## Reflection: Grappling with Complexity Graphing Sine and Cosine Functions (Day 2 of 2) - Section 2: Graphing horizontal shifts

I learned a different way to teach the horizontal shift from the Intern teaching today's lesson. I have always discussed finding the start point of the period and then adding the period to get the end point for the period. The intern used a different approach that made so much sense for the students that I plan to in cooperate  this technique next year.

I came into the lesson at the very end and saw students that usually struggle understanding how to find the end point by using the transformation. When the graph shifts horizontally the length of the period does not change. Students understand starting the period at zero. The example I observed was a problem where the graph shifted pi/4 to the right and the period was pi. A student explained that the start of the period was at pi/4. The student continued by stating that normally this graph would have the end of the period at pi but the end had to shift over pi/4 so the end of the period would be 9pi/4.

I was looking at the work of several students and they all had the shift correct and the x-axis labeled appropriately. This is usually a struggle for students. The students were working with the fractions easily which also amazed me. I was watching students using several mathematical practices include MP1, MP4, MP7.

The next day when the students worked on tangent and cotangent, the students immediately determined how graphs were transformed with horizontal shifts. More students were reasoning more with the sinusoidal graphs. I hope this helps students when they write sinusoidal models.

Learning from Student Teacher
Grappling with Complexity: Learning from Student Teacher

# Graphing Sine and Cosine Functions (Day 2 of 2)

Unit 8: Graphing Trigonometric Functions
Lesson 6 of 13

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