MA 3238: Trigonometry and Probability and Statistics

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Subject Area

Mathematics

Credits 1

Years

Level

High School

Grades

10,

11,

Trigonometry complements Algebra II by providing preparation for typical college mathematics courses below the level of calculus. The course offers a thorough treatment of trigonometric and circular functions. Graphs and properties of the six functions are presented in depth. Other topics include trigonometric equations, inverse trigonometric functions, and identities, solutions of triangles and applications of trigonometry. 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.

Prerequisite Courses

MA 3135: Algebra II

Parent Docs

Trigonometry 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	Triangles in Full Circle	What Goes Around Comes Around
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 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.	What do triangles and circles have in common? Now we begin a new story by anAalyzing circular patterns generated from triangle ratios. These patterns are the foundation for studying cyclic events in the next part of our story.	How can we predict future events that are reoccurring periodically? Once we have defined the characteristics of a periodic function we will apply our understanding to create models for real-life cyclic events such as the path of a Ferris wheel, the changing ocean tides, or the moon's phases.
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 to answer questions regarding the collected data.	II can determine the probability of an event and how to use probability to make decisions based on predicted outcomes I can use properties of a normal distribution to answer relevant questions about individuals and groups within a population.	I can determine if a triangle should be solved by applying the laws and properties of triangles to solve real-world problems. I can analyze patterns of the unit circle and its connections to the six trigonometric ratios. I can construct an accurate model of the unit circle.	I can describe how changes in amplitude, period, phase shift, and vertical shift changes affect a trigonometric graph. I can apply transformations of periodic functions from their parent function to model a real-world event. I can verify basic trigonometric identities, recognize graphs of inverse trigonometric functions, and solve trigonometric equations.

Prob/Stat and Trigonometry: 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.
	Unit 7: Solving Triangles	Pirate Attack Football Tackle Problem Commute?	I can determine if a triangle should be solved by applying the laws and properties of triangles to solve real-world problems.
	Unit 8: Circular Trigonometric Functions	Unit Circle Patterns Coming Full Circle	I can analyze patterns of the unit circle and its connections to the six trigonometric ratios.
	Unit 8: Circular Trigonometric Functions	Create the Unit Circle	I can construct an accurate model of the unit circle.
	Unit 9: Graphs of Trigonometric Functions	Trig Art Masterpiece	I can describe how changes in amplitude, period, phase shift, and vertical shift affect a trigonometric graph.
	Unit 9: Graphs of Trigonometric Functions	Modeling a Ferris Wheel Nexxt Full Moon? Tidal Wave Task	I can apply transformations of periodic functions from their parent function to model a real-world event.
	Unit 10: Trigonometric Identities and Equations	Why is tangent called tangent?	I can verify basic trigonometric identities, recognize graphs of inverse trigonometric functions, and solve trigonometric equations