# Geometry Right Triangles unit project: Barbie Zipline Day 3

This is the conclusion of a three day lesson applying right triangles. Here is day 1 and day 2.  Eric is my apprentice teacher and he initiated this discussion:

Eric: Yesterday we prepared to go outside, what information did we collect?

student: How much rope we need and what angle.

Eric: Where is the angle? Here or here? What else did we find?

student: The height of the flagpole.

student: The distance away from the flagpole

Eric: One person from each group come up to the board and write your angle and distance from the flagpole on the board.

Eric: Let’s make a plan before we go outside.

We then discussed and agreed that we should actually measure the height of the flagpole  when we put barbie on the pole. We also decided to find the exact ground distance to create a 30 degree angle, but that it looks like it should be approximately 45 feet from the base of the flagpole. Students also agreed that they would like to confirm their thinking that this angle will result in a safe speed for Barbie to zipline down from the top of the flagpole.

### The Wrap Up

Eric made a sheet for students to reflect on the lesson.

# Geometry Right Triangles unit project: Barbie Zipline Day 2

Students sat with their partners from Barbie zipline day 1 and we begin by reviewing the scenario and their calculated flagpole height.

Next we discussed how this zipline will work. I used a string and a binder clip to make a model zipline, using a very steep slope for the zipline and I asked students to predict what would happen if Barbie came down a zipline like this.  They agreed that she would fall too fast and get hurt. Next, I held the string almost horizontal and asked how this zipline would work – and students agreed that she would get stuck or mover too slowly.

I explained that the goal for this day is to use a model in class to determine a plan for Barbie to zipline down safely from the top of the flagpole. By the end of class, students had to know what angle of elevation they planned to use and how far from the base of the flagpole they needed to place the end of the zipline.

This day felt a little chaotic, but students did end up finding errors in their measurements by verifying their calculations in a variety of ways. The worksheet below incorporated a range of geometry topics including:

• Pythagorean Theorem
• right triangle trigonometry to calculate lengths
• inverse trigonometric functions to determine angles
• similar triangles

Tomorrow, we test our calculations outside on the the flagpole.

# Geometry Right Triangles unit project: Barbie Zipline Day 1

I have seen posts about Barbie zipline on occasion over the past few years. I’ve avoided the lesson because it seemed like a lot of advance prep work and typically I don’t allow enough time plan this far ahead and work through constructing a zip line trial run to make sure it all works in advance. To keep it completely real, I also hadn’t seen any description or resources that I thought would fit my classes well. But I found myself approaching the end of a right triangle unit in geometry with 2 full block periods mapped on my unit plan labeled “Right triangle synthesis project – need to create.”

This is my first semester with a full time apprentice teacher, Eric, so I have help and some new motivation to make this a fun project for everyone this time too. This time of the school year, with short days, cold temperatures and no end in sight, it seems a lot of students appear pretty bored with school and many of the staff here are also struggling. I really just needed to lighten things up for the students and myself. The next logical thought: Queue Barbie and high quality pulleys.

### Day 1 (80 minutes): How tall is the flagpole?

#### The set up

Randomly assign teams (I used pairs)

Introduce the activity with this fantastic video from Jed Butler:

We leaned heavily on Jed’s blog post and started with the activity guides included in his post, modifying them a little to incorporate his thoughts on how the lesson could be improved and our learning goals.

1. I like having students select a team name because it forces them to talk to each other before they being working with content. It increases collaboration and breaks down barriers with a safe opening topic for conversation.
2. Given the image below, use Mr. R to estimate the height of the flagpole. This led to students getting rulers and measuring on the image and a rich discussion on whether 4 inches is the same as 0.4 feet.

3. #### Discussion

• Eric: What are some ways we could find the height of the flagpole?
• student: climb up the flagpole?
• student: find the angle?
• Eric: What angle?
• student: The angle of elevation?
• Eric: Where does the angle of elevation go (sketches diagram)?
• student: Do we know how tall Ken is?
• student: Are we Ken in this situation?
• Eric: What can we measure?
• student: You could measure the distance from the flagpole to the person.
• student: We could use that angle tool thing that Mrs. B carries around.
• student: oooohhhhhh. yeah.
• Eric: How could we use that? What else would we need to measure? Would we all have the same measurements?
• student: The hypotenuse!
• student: oh! So we could use tangent.
• Eric: I want you to measure two different times, switching roles. Why do you think we should do it twice?
• student: To see if we get the same answer?
• Eric: Will we all get the same answer?
• Student:  No.
• Eric Why not?
• student: Because it is not exact, but they should be really close.
• Eric: Work with your group and make a plan before we go outside.

#### 4.  Measure & Calculate

Outside measurements, then back in for calculations, using this sheet from Jed Butler’s description as a guide.

Favorite question while measuring angles outside:

• student: Is it possible to get the same angle of elevation if may partner and I are different heights?
• Eric: What do you think?

5. Enter both of your calculated flagpole heights into the google form (accessed using a bit.ly address from their cell phones).

#### 6.  Justify flagpole height

Project the spreadsheet from the google form as students enter their flagpole heights.

• Eric: We don’t know the actual height of the flagpole. Here are all of your calculated heights. We need to determine what number to use as the height of the flagpole. What are some was to analyze data?
• students: average, mean, median, outliers, graphs, range…..
• Eric:  Determine what height you believe the flagpole is and use one or more of these measures to justify your conclusion.

Day 2: Design a model and calculate angle of elevation, zipline length, and ground distance.