MA 3200: Discrete Mathematics and Probability and Statistics

Subject Area

Credits 1

Years

Level

High School

Discrete Mathematics offers methods of problem solving which are not normally found in the algebra, geometry, trigonometry, or mathematical analysis courses. Problems in the area of management science such as modeling problems with graphs, scheduling, designing efficient delivery routes and optimization are emphasized along with social decision- making topics including fair division. Probability and Statistics provides an understanding of the kinds of regularity that occur in random functions and provides experiences in associating probabilistic mathematical models with phenomena in the real world. Topics include averages, measures of variation, frequency distributions and probability functions associated with random variables, binomial distributions, sampling, the normal curve, and statistical methods available for decision making.

Prerequisites

Algebra II (MA 3135), Algebra II/Trigonometry (MA 3137), or Algebra, Functions, and Data Analysis (MA 3134)

Parent Docs

Discrete Mathematics and Probability and Statistics Parent Doc 2021-2022

Storyboard

Essential Questions: How do I become a mathematical problem solver to better understand the world around me? In what ways can I communicate and represent my mathematical thinking?
Title	Surveying the World	Predicting the Future	Making Decisions Fairly	Building Community
Focus of the Story	How do we collect and analyze data? We start our story by collecting data through exploration activities such as surveys and then interpret the data by creating graphical displays to analyze relationships found among the data collected.	How can we predict future events? Next, we discover connections between the experimental data collected and its ability to predict future events by exploring the concepts of probability and randomness. We then learn to justify and explain our findings through statistical evidence.	How can we use mathematics to make equitable decisions? Our story shifts to discrete mathematics where we explore, compare, and apply different methods of determining elections. We then investigate how to fairly divide limited resources amongst several parties to ensure fairness.	How can we apply mathematics to solve problems in our communities? Finally, our journey will end with learning to resolve conflict by applying graph theory. We will determine ways to improve the organizations and communities around us by applying principles of optimization.
Transfer Goals	Explore: Make sense of the world mathematically by asking questions and making connections through inquiry.	Explain: Communicate mathematical thinking by justifying solutions using multiple representations while attending to precision.	Analyze: Investigate, formulate, and construct viable arguments by taking risks, persevering, and thinking flexibly.	Apply: Utilize effective strategies, processes, and tools to model new situations and/or real-world experiences.
Learning Targets	I can collect meaningful data from samples and experiments to support hypotheses and answer relevant questions about a population. I can calculate numerical summaries and create graphical displays from sample and experimental data. I can describe and analyze the relationship between two quantitative variables to support hypotheses and answer questions regarding the collected data.	I can determine the probability of an event and how to use probability to make decisions based on predicted outcomes. I can use the properties of a normal distribution to answer relevant questions about individuals and groups within a population.	I can determine the winner of a vote using the fairest method. I can apply various methods to divide resources in apportionment problems.	I can determine the optimal solution to a conflict resolution problem. I can find the optimal path or circuit in a graph. I can apply algorithms to create a minimum spanning tree.

Probability/Statistics and Discrete: Assessment Matrix
Title	Unit	Rich Tasks:	Learning Target
	Unit 1: Collecting Data	Stadium Seating Research Proposal Anchored Putting	I can collect meaningful data from samples and experiments to support hypotheses and answer relevant questions about a population.
	Unit 2: Analyzing Categorical Data	Categorical Analysis Social Media	I can calculate numerical summaries and create graphical displays from sample and experimental data. (qualitative)
	Unit 3: Analyzing One Variable Quantitative Data	1 in 6 Wins	I can calculate numerical summaries and create graphical displays from sample and experimental data. (quantitative).
	Unit 4: Analyzing Two Variable Quantitative Data	Barbie Bungie Intro How Close Can You Get to the Finish Line?	I can describe and analyze the relationship between two quantitative variables to support hypotheses and answer questions regarding the collected data.
	Unit 5: Probability	Prefer English or Math Can we predict…?	I can determine the probability of an event and how to use probability to make decisions based on predicted outcomes.
	Unit 6: Normal Distribution	Standardized: Who is the G.O.A.T? Normal Distribution	I can use the properties of a normal distribution to answer relevant questions about individuals and groups within a population.
	Election Theory & Weighted Averages	Group Ranking	I can determine the winner of a vote using the fairest method.
	Fair Division & Apportionment	To Be or Not to Be	I can apply various methods to divide resources in apportionment problems.
	Graph Theory	Conflict Resolution*	I can determine the optimal solution to a conflict resolution problem.
		Build a Town	I can find the optimal path or circuit in a graph.
		Streets of Euler	I can find the optimal path or circuit in a graph.
	Optimization	Money for Nothing	I can apply algorithms to create a minimum spanning tree