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# Calculator Investigation: Special Right Triangles (Day 1 of 2)

Lesson 2 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*

To warm-up for today’s lesson, we will review basic right triangle properties. I start by present the clicker question on page 2 of the Flipchart_Special Triangles (Day 1 of 2) . The warmup tasks ask students to find missing side lengths for a right triangle. On page 3 of the flipchart, students use their knowledge of the sum of interior angles of a triangle to find the missing angle. After students have responded, I plan to review the correct answers to insure students are ready for today’s activity.

**Technology Note**: If you have access to software that plays a flipchart file, Flipchart_Special Triangles (Day 1 of 2).flipchart is included in the resource section.

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Today's lesson requires students to work through a .tns file on their inspire calculators. I plan to have the files already on the calculators before the start of class.

My goal for today is to provide my students with an opportunity to review the properties of 30-60-90 and isosceles right triangles. Since this is a review lesson, students will be working through the Special Right Triangles TI-Nspire activity from the Texas Instruments website individually. The original lesson can be accessed here.

Students will be working through Student Worksheet - Special_Right_Triangles.

For some teacher hints and tips from TI, see Teacher Resource - Special_Right_Triangles.

I like how this activity guides students into creating the special triangles based on facts they already know. For example, students derive the 45-45-90 special right triangle by cutting a rectangle in half diagonally. They then analyze a variety of side length ratios to make a conclusion that is true for all special right triangles of that size. This activity builds on the concepts of similar right triangles that students studied yesterday. So before my students dive into the activity, I am going to have a student quickly summarize what we did yesterday. It will help students to build on this prior knowledge. Their focus today should not be the fact that side length ratios hold in similar triangles. More specifically, I want my students to review and retain the ratios for 45-45-90 and 30-60-90 right triangles.

Students should demonstrate a variety of Mathematical Practices as the work through the activity today. I will be giving my students part of tomorrow’s class to finish the activity.

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#### Closure: Clicker Checks

*5 min*

As a quick check for understanding, I have students answer the questions located on pages 4 and 5 of the Flipchart_Special Triangles (Day 1 of 2). Students should be asked to complete the question on page 4 if they have completed question 3 on the calculator activity, as this question assess knowledge of 30-60-90 special triangle. Students should be asked to complete the question on page 5 of the flipchart if they have completed through question 7 on the calculator activity as this question assess knowledge of a 45-45-90 special triangle.

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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