Reflection: Vertical Alignment Introduction to the Slope Ratio (Tangent) - Section 3: Partner Classwork: Slope Ratio Task

 

In the past, I had students work on the Slope Ratio Task in pairs, then share out with the whole-class so we could collectively develop a sense of similar slope triangles for a given line.  This year, however, I wanted to do connect the geometry world with the algebra world my students had experienced prior to entering this class, the one they would go back to after summer break.

The team of Algebra 2 teachers at my school frequently uses Desmos, a free online graphing calculator.  Since students have had lots of experience graphing lines, I thought I would try to pique their interest in this task by showing them how to graph a line on Desmos, which ultimately created an engaging and rich discussion.  With the aid of Desmos and an LCD projector, I had hooked students in.  Not only were we doing a little review on linear relationships from Algebra 1 and talking about the slope angle of the given line y=(1/5)x, but we were also discussing the equivalence between all the slope ratios for that line.  With this dynamic technology, we were able to graph a line parallel to y=(1/5)x—thus, with the same slope angle—to show the slope ratios were still equivalent even though they were two distinct lines.  We were able to add a new line to the graph, y=(2/5)x, which necessarily has a different slope, to show how the slope ratios for that line differed from that of y=(1/5)x.

While my questions throughout this whole-class discussion led students to similar thought processes and ideas they would have engaged in had they worked on the task on paper in pairs, students were so much more engaged and were able to pose questions they wondered about to organically and authentically shape a true whole-class exploration of slope angles and slope ratios, the foundation of our understanding of the tangent ratio.

  How Desmos Created an Opportunity for an Authentic Whole-Class Exploration
  Vertical Alignment: How Desmos Created an Opportunity for an Authentic Whole-Class Exploration
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Introduction to the Slope Ratio (Tangent)

Unit 12: Triangle Similarity and Trigonometric Ratios
Lesson 4 of 11

Objective: Students will be able to use similarity and to make sense of the meaning of the slope ratio (tangent ratio).

Big Idea: By drawing several examples of right triangles that satisfy the same slope angle, students develop an understanding of the definition of tangent.

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Subject(s):
Math, Geometry, Trigonometry, tangent ratio
  45 minutes
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