I had first read about Barbie zipline on Andrew Stadel's blog and in my favorite book, Classroom Chef by Matt Vaudrey and John Stevens. If you haven't seen either of these, GO NOW! I have always wanted to try this but never found the prime opportunity to run it in my class. Call it a lack of faith in myself as a teacher or a lack of faith in the process that I know works in math class. EIther way, I delayed and delayed what I knew would be successful because of what Andrew Stadel would call my own paradox of my version of the classroom clock. Through being inspired by my students' everlasting intrigue and love of mathematics and by all of MTBOS and NCTM friends pushing me out of my comfort... I dove in.
I started with Andrew Stadel's model of having my students investigate "slopes" of triangles.
My students had talked about slope, they had investigated rate of change via visualpatterns.org so this wasn't new, but it was different as we had never talked about triangles. I love this introduction because it gives way to a great conversation about what makes a triangle steep:
S1 "Triangle F is the most steep"
Me "That's interesting, why?"
S1 "If you feel down it, like if you were on a mountain like that, you'd roll really
Me "Oh, that sounds awful. How do you know you'd roll really fast?"
S1 "Because it's super steep!"
Me "But what makes that steep? What about the triangle or mountain makes
one steeper than the other?
S1 "Well it goes really tall but isn't very wide."
S2 "Isn't that like slope? It falls a greater distance than it runs?"
Nice. We then continued the discussion to define the least steep or just right triangles.
We then took some time to describe what a zip line is and how we would describe zip lining to someone who either had never been zip lining or did not know what zip lining was at all. This was necessary because many middle schoolers like to believe they are impervious to danger, thrill seekers and would design death zip lines because "they are fun." It is always good to hear some natural fears arise from students who have never been zip lining due to their fears.
Out of this discussion came a need to define ziplines as something fun but safe at the same time. That you need a harness, helmet, and rope to attach to. We then set out to google forms to describe characteristics of death zip lines, boring zip lines and zip lines that are "just right."
Setting up the process:
Like with 3 act problems, I will not give information unless it's asked for... so I asked them on the forms what information would they need to know
Setting the stage :
I finally told the students they would be designing and making a zipline.
S "A real zip line?! Line we can use it!?"
Me "No *taking out a toy Police Man* for him!"
S "Oh cool! Can my dog use it? Probably not. I want to make mine go fast and
safe and FAST and through trees... wait! Do we get to be our own
companies? Can we make advertisements and a website and film our guy
having a fun time?
Yes. Let's do that.
So I asked them how they think we could safely design a zip line for our 26 ft ledge down to a parking lot without doing trial and error on the large scale. We didn't want to waste resources or kill our dollar store Police Man. They suggested we make a model in the classroom after designing it on paper. Naturally I had them design it on Desmos first:
Of course as a business we had to discuss start up costs and liability insurance.
S1 "$100 per rider?! How will we ever make our money back?"
S2 "We could charge them more than the insurance..."
We curbed the discussion for after as worry about a price before having a product seemed to be a bit silly.
Then they designed it on paper and talked about slope, used the pythagorean theorem to find out how much rope they would need to figure out how much their business would cost. I had predetermined the height of the in class launch to be 5ft high and asked how we could "scale it up" to the real model that would be 26ft tall. The students had never been formally taught how to scale or ratios, but they suggested the sides should increase at the same rate. For example, as one student explained, if you had a height of 2ft and a length of 3ft and you increase the height to 6ft you have to triple to the base too. We made a few triangles to investigate this thought and noticed the slopes never changed.
So then we built their designs in our classroom to see how their zip lines ran. We also put their designs out to the twitterverse and asked which design they preferred and why. Sadly, as you will see below, many of their original designs (though they look fun for a toy launch) were not safe for our police man. Twitter spoke loud and clear. I wanted them to receive this feedback, not from me and to then take a look and reflect on what they have done.
Nothing is perfect the first time you design it. There is always room for improvement and reflection. Enter Desmos with their zip line overlaid onto a real zip line photo. Time for some massive reflection, kids. What do YOU notice and wonder?
It is amazing what kids can reflect on when you give them the freedom to think for themselves. Too often in classes we do the thinking for them, even if unintentionally, by guiding them to what we think is right. I enjoyed not having a preconceived idea of what was a correct slope or how fast/dangerous a run would be before they tested it. I was just as into seeing what happened as they were. Which gave my students the opportunity to learn from their mistakes without my hands in the mix.
I had them go back to the drawing board, if they wanted to, and redesign their lines. Every single group redesigned. First they asked to have the image of the Desmos zip line and theirs, they noticed they could try a scale model 5 high and 22-25ft long and it would be faster than the picture zipline but much (over twice as some students claimed) more safe than their first design. They tried it in the class.
Students gave the final OK on their scale model and prepared to go full scale the next day. They suited up their toys with harnesses and carabiners and anxiously left class to arrive back tomorrow for their final launches
MS Math Department Head located in Massachusetts. I mainly work with LBDB students teaching them meaningful mathematical procedures through context. I also look to open students' eyes to the mathematical world around them