##
* *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*

# Calculator Investigation: Special Right Triangles (Day 2 of 2)

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.

*50 minutes*

In the beginning part of class students will finish the Special Triangles Nspire activity from yesterday, Student Worksheet - Special_Right_Triangles. If you’d like to see the original lesson published by Texas Instruments you can find it here. The goal for this assignment is that students are able to identify the ratios that hold for the side lengths of special right triangles. During this section of the lesson, some key mathematical practices will be addressed: Special Right Triangle, Video Narrative, Mathematical Practices.

As students begin to wrap up their work on this investigation, I plan to have an informal share-out of their answers to question 8b. I will ask the class for volunteers to share the special triangles they learned about and any special relationships they found between the legs and hypotenuse. If students don’t readily volunteer to share, I will use a random calling method and ask each students that is selected to give me just one more fact. Again, I would start by asking. "What special triangles did we study? Then what did you notice about how the legs are related? How are the legs and hypotenuse related?" Etc. I will summarize their findings on the front board. This summary will help lead students into the next activity, the quick quizzes closure.

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#### Closure: Quick Quizzes

*15 min*

To assess student’s current understanding of special right triangles students will take their first quick quiz (Version 1) on the clicker. For more information on how I plan to implement these quick quizzes, check out this video Special Right Triangles quick quiz closure.

Here are the Special Right Triangle Quick Quizzes that are described in the video:

If you have access to a flipchart player, here is the flipchart with the answers programed in for the quizzes for quick grading: Quick Quiz Clicker Check - Special Right Triangles.flipchart

*expand content*

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: What's so special about similar right triangles?
- LESSON 2: Calculator Investigation: Special Right Triangles (Day 1 of 2)
- LESSON 3: Calculator Investigation: Special Right Triangles (Day 2 of 2)
- LESSON 4: Using Trigonometric Ratios (Day 1 of 2)
- LESSON 5: Using Trigonometric Ratios (Day 2 of 2)
- LESSON 6: Clinometer Project (Day 1 of 2)
- LESSON 7: Clinometer Project (Day 2 of 2)
- LESSON 8: Applications of Right Triangle Trig
- LESSON 9: Law of Sines Basics
- LESSON 10: Ambigouous Cases of the Law of Sines
- LESSON 11: Law of Cosines
- LESSON 12: Short Lesson: Quick Clicker Quizzes
- LESSON 13: More on the Laws: Real World Application
- LESSON 14: Trig Jeopardy
- LESSON 15: Fundamentals of Trig Review - Day 1 of 2
- LESSON 16: Fundamentals of Trig Review - Day 2 of 2
- LESSON 17: Fundamentals of Trigonometry Unit Assessment