This lesson is intended to further develop students’ understanding of trigonometric functions and graphs. Students investigate how the constants a, b and c of the general forms of the sin and cos functions affect the graph of the function. This lesson strongly exhibits Core Action 2 and Core Action 3.
Trigonometric Functions and Graphs (Terry)Download
The teacher makes an explicit connection to prior learning by asking all groups to find a graph that matches the one equation. As students work in their small groups, theyexplain their mathematical thinking. This is a consistent expectation for every
student and the students freely elaborate on their thinking, often without prompting from the teacher.
The teacher checks for understanding throughout the lesson using informal, but deliberate questioning methods. The teacher invites another group to talk through the mathematical explanation and students elaborate to explain their thinking.
Here, students are being asked to challenge some of their existing mathematical thinking regarding period, amplitude and frequency.
In this part of the lesson, the teacher has provided opportunities for students to work with and practice course-level problems and exercises within a small group. Additionally, the teacher has created the conditions for student conversations where students are encouraged to talk about each other's thinking by listing examples of accountable talk. Students are provided with five questions to answer while working with their groups.
In this part of the lesson, the teacher deliberately checks for understanding throughout and adapts the lesson to meet the condition of the students' learning. She intentionally asks the students to reason about the negative values on the graph. Students are asked about their confidence with their matching on the other pairs.
Here, students use precise mathematical language in their explanations and discussions. The teacher asks students to explain and justify work and provides feedback that helps students revise initial work. The teacher asks someone else to clarify the relationship between the period and the variable b in a trigonometric function.
The teacher deliberately checks for understanding of amplitude and what is happening on the graph when x = 0. The teacher poses high quality questions that prompts students to share their developing thinking about the content. Students continue to ask clarifying questions to monitor their own understanding.