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.
Math
Unit 8
11th Grade
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.
Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
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 |
Topic A: Probability
Topic B: The Normal Distribution
Topic C: Statistical Inferences and Conclusions
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 7
Trigonometric Identities and Equations
Unit 9
Limits and Continuity