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Students constructed a shared definition of a periodic function and describe features of periodic functions that are important to determining if a function is periodic or not. Students are also introduced to a specific periodic function, the cosine function, through analyzing its equation and graph. 

This Illustrative Mathematics task assesses if students can construct a trigonometric model that represents a context.

This interactive graph from Desmos allows you (or a student) to change the parameters of a sine function to determine how those parameters impact the equation itself. One way to use this is to have a pair of students come up to the front of the room to work on determining which parameter does what, while other students watch the changing parameters and attempt to come up with their own conclusions.

Students will be given different cosine graphs and must match them to the appropriate tables while noting what key points or features help them make connections and note the cyclical nature of both the tables and the graphs.

Students will match cosine function rules with appropriate tables of values while paying attention to how changing the different parts of the equation can affect the values of coordinate pairs in the table.

Dan Meyer 3 Act Math activity. In the video there is a Ferris wheel with smaller ferris wheels at the circumference. Students need to predict path for one of the carriages on the smaller Ferris wheels. It might be useful to incorporate strategies for observing, listening to and recording student work during this activity.

This webpage may help as a refresher for yourself as a teacher for the mathematics of angles on a unit circle.

After this unit, how prepared are your students for the end-of-course Regents examination?  The end of unit assessment is designed to surface how students understand the mathematics in the unit.  It includes spiralled multiple choice and constructed response questions, comparable to those on the end-of-course Regents examination.  A rich task, that allows for multiple entry points and authentic assessment of student learning, may be available for some units and can be included as part of the end of unit assessment.  All elements of the end of unit assessment are aligned to the NYS Mathematics Learning Standards and PARCC Model Frameworks prioritization. 

This blog post describes the math behind a game you can use to practice using the equation of a circle, Battleship.

A Classroom Challenge (aka formative assessment lesson) is a classroom-ready lesson that supports formative assessment. The lesson’s approach first allows students to demonstrate their prior understandings and abilities in employing the mathematical practices, and then involves students in resolving their own difficulties and misconceptions through structured discussion.

Connect to what students know about the Pythagorean Theorem and reading coordinates to find the center of a circle.

Either chunk the diagram in order to find the center of the circle or connect to what students know about completing the square to therefore find the equation of the circle.