Reflection: Student Ownership Calculator Investigation: Special Right Triangles (Day 2 of 2) - Section 1: Investigation Continued: Special Right Triangles


In this assignment, students were able to take ownership of their learning as they reviewed their understanding of how the side lengths of special right triangles are related. As a quick assessment of students’ understandings, I found it helpful to look at Questions 4b and 8b of their completed work. In these questions, students were asked to describe the relationship that would always exist among the sides lengths of the two special right triangles.

The student whose work is shown in Student Work 1 stated the relationship of the 45, 45, 90 triangle side lengths perfectly in question 8b. It is clearly in her own words and gives me a sense that she really understood the relationship. However, this student did not state a correct answer for the 30, 60, 90 triangle in question 4b.

The student's peer in Student Work 2 struggled to make connections to their prior learning. I have made a note to provide this student with some remediation. She demonstrated an understanding that in a 30, 60, 90 triangle the shorter leg is half of the hypotenuse. But, she did not make a connection to the longer leg. Similarly, in the 45, 45, 90 triangle she understands the legs are the same length, but she did not communicate how to obtain the hypotenuse.

Student Work 3 shows a fairly common issue in my class. The student demonstrates a partial understanding of the side length relationships of a 30-60-90 triangle.  He did not describe how the longer leg is related to the shorter leg.

Student Work 4 shows a great answer to question 4b. Love it! And, it includes an interesting answer to question 8b. I wonder if he realizes this could be written like how he answered question 4b… with side lengths of n and a hypotenuse of n times radical 2.

  Student Ownership: Student Work
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Calculator Investigation: Special Right Triangles (Day 2 of 2)

Unit 12: Fundamentals of Trigonometry
Lesson 3 of 17

Objective: SWBAT identify the relationships between the lengths of the legs and the length of the hypotenuse of special right triangles.

Big Idea: Students use their Nspire Calculators to explore special right triangles and establish side length ratios which will be the foundation of our study of trigonometry.

  Print Lesson
Math, Trigonometry, PreCalculus, special right triangles, Nspire Calculators, trigonometric ratios introduction, ratios
  50 minutes
special triangles
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