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# Clinometer Project (Day 1 of 2)

Lesson 6 of 17

## Objective: SWBAT use trigonometric ratios to solve real-world measurement problems.

## Big Idea: Students build clinometers in preparation for indirectly measuring the height of objects that we would not normally be able to measure.

*50 minutes*

#### Warm-up

*5 min*

Today's warm-up question is located on page 2 of Clinometer Project Day 1. This question will test whether students can extend their current knowledge of right triangle trigonometry to a real world situation. It is also introducing students to the type of measurement problems they will be tackling during the Clinometer Project.

If I think my students are up for a challenge, I may hide the picture on the task and see if my students can come up with a sketch on their own. I have included the diagram in case I feel my students needed to see the problem, rather than just read about it.

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#### Homework Quiz

*10 min*

After today's warm-up I am going to have students complete the Homework Quiz #1-3. The quiz is a random sampling of questions to quickly assess student’s current progress with right triangle trig. I use these quizzes to indicate if students are benefiting from doing their homework.

**Technology Note**: If you have a personal response systems the quiz is programmed into the Homework Quiz #1-3.flipchart file.

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Using page 4 and 5 of today’s Flipchart_Clinometer Project Day 1, I am going to introduce the concept of indirect measurement. Using the Eiffel Tower problem on page 5, I am going to try to draw out of students the idea that they would be able to accurately measure the distance they are standing away from the Tower. Then, I'll say, "If only we had a way to calculate the angle of elevation from our eye level to the top of the tower, then it would be easy to calculate the height of the Eiffel Tower using right triangle trig."

It never fails that one or more students will argue that it would be easier to just measure the height. So, I will entertain the conversation with questions like, "What would that actually entail? What plan can we successfully implement to do that?" I try not to be patient and not shoot students down, so that we arrive at a good starting point for constructing and using clinometers.

Once I accomplish the task of helping students develop the idea that we need something to help us measure the angle of elevation, I will then show them the following video (also on Page 6 of the Flipchart_file).

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#### Making Clinometers

*15 min*

In order to make clinometers each team of students will need the following supplies:

- a straw
- a protractor
- a weighted mass (paperclip, eraser, washer or something of the sorts)
- string
- tape

I provide my students with the Clinometer Project packet. The packet inlcudes step-by-step instructions for how to build a clinometer.

Completed Clinometers should be stored in the classroom to be used for Day 2 of this Lesson.

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#### Closure

*10 min*

For today's closing activity students will need a meter stick and completed clinometer.

As a quick wrap up, I plan to have students practice using their clinometer to determine the height of an **X** on the wall in the classroom. (This could also be done at the start of Day 2 if students need more time to build their clinometers.) Students should complete this example problem on Page 2 in their packets. To prepare for this activity, I have placed four **X**’s around the room, all at the same height. So, as students finish building a clinometer, they can practice measuring without getting in each other’s way.

With about 5 minutes remaining in the period, I ask students to return to their seats. I will tell students high the **X**'s are. I give the answer in centimeters, meters, and inches, as I had not requested my students to complete the measurements with a particular unit of measurement.

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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