**Teacher's Guiding Questions**

- What are vocabulary words that we can use to describe a right triangle?
- How can we apply what we know about squares to develop a relationship between the sides of a right triangle?
- What is the Pythagorean Theorem?
- How can we use the Pythagorean Theorem to find the missing side length in a triangle?
- When can we use the Pythagorean Theorem to answer problems in the real world?
- What are the obstacles that engineers have when constructing a tower?
- How are cell phone towers connected to the ground?
- What is a “guy line”?
- What is a way we can determine the length of a guy line?
- How could we determine where a guy line needs to be attached on a cell phone tower?

**ACS (Real world applications; career connections; societal impact)**

Real World Applications:

Cellular and radio communications are highly used in modern society. These types of communication would not be possible without the constructions of towers that allow certain devices to work. These towers must be able to withstand a variety of adverse conditions including wind, rain, and snow.

Career Connections:

Those in the civil engineering field are involved heavily with zoning rules and regulations which factor heavily in the process of constructing a cellular or radio tower. There is also a field of engineering referred to as broadcast engineering that is directly involved with the construction of these towers. The building of the tower will be addressed when the students construct a model tower in the final challenge.

Societal Impact:

Cellular and radio communications are relied upon when delivering a variety of messages in our society. These types of communication are not only used in interpersonal relationships, but are also invaluable tools in the business sector. Students through their everyday lives have a sense of the importance of this topic.

**Engineering Design Process (EDP)**

- Identify and Define: Students will identify the problem when they receive their individual height/ geographical requirement that they have to meet.
- Gather Information: Students will research how cell phone towers are built and the purpose of guy lines.
- Identify Alternatives: Each group member will be required to design blueprint of what the ramp should look like.
- Select Best Solution to Try: Each group must discuss the pros and cons of each design and decide which one will best meet the challenge.
- Implement Solution: Students will create a final design drawing that includes labeled dimensions and materials. They will then construct the prototype.
- Test and Evaluate: Each group will test their solution. Then they will describe the test and results. They will also explain whether the design was effective and provide reasons.
- Communicate: Each group will give a short presentation on their tower and how it performed when it was tested against the adverse wind conditions.

##### Unit Academic Standard

CCSS.MATH.CONTENT.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

##### Unit Activities

**Unit 3: Cellular and radio communication – Design a model tower that has the ability to withstand adverse weather conditions.**

**Lesson 1: Exploring the Pythagorean Theorem and its ability to solve problems (2, 50 minute class periods)**

*Lesson 1 introduces the Pythagorean Theorem at the most basic of levels and gives students the opportunity to explore the proof on the Pythagorean Theorem in a concrete manner before then extending that knowledge with practice of this theorem to solve situational problems. Throughout this lesson students are getting the basic skill of applying the Pythagorean Theorem however it should be noted that the instructor should continually refer to the challenge that was issued at the beginning of the unit. The students should be able to visualize the guy lines being a right angle. This allows for the students to see the math application as it applies to their challenge.*

Activity 1:

Introduction of the Big Idea, Generating the Essential Question, Challenge, Hook (see description in the previous section of this document, and guiding questions. * *

Activity 2:

Explaining the proof of the Pythagorean Theorem in a hands on fashion (building the proof with square tiles). Before the instructor delves straight into this lesson, it might be helpful to draw on the board a model tower with guy lines. Show the students what shape this looks like. The students should be able to conclude that it is a right triangle. ** **

**Lesson 2: Synthesizing knowledge of Pythagorean Theorem into an effective tower design (6, 50 minute class periods) **

*After their work in Lesson 1, students now have a baseline understanding of what the Pythagorean Theorem is and the mechanics of how to use the theorem to solve real world problems. In this lesson, students now move more to the application of this topic and the ultimate challenge of building an effective tower.*

Activity 1:

In this activity students will have to become “certified” in using the Pythagorean Theorem in real world problems. Students will be responsible for turning in three separate artifacts to demonstrate their knowledge. Certifications that the students must complete will have varying levels of difficultly to meet the varying needs of students.

Activity 2:

Design a tower that can withstand adverse weather conditions.

##### Where the CBL and EDP appear in the Unit

Challenge based learning appears in Lesson 1, Activity 1 when the students are presented with a challenge. Of building a cell/radio tower. Both CBL and EDP appear in Lesson 2, Activity 2 when the students are constructing their cell phone tower. The key piece is that the students should arrive at the solution to add guy lines to their tower without the instructor giving this to the students.

##### Misconceptions

Students may think that you can add two legs of a triangle to get the hypotenuse

Students may confuse the legs with the hypotenuse

Students may not be able to identify which variable corresponds with the appropriate side of the triangle

##### Additional Resources

YouTube (See links embedded in the document)

http://teacherweb.com/GA/MarionCountyMiddleHigh/Welch8thmath/Pythagorean-Word-Problems3.pdf

##### Pre-Unit Assessment Instrument

##### Post-Unit Assessment Instrument

##### How to Make This a Hierarchical Unit

CCSS.MATH.CONTENT.HSG.SRT.D.11

(+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

When doing this problem with high school students, instead of providing students with a set length for their guy lines, instructors could provide angle measurements for the guy lines which would result in students having to use the Law of Sines and the Law of Cosines to find the unknown measurements.