### Barbie Zip Line

Inspiration from Matt, John, and Jedidiah helped me shape my Barbie Zip Line task today. Whenever I prepare new tasks for my students, I have been trying to keep mathematical modeling, student ownership/creativity, performance tasks, and openness in the back of my mind. That's a lot, right? Plus, there's a hundred other little things, but let's focus on the list above. As I reflect on today, I'll share how I would improve this for next time.

Supplies (in order of attachment):
• Barbie doll, or an action figure like G.I. Joe, Superman, or Captain America
• Velcro: One-wrap (don't get Sticky Back)
• Carabiners
• Swivel Spring Snap (optional)
• Fixed Pulley
• Rope (thin enough to fit through the pulley)
My first piece of advice after learning from today: don't skimp on the pulley system. I made two and I should have made (bought) more. I would spend the money and have enough pulley systems for the number of groups you plan on having. Second, you could connect the pulley straight to the carabiner and avoid using (buying) the swivel spring. Third, velcro (harness) is the best way to quickly attach your pulley system to the zip line rider.

Buy enough rope so that you can have lengths that are 10 feet apart. In other words, have different rope lengths: 30 ft., 40 ft., 50 ft., 60 ft., etc. This will play well into the mathematical modeling part of the task (see below). It will also help make it easier to get the pulley systems on and off of the zip line. Solving the task yourself will also help determine the rope lengths you'll need for your school site.

Depending where (and who) you teach, some students have been zip-lining before. Ask! It never hurts. Maybe they can share their experience. Plus, this gives you a chance, at some point (if you feel necessary), to talk about how they're sitting in front of you, ALIVE, because someone was able to do some solid math and build a sound enough structure for them to zip line on. Just sayin'.

I low-balled my students today on their budget. I should have raised it to \$2500 or \$3000. Figure out what will work for your site. However, this mistake allowed me to give some early finishers an extension: find a more reasonable starting budget.

Here are the opening costs of your zip line company:
Students had to receive approval from their Summer Academy principal by showing their designs. I highly encourage this move. Students see someone else taking a vested interest in their learning. The principal gets an informal glimpse of your classroom. And students have to be prepared to explain the math and their problem-solving approach. If your principal is unavailable, get someone else: teacher, custodian, campus security, etc. It could be you, but you're already doing the formative approval (assessment) in class.

All these prices can change depending on your tastes. I included a liability insurance just for fun. The materials for the harness and pulley system need to be of high quality, so don't make them cheap. \$50 might have been too cheap. The most important material is the steel cable (rope). This will help create multiple solution strategies. It's beautiful. Overall, I was pleased with my price points.
I found that having students create three rides is essential to this task. At least three rides. Sometimes tasks generate such a strong focus on the ONE CORRECT WAY to construct an answer or problem-solve. This adds pressure and can rob students of discovering mistakes or playing around with numbers. By creating separate zip lines for both certain death and boredom (getting stuck), it does many beautiful things.

Students innately know what type of zip line would kill barbie: a steep zip line. They can sketch that on their whiteboard, no problem. On the flip side, students have a good understanding of a boring zip line: practically a horizontal line. They can also sketch that on their whiteboard. Both sketches can be done without using numbers, formulas, or mathematical notation. It creates an entry point for all students. So here's what they had to say:
Leyla: We have a chance to see what not to do.
Trevor: It reminds me of when we do Estimation [180] and you ask us to give a too low and too high. It helps us find a reasonable number in the middle.
Deena: It shows us what a wrong answer or zip line would be.
Students were able to draw steep zip lines, label the height 20 feet, guess the ground distance to be about 5 or 10 feet, and use the Pythagorean Theorem to calculate the length of the cable (hypotenuse).
Mathematical Modeling and Multiple Solutions:
Students were able to design their own zip line by playing around with the numbers between their certain-death zip line and boring zip line. I told them to dream big on the whiteboards as if money wasn't a factor right now. Most did. Most.

I had a couple groups first figure out the cost of all the materials (\$700) and subtract it from the \$1500 budget, giving their group \$800 to spend on cable. With \$20/foot, they could use 40 feet of cable for their zip line. They identified the height and the hypotenuse of the right triangle. Impressive.

One of these two groups felt this wasn't enough cable and it was still too steep. Michelle had been zip-lining in real life so she knew. This was my mistake, but it turned into an opportunity for me to extend this task. I asked them to create a new budget for me so the cable was longer, but within reason. If you need more of an extension, have them come up with a formula to determine the amount of cable and distance on the ground, given a specific amount of money.

Before they could go outside and test their zip line, students had to complete this list:
I had students transfer their work to their graph paper composition books before they took it to the principal. I'll insert some pictures:

Here's the permit:

It was a blast! Students loved it. Here's another extension:
Have students design a system that gets the pulleys and/or dolls back up to the top of the zip line.

[insert video here]

By the way, I did teach the Pythagorean Theorem in there somewhere. Where? You might ask. I don't remember: ALL throughout the task. Use discretion. Some students need it first. Some need it after you've let them mess around on the whiteboards.

Zip,
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