What Makes It Special? Remembering Relationships

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This video will be used to re-enforce the relationships between the sides and angles in special right triangles. The video has a catchy song that will help students remember the relationships.

This activity results from the ALEX Resource Development Summit.

Phase

After/Explain/Elaborate
Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.35

Discover and apply relationships in similar right triangles.

UP:MA19.GDA.35

Vocabulary

  • Side ratios
  • Trigonometric ratios
  • Sine
  • Cosine
  • Tangent
  • Secant
  • Cosecant
  • Cotangent
  • Complementary anglesconverse

Knowledge

Students know:
  • Techniques to construct similar triangles.
  • Properties of similar triangles.
  • Methods for finding sine and cosine ratios in a right triangle (e.g., use of triangle properties: similarity. Pythagorean Theorem. isosceles and equilateral characteristics for 45-45-90 and 30-60-90 triangles and technology for others).
  • Methods of using the trigonometric ratios to solve for sides or angles in a right triangle.
  • The Pythagorean Theorem and its use in solving for unknown parts of a right triangle.

Skills

Students are able to:
  • Accurately find the side ratios of triangles.
  • Explain and justify relationships between the side ratios of a right triangle and the angles of a right triangle.

Understanding

Students understand that:
  • The ratios of the sides of right triangles are dependent on the size of the angles of the triangle.
  • The sine of an angle is equal to the cosine of the complement of the angle.
  • Switching between using a given angle or its complement and between sine or cosine ratios may be used when solving contextual problems.

Learning Objectives

Students will discover and apply relationships in similar right triangles. 


Students will derive and apply the constant ratios of the sides in special right triangles (45Ëš-45Ëš-90Ëš and 30Ëš-60Ëš-90Ëš).

Activity Details

  1. The teacher will play the video Special Right Triangle Jam.
  2. After watching the video, students will complete the Exit Ticket where they will write the angle and side relationships between a 30°-60°-90° right triangle and a 45°-45°-90° right triangle.

Assessment Strategies

The teacher will check the exit tickets to determine if any misconceptions exist.  

The teacher can correct misconceptions with individual students or through a whole group lesson.

Variation Tips

After viewing the video, the teacher could have the students sing along to the video.  

The teacher could pair students and have students say the relationships between the sides and angles of special right triangles to each other.

The teacher could combine the two different exit tickets to create a 4 questions exit ticket.

Background / Preparation

  1. The teacher will need a computer connected to a classroom projector and speakers for the Special Right Triangle Jam Video.
  2. The teacher will need to make copies of the Exit Ticket for each student in advance. (There are 2 different exit tickets per page.)
https://youtu.be/DquDw_CAwsA

Approved Date

Owner (Author)

mrswhite
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