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.

The task (handouts found here):
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,
1152

Fun With A Name Tent

As I ask my new students to make a name tent with an 8.5" x 11" sheet of paper on the first day of Summer Academy, I think, "Let's have a little competition." This wasn't in my lesson plan. Ha!

If you haven't noticed, I have become obsessed with classroom competitions. Here are two posts in case you missed them:
Fun With A Dot and A Line
Fun With A Sticky

Therefore, I'm adding today's post of Fun With A Name Tent to the "Fun With A" series. A name tent looks like this:

I use name tents for teacher trainings or on the first week of class with students so I can quickly learn their names. Right as I tell my new students to make a name tent, I announce, "Let's see who can fold their name tent into the best thirds?"

Game on!

If you have read (or remember) my two posts from above, you know this activity will go something like this:

• Students get time to create their best thirds.
• Students decide in their group (of four) who has the best name tent.
• Students vote (whole group) by eyeballing the tents and make a prioritized list. 
• Students define how we decide the best thirds.
• Students define what to measure.

Here are some whiteboard shots of my lazy writing as I quickly jot down what students say. It's fascinating.

I handed each group a name tent that was in the running for the best thirds. Some groups used inches and some groups used centimeters to measure.

I didn't care nor tell them what unit of measurement to use. I walked around and questioned which unit of measurement they were using and asked them to explain why they chose that specific unit of measurement. We later had a discussion (almost arguments) about which made more sense for this task. Most students eventually were convinced by their peers that centimeters would be more accurate here. My second class had two tents that were extremely close, but couldn't tell which was better:

We had to compare 0.5 centimeters to 0.25 inches to see who had the smallest error, Leyla or Srihitha? It was awesome! We had to decide if we wanted to convert the inches to centimeters or vice versa. You can see that Leyla won by 0.135 centimeters. DANG! Those are some good folds.

Next, I introduced them to Estimation 180 by estimating my height. They'll be keeping track of their estimates in their compositions books.

My favorite part was this exchange:

Brianna: Will you tell us your height?

Me: No.

Brianna: What?

Class (disappointed): Ohhhhh!

Brianna: That's not fair. Then why are we doing all this work?

Me: I understand. I said I'm not telling you my height.

And then BAM! I take out my measuring tape!

Me: Brianna, stand on your desk chair and you can measure how tall I am.

Brianna: Oh, cool! 

We proceed to estimate my wife's height and then we estimate the TOTAL height of the class. This was fun. I asked, "What would be useful to know and how would we go about getting it?" borrowed from Dan.

My favorite was Mansi. She suggested that we multiply the number of students (20) by 5 feet since most students were about 5 feet tall. Then we add or subtract the difference of each student's height in relationship to 5 feet. We started a Mansi column in our Google spreadsheet. This would make for a pretty cool lesson on integers.

Before we went outside, I had the students get in order from what they thought was shortest to tallest. If you keep track of the data in a spreadsheet, use the spreadsheet to verify their order: another great tool from a spreadsheet.

With this organized data, you could do a lesson on mean, median, mode, and range. Even mean absolute deviation if you're up to it. Another great part was Dylan noticing a student was absent today. "We don't know the height of the kid who isn't here today."

You could take this task and apply the mean or the mode. Have students predict the height of the absent kid. Furthermore, you could segue into probability if you like. What are the chances the absent kid is the mean height? the mode height?

How sweet of my first class, they wanted to include my height in the total height. We went outside and looked for an area long enough to fit our calculated total height of approximately 103 feet.

We went a little bit past 103 feet because some students were considerate enough to avoid placing their feet next to someone else's head. The dismissal time was rapidly approaching so I let it slide. One clap on three for Reese. She had the closest estimate of 102 feet.

One. Two. Three.

CLAP!

Thirds,
1050

A Few Updates

Update 1:
I finally finished Act 3 for my Deodorant lesson. I hope you check it out and can give me some feedback; I think it could be much better with your help. If nothing else, check out how long it took to use 5 sticks of deodorant. Mathematical Modeling should really be at the forefront of this task. It might appear linear, but I would bet a year's supply of deodorant that an adolescent's deodorant use will be far different than mine. I also guarantee students will think of variables ranging from climate to age to geographical location to genetics to more. I think you'll have some excellent conversations with the deodorant task. My favorite part is the sequel: How many sticks of deodorant would one use in a lifetime?

Way back when this task first started, I opened up a little estimation competition in the comments at 101qs. Don't listen to a word Nathan Kraft says. The person with the closest guess would win an Estimation 180 prize. With so many close estimates, the following gentlemen will be the first to receive the new Estimation 180 stickers, hot off the press!

Congratulations to:
1st place: Chris Robinson (May 14, 2014)
2nd place: Robert Kaplinsky (May 5, 2014)
2nd place: Michael Fenton (May 15, 2014)
3rd place: James Cleveland (May 3, 2014)

Update 2:
Estimation 180 will be getting a facelift and other updates over the summer. Here are a few things to look out for:

• New logo
• New fields for entering student estimates
• Clean spreadsheets containing "other estimates"
• Updated Lessons
• Search by Categories
• Sentence frames for student reasoning

I'm most excited about the last update; sentence frames. I occasionally browse over student responses and notice many students entered "I guessed." I think it would be extremely helpful for teachers to provide their students with sentence frames in order to better articulate their reasoning. I will be focusing on this tool in upcoming presentations and workshops.

The new logo was done by my niece. I love her simple design, the two 180 degree arrows, the metric reference, and her idea to transform me into a stick man. That reminds me, I still owe her a pizza!

I hope to get a few t-shirts made too. You can sport them at your next PLC, department meeting, casual Friday, or math conference. Any takers?

Update 3:
I've accepted a Teacher On Special Assignment (TOSA) position with my district for next year. It's a bittersweet feeling at this point. On one hand, I'm very excited because I'll be working at various secondary sites throughout my district, collaborating with other math teachers, helping design lessons and implementing various technology. My official title will be a Digital Learning Coach. I hope to seek advice from people like John Stevens, who have been doing this for some time now. As I pack up my room, I already miss my own classroom and students. However, I look forward to learning a great deal from the teachers I will be fortunate to work with and the students I'll be able to interact with at each site.

Updates,
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