**Ariane Masuda and Sybil Shaver**

**Title: **Trig identities and using the unit circle to solve trig equations that come from physics

**Links: **Activity Info (trig identities) and Activity Info (trig equations)

**Description:** Students usually have difficulties in proving trig identities. We developed a series of steps that will make the task easier to accomplish. pdfs and latex files for worksheets available.

**Timing suggestion:** The trig identities lesson will take one class (Lesson 23). The STEM application will follow the lesson on solving basic trig equations (Lesson 24). We expect that it will take about 1 hour of class time, with about 1 hour out-of-class reading the background material and working additional example(s).

**Holly Carley**

**Title:** Rational and Integer Exponents

**Link: **Activity Info

**Description: **Lesson 1. In-class activities. pdf and latex source files for worksheets on integer and rational exponents involving applications to proportions, volume, surface area, and relative error.

**Timing suggestion: **No time outside of class should be required. The proportion worksheet is to be given before discussion of rational exponents (15 minutes) and the integer exponent worksheet after the integer exponent discussion (10 minutes).

**Laura Ghezzi**

**Title:** Let’s talk about money! Compound Interest Activity.**Link: **Activity Info

**Description:** This is an in-class activity. Pdf of worksheet.

**Timing suggestion: **Lesson 28

**Lori Younge**

**Title**: Applications of Quadratic Equations

**Link: **Activity Info

**Description: **This application is composed of a series of questions to be answered based on a quadratic function that models a specific situation. There are three different quadratic functions: one models the number of bacteria in a petri dish, the second models the value of a stock portfolio, and the third models the cost in producing tennis balls. This is an in-class activity. Pdfs of worksheets.

**Timing suggestion: **Lesson 12. This activity is to be done after covering the methods to solving quadratic equations and after discussing the graphs of quadratic functions.

**Lucie Mingla**

**Title: **Complex Numbers and Quadratic Equations in Electric Circuits

**Link: **Activity Info

**Description:** A flipped classroom in combination with active learning strategies (group work) will be used to teach the concept of complex numbers. The focus will be complex numbers as solutions of quadratic equations, operations with complex numbers and especially using complex numbers in STEM applications such as AC circuits. OERs related to circuits will give students the chance to learn more about series, parallel, AC, and DC circuits as well as Ohm’s and Kirchoff’s laws that apply. Presentation, worksheets, solutions, video and rubric.

**Timing suggestion: **Lessons 9 and 10.

**Suman Ganguli**

**Title:** Integer and Rational Exponents via Compound Interest Formulas

**Link:** Activity Info

**Description:** We will facilitate student investigation of integer and rational exponents via applications to compound interest, specifically: (1) integer exponents, via derivation and exploration of the annual compound interest formula. (2) rational exponents, via (a) inverting the compound formula above to solve for rate of return; (b) extending the annual compound interest formula to account for multiple compound periods. Pdfs and LaTeX files.

**Timing suggestion:** This application will consist of 2 modules which will be used at the following points of the semester:

1) Lesson 4 (Rational Exponents): Module on Annual Compound Interest Formula & Rates of Return

2) Lesson 28 (Compound Interest): Module on Compound Interest with Multiple Compound Periods

**Title: **An Application of Trigonometry: Estimating the Height of a Building

**Link: **Activity Info

**Description:** Students carry out an application of trigonometry that is otherwise only presented in the abstract in the course: using trigonometry to estimate the height of a building. Students produce an estimate of the height of the Empire State Building by (1) estimating the distance from CityTech to the Empire State Building from a map and (2) estimating the angle of elevation using a clinometer (either a physical clinometer, using a protractor; or a digital clinometer smartphone app). Pdf and LaTeX doc of worksheet.

**Timing suggestion: **Lesson 19

**Vladina Antoine**

**Title: **An Application of the Ambiguous Case of the Law of Sines

**Link: **Activity Info

**Description:** This stem application involves an activity on the Law of Sines, with emphasis on the Ambiguous Case. The students will have prior knowledge of the properties of triangles, how to use the unit circle to determine the measurement of angles of the triangles and the conditions necessary for applying the Law of Sines. Worksheet doc and rubric.

**Timing suggestion:** This application will be used after Lesson 25 – Oblique Triangles and the Law of Sines & Law of Cosines from the syllabus has been taught.

**Duvvuri Varalakshmi**

**Title:** Distance Formula, Equation of a Circle

**Link:** Activity Info

**Description**: To find the equation to a circle using the distance formula, given the center and radius of the circle. Given the equation of the circle, how to find the center and radius. How to graph a circle. The theory of circles and circular motion is widely used in transporting systems (e.g. bicycles etc) as well as in technological advancements to provide entertainment for people of all ages (e.g. Ferris Wheel). Doc of worksheet.

**Timing suggestion: **Lesson 17

**Kate Poirier**

**Title: **Graphs of Sine and Cosine

**Links: **Activity Info, Desmos, Assessment

**Description:** The position of a ferris wheel car is used to motivate the definitions and graphs of the sine and cosine functions using circular motion. The Desmos Activity is a step-by-step introduction to both of the functions and their graphs. A post-activity quiz is also given.

**Timing suggestion:** Lesson 18

**Victor Sirelson**

**Title:** Faces of the Unit Circle

**Links: **Activity Info, Desmos

**Description:** This project focuses on the unit circle and its ramifications. It contains a Desmos application which will illustrate a number of concepts including (but not limited to): defining a triangle by a point on the unit circle; the definition of the sine and cosine in terms of the coordinates of the point on the circle; the correspondence between angles, arcs on the circle, trig functions; radians and how they fit on the circle; the four quadrants; equivalent angles and quadrants; periodicity. Desmos activity.

**Timing suggestion: **Trigonometry lessons 20, 21, 22 and 23.

**Dongmei Yu**

**Title:** Graphing quadratic functions; Trigonometric equations and non-linear system equations.

**Link: **Activity Info

**Description:** Investigation of Quadratic Functions and Parabolas via graphing practices, specifically:

- Shifting Parabolas
- Parabola Vertices
- Deriving the form from the graphing.

Pdf of worksheets.

**Timing suggestion: **Lesson 13 and Lesson 24

**Sun Young Ban**

**Title: **Calculate the slope of a line

**Link: **Activity Info

**Description: **The goal of this unit plan is for all students to understand how to write an equation of a line (\(y = mx+b\)) when they are given the graph of a line, at least two points on a line, or the slope and point of a line. Students will be able to graph linear equations, and interpret data that is represented graphically. Students will also be able to know how to solve for a variable (i.e., solve for \(x\)), understand the four quadrants of a graph, and how to graph a line. By the end of the unit the students will be able to identify and calculate the slope of a line (\(m =\) slope of line), the \(y\)-intercept of a line (\(b = y\)-intercept), how to graph a line using the equation of line formula (\(y = mx+b\)), and write the equation of a line from a single line on a graph, two points of a line, or the slope and a point of a line. Lesson plan, pdf of worksheet and Powerpoint presentation.

**Timing suggestion: **Supplement to Lesson 14