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
Presentation to Students 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 objects In our third project, you and a partner will use inclinometers to aid in discovering the height of objects 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!
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
STUDENT SAMPLE 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 sin 80 = 𝐼 6 6 ∗ sin 80 = 𝐼 6 ∗ 0.9848 = 𝐼 6 meters 5.9088 = 𝐼 Jonathan can climb 5.9088 meters. Someone should definitely hold the ladder for him, though. 80 ° is pretty steep. 80°
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 of 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 . " ❤️ ² Basic Trigonometry: Sin, Cos, Tan (mathbff)." YouTube . Mathbff.com, 15 Jan. Mathbff • 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.
Recommend
More recommend
