SIMILARITY IN RIGHT TRIANGLES TEACHER OVERVIEW FIRST DAY Students - - PowerPoint PPT Presentation

SIMILARITY IN RIGHT TRIANGLES

TEACHER OVERVIEW

FIRST DAY

• Students will be shown Introductory PowerPoint
• That PowerPoint is on the following slides

Students will take the pre-assessment

WHAT WILL WE BE LEARNING?

Pythagorean Theorem Trigonometry Practical Applications of Trigonometry

Presentation to Students

WHY ARE WE LEARNING IT?

These topics in particular are very valuable, both inside and outside of the classroom  Pythagorean theorem can help students determine right angles, and can be used to identify triangles as acute or obtuse.  In the first project, you will explore the Pythagorean theorem and prove its validity

Presentation to Students

WHY ARE WE LEARNING IT?

 Trigonometry has many uses, including:  Identifying grade/slope of roadways, rooftops, and other surfaces  In our second project, you will look at various word problems that explore these issues, and then develop your own.

Presentation to Students

WHY ARE WE LEARNING IT?

 Trigonometry has many uses, including:  Navigation  Inclinometers (see project 3) are often used to identify a person’s latitude  Discovering the height or distance of immeasurable

• bjects

 In our third project, you and a partner will use inclinometers to aid in discovering the height of

• bjects around the school that you normally couldn’t

measure.

Presentation to Students

RESOURCES

All of our instructional material will be posted in Moodle

www.314cone.com/moodle

 Sample Assignments, Directions, Rubrics and other resources will all be available there  Quizzes, Tests, Do Nows, and other online assignments will be there as well.

Presentation to Students

RIGHT NOW:

Make sure you can log into Moodle!

Once you log in: Go to Chapter 8 and Take the Similarity Review Assessment!

Presentation to Students

PREASSESSMENT

• Created by teacher, student takes through Moodle:

PREASSESSMENT

• Results will determine student groups for the unit and the student pairs for the third

project.

MOODLE

• All Resources will be posted through Moodle

PYTHAGOREAN THEOREM PROJECT

• Traditional Lesson on Geometric Mean will be followed by the first project
• Students will create a PowerPoint proving the Pythagorean Theorem
• Resources will be provided through Moodle
• Students will be encouraged to research on their own
• Note: This proof gets its own standard, so its important that students understand it as

fully as possible.

TRIGONOMETRY PROJECT

• Understanding of Pythagorean Theorem and Geometric Mean will segue into Trig.
• Basic explanation of SOHCAHTOA and supplementary videos from

YouTube (such as https://youtu.be/X5uFqpypDy4, below) posted on Moodle

• There will be a brief quiz before the Word Problem Project

TRIGONOMETRY PROJECT

• Students will be tasked with

creating a word problem using trigonometry

• Trig functions will be

generated at random using Excel.

• Functions will be paired with

student names and then exported as a mail merge.

• Each student will get a unique

assignment

TRIGONOMETRY PROJECT

By STUDENT 1

STUDENT SAMPLE

Tired of being picked on for his squeaky voice, Jonathan decides to set up a ladder so that he can finally reach puberty. He borrows his father’s 6 meter extension ladder and leans it against the wall at an 80°

• angle. How far up can Jonathan reach?

STUDENT SAMPLE

Answer

80° 6 meters

sin 80 = 𝐼 6 6 ∗ sin 80 = 𝐼 6 ∗ 0.9848 = 𝐼 5.9088 = 𝐼

Jonathan can climb 5.9088 meters.

Someone should definitely hold the ladder for him, though. 80 ° is pretty steep.

STUDENT SAMPLE

STUDENT SAMPLE

INCLINOMETER PROJECT

• Towards the end of the unit, students will work in pairs to create an inclinometer
• All materials for inclinometer will be provided by teacher
• Instructions available on Moodle, including embedded tutorial videos (such as

https://youtu.be/x_WOx8SRMeg, below)

INCLINOMETER PROJECT

Students will use the inclinometer to measure predetermined objects around the school

• Students will be graded both on the inclinometer and the result of their
• measurments

Note

• : Inclinometer project can be made more advanced by having students create the

protractor element from scratch.

My students are lower

• level, so I did not develop the project to be this difficult.

LAST DAY

• Students will be traditionally assessed on the unit through Moodle
• Students will complete a self-reflection assignment at the end of the unit.

STANDARDS ADDRESSED:

• G-SRT
• 4 Prove theorems about triangles. Theorems include: a line parallel to one side
• f a triangle divides the other two proportionally, and conversely; the Pythagorean

Theorem.

• G-SRT
• 6: Understand that by similarity, side ratios in right triangles are properties of

the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

• G-SRT
• 8: Use trigonometric ratios and the Pythagorean Theorem to solve right

triangles in applied problems.

WORKS CITED

Videos

• Mathbff
• . "❤️² Basic Trigonometry: Sin, Cos, Tan (mathbff)." YouTube. Mathbff.com, 15 Jan.
• 2014. Web. 25 Mar. 2017.

MathMeij

• . "Using an Inclinometer." YouTube. N.p., 13 Apr. 2013. Web. 25 Mar. 2017.

WORKS CITED

Resources

• Carter, John A., Gilbert J. Cuevas, Roger Day, and Carol E. Malloy.
• Glencoe Geometry. Bothell,

WA: McGraw-Hill Education, 2014. Print. Mcgraw

• Hill. Geometry: Study Guide & Intervention Workbook. Place of Publication Not

Identified: Glencoe Mcgraw-Hill Schoo, 2008. Print.