to extend on each topic; including but not limited to lessons that require students to model different contexts using probability, experiment using probability simulations, gather experimental data and engage with randomization, and make inferences about populations that are relevant to them.
Pacing: 15 instructional days (13 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 8 and should be given on the suggested assessment day or after completing the unit.
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Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
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Proportion (Sample proportion/Population proportion) | Population |
Tree diagram | Mutually exclusive (Disjoint) |
Venn diagram | Complement |
Sample space | Addition rule |
Multiplication rule | Conditional probability |
Relative frequency | Two-way table |
Parameter | Medical testing |
Characteristic | Sample |
Sample survey | Experiment |
Observational study | True positive/True negative |
False positive/False negative |
S.CP.A.1
Determine probabilities of mutually exclusive events.
S.CP.A.1
S.CP.B.6
S.CP.B.7
Determine probabilities of events that are not mutually exclusive.
S.CP.A.3
Calculate conditional probabilities.
S.CP.A.2
S.CP.A.3
S.CP.A.5
Determine when events are independent and describe independent events using everday language.
S.CP.A.4
Calculate relative frequencies in two-way tables to analyze data and determine independence.
S.CP.A.2
S.CP.A.3
Use conditional probability to make decisions about medical testing.
S.IC.A.1
Describe the center, shape, and spread of distributions by reasoning visually about the mean, standard deviation, and shape of a histogram.
S.IC.A.2
S.IC.B.4
Derive and calculate population percentages based on a normal distribution of data.
S.IC.B.4
Use $${z-}$$scores to identify population percentiles.
S.IC.B.3
S.IC.B.6
Describe and compare statistical study methods.
S.IC.B.4
Use multiple random samples to estimate a population mean or proportion and verify the validity of the sampling method by analyzing the means and standard errors of samples.
S.IC.B.4
Calculate and describe the margin of error in context and use larger sample sizes to minimize the margin of error.
S.IC.B.5
Compare two treatments in experimental data and determine if the difference between the two treatments is significant.
Key: Major Cluster Supporting Cluster Additional Cluster
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