Tactile Trigonometry - Confex

[Pages:44]Tactile Trigonometry

A Hands-On Approach

NCTM Annual Meeting New Orleans, LA April 9-12, 2014

Amy Gersbach Seneca High School Tabernacle, NJ agersbach@

Ingrid Williams Shawnee High School - Retired Medford, NJ williamsfm@



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Table of Contents

Radian and Degree Measurements 1.) Discovering Radians 2.) Coterminal Angle Games

Right Triangle Trig 3.) Clinometers 4.) Children's Books

The Unit Circle 5.) Discovering the Unit Circle 6.) The Unit Circle Song 7.) Special Angle Games

Trig Graphing 8.) Spaghetti Sine Curves 9.) Tidal Wave Project 10.) Picture This Project

Trig Identities 11.) Trig Identity Games 12.) Movie Mystery

Law of Sines/Cosines 13.) Diorama Project 14.) Oblique Triangles Around the School

General Projects 15.) Facebook Project 16.) Family Ties Project 17.) Coming Attractions

p. 3-4 p. 5

p. 6-7 p. 8

p. 9 p. 10 p. 11-13

p. 14-16 p. 17-20 p. 21-23

p. 24-30 p. 31

p. 32-35 p. 36-37

p. 38-40 p. 41 p.42-43

To access this document (& more) online...

- Instructions and Rubrics for each project in a Word document - A master copy of the presentation handout and PowerPoint

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Lenape Regional High School District Discovering Radians

In Geometry you learned how to measure angles in degrees. Using degrees there is no relationship between the size of the circle (the radius) and the 360? around the circumference. To accommodate this, there is a measurement called a RADIAN which relates directly back to the radius of the circle. We will use the following activity to discover what a radian is.

Pick up the following materials A bag of candy a compass a ruler a blank sheet of paper (some of the bigger candies will need multiple sheets taped together) A protractor

Choose 7 pieces of candy and place them side by side on the paper. This will represent the radius of your circle. Use the ruler to draw the radius. (Make sure that you have enough space on your paper to form a circle ? this may require taping paper together.)

Use the compass to draw your circle with the radius that you just discovered.

Center the circle on an x-y coordinate plane.

Starting where the circle meets the positive x-axis, wrap your 7 pieces of candy around the outside of the circle, placing the diameter of the candy directly on the circle.

Make a mark on the circle at each endpoint of the 7 pieces. This distance is ONE RADIAN. Draw the a line back to the center of the circle from where you stopped (making a central angle). Then start again from that point.

Continue until you can no longer fit the candy on the circle.

How many (complete) times were you able to fit the pieces of candy around the circle? _____________

How many pieces of candy fit in the small segment that was remaining? _____________

Express the number of times you could fit the candy as a: Mixed number ____________ Improper Fraction (unsimplified)___________ Decimal ______________

(simplified) ___________

Do you recognize any of these numbers?

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Follow up questions 1.) How many radians are in 1 circle? 2.) Calculate how many degrees are in 1 radian.

Measure the size of each radian with your protractor. What did you get? 3.) Consider the distance around a circle. We call this the ______________________ and its formula is _____________.

How does that compare to what we just discovered as a radian?

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Lenape Regional High School District Coterminal Angles Activity

These activities were designed to be used early in the study of the Unit Circle.

Materials: Index cards with unit circle angles written on them. Use both radians and degrees, positive and negative angles.

Game #1 1.) Hand out one card per student and instruct them to find the person that has a card with the angle that is coterminal to the angle on their card. 2.) Once all students are paired up, ask the students to form a Unit Circle and place themselves around the circle according to the measure of their angle. Game #2 Tape all cards to the board facedown and play "Memory" or "Concentration" where students take turns coming to the board and they have to turn over a matching pair to score a point.

Note: This was designed using angles having a measure of 00 0 3600 or 0 2. You may also do this using angles of unlimited size.

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Lenape Regional High School District Right Triangle Trig Clinometer Project

Your mission: Our principal needs some very important information with from the custodial staff. Mr. Looney has enlisted your help to find some measurements in front of the school. You will work in groups of 3 or 4 to apply right triangle trigonometry to real world situations.

Your materials: a large tape measure a homemade clinometer paper & pencil a calculator a camera (or cell phone)

We need the following measurements: The height of the flag pole The height of the front entrance (to the bottom of the roof) The height of the first floor (the middle of the dark colored bricks) The height of the security camera The horizontal distance of the camera from the building The width (vertical distance) of the flag

The rules: You must stay where I can see you at all times. We will only be outside for about 15 minutes ? take all of your measurements outside and we will come inside to do the calculations. Be quiet ? do not disrupt any of the classes in the rooms near where we are working. Be very careful with the tape measures!!! HAVE FUN WITH THIS!!!

The final product: A large poster, including all 6 measurements Each piece must include a picture of the item, the right triangle, and the work necessary to solve. Make sure the names of all group members are on the FRONT of each poster.

These will hang in the hallways! Make them creative, unique, and exciting to look at!!!

Grading Rubric ? 30 points total

Each measurement is worth 5 points, broken up as: Calculations ? 3 points Picture ? 1 point Presentation/Creativity ? 1 point

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Lenape Regional High School District Right Triangle Trig Clinometer Project

Student Samples

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Lenape Regional High School District Right Triangle Trig Children's Book

DUE: ____________________ (loss of 10% for each day late)

Objective: Write and illustrate a children's story that revolves around finding a missing piece of a right triangle. Through your story you'll show an understanding of Right Triangle Trigonometry and the six basic trig functions. Your story should be entertaining, colorful, and original. You will also include all work, formulas and steps involved in solving your problem.

Specific Directions/Requirements: - Take three sheets of 8.5"x 11" paper and fold them in half ? forming a book that is 8.5" x 5.5" and has 6 pages (12 if

you count front and back). - Design a cover page that includes:

Your name(s) Story Title Illustration - The back cover will be all of your work ? clearly showing all calculations used in the book. Be sure to label each calculation so that it is clear what part of the book that corresponds to. - All 5 remaining "middle" pages include your story and some sort of Trig calculation (doesn't necessarily have to be the answer to the specific problem at hand).

Grading: Story - 5 points

o Title o AT LEAST 5 pages of STORY (not including title page or calculations page) o Logical, easy to follow, subject appropriate for children o Proper grammar & spelling used. Written in complete sentences. o Math application doesn't feel "forced" ? easily fits into the story provided.

Math ? 5 points o Formulas given (integrated into the story) o Steps to solve explained (integrated into the story) o Illustrations demonstrate the triangles at use. o At least 5 separate Trig problems included o Correct math is used

Calculations - 5 points o Calculations for 5 separate problems are included o Units are labeled o Round all decimals to TWO decimal places o Right triangles are included with calculations ? drawn cleanly. o Work is clear and easy to read.

Presentation - 5 points o neat and organized o colorful o typed or NEATLY written o illustrated with reasonable pictures (does not have to be hand drawn) o followed directions

- Grade will be out of 20 points, then scaled to be worth exactly 10% of your 2nd Marking Period Grade.

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