Students formalize their understanding of compound probability, develop an understanding of conditional probability, and understand and calculate permutations and combinations.
Math
Unit 8
10th Grade
In Unit 8, Probability, students extend their understanding of probability from seventh grade to a more formal approach to probability by applying formulas and definitions.
Students begin the unit using visual representations of lists, tree diagrams, and Venn diagrams to find the probability of events that intersect or represent the union or complement of outcomes. Students also formalize their understanding of compound probability. Then, students develop a conceptual and procedural understanding of conditional probability and how this can be used to determine whether variables are independent. In application, students use this knowledge to solve a set of applications on medical testing. Finally, as an optional part of the unit (covering plus (+) Common Core State Standards), students understand and calculate permutations and combinations. The students develop an understanding that whether order matters or not can affect the sample space of the total combinations or the number of chosen items within a set of items.
In Algebra 2, students will continue their study of probability by studying statistical inference and making decisions using probability.
Pacing: 12 instructional days (10 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
sample space | $$P$$ (desired outcome) |
complement | tree diagram |
with replacement | without replacement |
mutually exclusive (disjoint) | addition rule |
multiplication rule | equally likely (fair) |
compound probability | venn diagram |
conditional probability | dependent event |
independent event | relative frequency |
two-way table | medical testing |
false positive/false negative | true positive/true negative |
permutation | combination |
fundamental counting principle |
Topic A: Conditional Probability and the Rules of Probability
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
Circles