# Alex Perry's Mini-course: Introduction to Trigonometry

Introduction to Trigonometry

__Learning Objectives:__

**Students will be able to:**

- Define trigonometric ratios and solve problems involving right triangles.

-Recognize applications of trigonometric ratios in real-life situations.

-Apply geometric concepts in modeling situations.

**Needs Assessment**

1. *Instructional Problem*

Students often struggle with the concepts of trigonometric ratios, more specifically in their applications in the real world. It is important that students can connect their learning in the classroom to practical uses in the real world.

**2. Nature of what is to be learned**

How to teach students to use trigonometric ratios to estimate distance between two locations, as well as to find heights of structures in their community.

**3. About the learner**

This unit is designed for use by used by high school level mathematics teachers, specifically those teaching a course in Algebra or Geometry. This unit is designed to give teachers a different way to introduce the concepts of trigonometry to students in a more engaging method.

**Performance Objectives**

-Students will be able to measure angles of elevation and distance using simple tools. Students will then be able to use angles of elevation and measured distances to calculate heights of structures around their community using their mathematical intuition.

**Task Analysis/ Sequencing**

**1.Prerequisite skills**

Understanding concepts, procedures and principals related to:

· Measuring angles

· Finding distance using a Trundle Wheel

· Solving multi-step equations

· Basic polygons

__Inquiry based design features__

**Active Construction:**

Driving Question: Find the height of a skyscraper.

Students have an understanding of measurements and methods used to measure various objects. The task of measuring a skyscraper proposes a question that requires students to investigate/discover a new method of measurement. This question is open ended in the sense that there could be any number of ways to find the solution. Student motivation is promoted by actively engaging all learners in the lesson and make observations in their own community.

**Situated Learning:**

The driving question involves finding an actual method for measuring in a real-world scenario. The unit will take place in the classroom as well as outside. Learners will be able to observe the different dynamics of the question through observations. Situating the learning in the context of the problem (In this unit a city), gives learners a more meaningful and authentic learning environment. They are able to observe all aspects and of the surroundings to generalize better to a wider range of situations that they may have overlooked in a different setting.

**Social Interaction:**

Step 1: Students will work collaboratively in small groups to investigate the driving question.

Step 2: groups will share their findings and ideas as a whole group in an attempt to further debate their ideas. The instructor will facilitate in order to structure the different ideas presented and attempt to help generalize a common method for a solution.

This back-and-forth sharing, using, and debating of ideas helps to create a community of learners (Krajcik)

**Cognitive Tools:**

Students will be provided with the following tools to help amplify and expand the students’ learning:

- Graphing paper

- Graphing Calculator

- Ruler

- Measuring Wheel

- Sextant

**Creation of Artifacts:**

Students will develop a physical scale representation of a building of their choosing. This visual consists of a poster detailing the measurements made as well as the calculations the student used to find the building’s height (using trigonometry ratios).

__Units__