**Title:** "Woody Sine"

**Description:**
The students will discover the shape of the sine function without creating a t-chart. The students will create a sine function using toothpicks. The students will then discover how the amplitude (height) and the period (number of compete waves) change when the basic graph created from the broken tooth picks was changed. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.

**Standard(s): **

[MA2013] PRE (9-12) 16: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. (*Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.*)* [F-IF4] (Alabama)

[MA2013] ALT (9-12) 34: Identify the effect on the graph of replacing *f*(*x*) by *f*(*x*) + *k*, *k* *f*(*x*), *f*(*kx*), and *f*(*x* + *k*) for specific values of *k* (both positive and negative); find the value of *k* given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
[F-BF3]

[MA2013] ALT (9-12) 37: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. [F-TF1]

[MA2013] ALT (9-12) 38: Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. [F-TF2]

[MA2013] ALT (9-12) 40: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [F-TF5]

[MA2013] PRE (9-12) 26: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses. (Alabama)

[MA2013] PRE (9-12) 29: (+) Use special triangles to determine geometrically the values of sine, cosine, and tangent for ^{π}/_{3}, ^{π}/_{4}, and ^{π}/_{6}, and use the unit circle to express the values of sine, cosine, and tangent for π - *x*,
π + *x*, and 2π - *x* in terms of their values for *x*, where *x* is any real number. [F-TF3]

[MA2013] PRE (9-12) 30: (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions. [F-TF4]