Resources at the end.

## Twelve Days Out

In early May, Claire and I were talking about non-traditional math lessons to make her department more interesting. She’s already using Visual Patterns with Algebra students and is pleased with the spike in their reasoning skills, but…

“There’s tons of cool stuff on the internet and I don’t know where it is or how to use it.”

I had to bite my tongue to keep from shouting, “CAN I SHOW YOU SOME OF IT?!”

## Seven Days Out

After a few prep periods of chatting about math curriculum and Common Core standards, we decide on a three-day Barbie Bungee performance task.

The last time my class did this lesson, we realized that I didn’t adequately set up the reason for this silliness. This time, Mrs. Verti and I worked hard to connect the individual data to the jumps and emphasizing their value to calculate the medium jump and big jump.

After deciding to make *bungees* the dependent variable, I couldn’t decide if we should have stations inside the classroom or give the platforms to each group to hang outside.

Claire pointed out that we have two wildly different ability levels (Honors Pre-Calculus and Freshman General Algebra), so we can try both methods.

Sweet.

## Four Days Out

Claire and I meet on Friday before Memorial Day to discuss any remaining details. She confesses she’s a big nervous; that this is a weird, different way to do math class.

I assure her; *weird* and *different *is where I live. And if it bombs, that’ll be on me and not her.

## Two Days Out

After three years of hauling around awkwardly-shaped platforms, I realize what’s missing: hinges.

Further, I realize, after I build six new platforms, it’s hardly any work to retro-fit the old ones so they will fold flat into my storage bin.

Plus I had some adorable helpers.

## Day One – Data Collection

First period is Pre-Calculus Honors. I meet them at the door and shake their hand, then they grab the study guide off the back table and staple it. Mrs. Verti gives details about the final exam next week and it’s my turn.

Deep breath.

“Good morning!” Big smile.

“Grrd Muh-huhhh.” The class moans, unsure of what to do with me.

“My name is Mr. Vaudrey. Everyone say *Vaudrey*.”

*Vaudrey*.

“Vaudrey.”

*Vaudrey.*

“Thank you. I’m here today to talk about *this*.”

Students: Oh, snap! Where are they? Is that a missile silo? That makes me dizzy. Mark, you wanna do that? No!

The smooth jazz fades out and Mrs. Verti pulls the lights back on. “What do you suppose,” I begin, pausing for their full attention. This class doesn’t know me, and the end of May is a pretty awful time to try a demo lesson. For the next three days to go well, I need to flex my teacher muscles early.

“What do you suppose they were talking about as they drove through the Russian wilderness to go jump into a missile silo? Talk to your neighbor; what things are important to the jumpers?”

This was a great spot for a music cue, but they wouldn’t know what to do with it, so I just wander the class and listen. After a minute, I take some student answers.

Vaudrey: What do you suppose they were talking about? Yes, go ahead.

Student 1: How to not die. *smirk*

Vaudrey: What do you mean? Can they control that?

Student 1: Well, yeah. Like, they have to have enough rope to reach across the thing.

Vaudrey: Somebody else, why is that important?

Student 2: If the rope doesn’t reach across, then they just fall into the thing.

Vaudrey: Okay, so we need *lots* of rope. Lots and lots of rope.

Student 1: Well, not too much.

Vaudrey: Why not too much?

Student 3: Cuz they’ll hit the bottom and die!

Vaudrey: Ah, so just barely enough to reach across the missile silo? That’s the perfect jump?

Student 2: Yeah.

Student 4: No! Cuz then you’re just hanging at the top!

Vaudrey: Tell us more about that.

Student 4: Well… like, you’re stuck on top.

Vaudrey: Isn’t that good? You won’t hit your head.

Student 1: But that’s boring.

Vaudrey: Why?

Student 1: The whole point is to jump in, not… like…

Vaudrey: Okay, I think I understand. If we use too much rope, it’s not…

[pregnant pause]

Student 5: Safe.

Vaudrey: Not safe, because (thunks desk dramatically) you’ll die. But we want to use enough rope the jump is…

[pregnant pause]

Students 3 and 1: Fun.

Vaudrey: Fun. So we want to have fun, but also be safe.

NOTE: A 50-foot jump is a little fun, an 80-foot jump is more fun because the ground is closer. I should have asked them to *define* the fun here. Something like, “What’s the most fun jump you could have?”

Next year.

Vaudrey: Today, we’re going to recreate that jump using…[dramatic pause as I lift the bag of Barbies and slowly pull one out] …dolls.

After making their own groups and building a short bungee, we head outside with our data-sheets, dolls, bungees, and platforms. There was a light drizzle as students hung their platforms on the fence and began gathering data.

After a few minutes, students began to notice the nearby baseball field, with its much-taller fence.

Then we returned to class to discuss (in groups) how many bungees we’d need for tomorrow, when we’d go into the gym to jump off the top of the bleachers.

Student 5: We’re gonna jump off the bleachers?!

Verti: No, your *doll* is. The one you’ve been using all day.

Student 5: Ohhhh.

First period ends and we repeat the process with two Algebra classes and two more Pre-Calc Honors classes.

Freshman Algebra is–obviously–louder, sillier, and requires more directions, but they rotate through the twelve stations around the room just fine.

Here’s a good snapshot.

### Day One Student Quotes:

We took our jumps too close together, we should have spread it out more.

The numbers are making me nervous, I’m gonna average to sort out my life.

I had PE first period, so I saw you guys. I don’t know what we’re doing, but I know it’s something fun outside.

I feel like this cute stuff is made for elementary school.Student 1: This is a “performance task”? Noooo! That means it has to be right.

Student 2: Yeah, see? [holds up his phone showing this tweet]

```
```Tomorrow, @claireverti‘s class starts #barbiebungee. Get ready. Epic performance task with blog post to follow. pic.twitter.com/rfHWa3QL2J

— Matt Vaudrey (@MrVaudrey) May 26, 2015

Pre-Calculus Student: This feels like the ambiguous case. I don’t like it.

Freshman: Do you wanna join Alien Club?

Vaudrey: What are my duties as a member?

Freshman: You have to take an oath (makes the Vulcan symbol).

Vaudrey: No, thank you.

That freshman continued to talk about Alien Club the next two days.

## Day 2 – Desmos and Bleachers

First period begins sweaty at 7:40.

I’m sweaty because I hauled six tubs of iPads to room 908, but I’m hoping the payoff is worth it.

On the wall is the first of several slides directing students to submit their raw data from yesterday. It’s noteworthy here that these students haven’t used the iPad much in class all year, but required very little prompting to open the internet and navigate to the URL I gave.

This wasn’t the first nor the last time I noticed rich kids are *way* more motivated than … well… my usual clientele.

After submitting raw data (more on that later), we directed them to the second URL, which was a Desmos graph I had built ahead of time for them to input their data.

Vaudrey: Here, you will input your data from yesterday. If you don’t have any jumps for six bungees, leave it blank. If you have multiple jumps for two bungees, enter the others at the bottom. Then… watch this… drag the sliders to fit your line to the graph. Everyone say, “Ooooo”.

Class: oooOOOOOooo

Vaudrey: Go.

One of the marks of a Common Core classroom is minimal instruction from the teacher. I am confident that students can figure out how to drag sliders and input data, so I don’t need to waste my words giving more explicit instructions.

And yes, that is a skill that classes must develop; the previous 10 years of school have trained them well to value compliance over curiosity.

It takes a while to shake off those blinders.

After a few minutes of playing, I show the class how to click on the intersection of the purple and green lines. We talk about what that number means and begin building a bungee with that length.

Student: What do I do if my line doesn’t hit all the points?

Vaudrey: Do you all have the same intersection?

Student: He has 16, she has 18, and I have 21.

Vaudrey: Would you rather have too few bungees or too many? Discuss with your group.

```
```Mathematician-scientist-adventure seeking Barbie. How many rubber bands? #barbiebungee pic.twitter.com/I2BcPAwoWU

— Claire Verti (@ClaireVerti) May 28, 2015

Once groups agreed on their bungee length, we set off for the gym and dropped two at a time off the top (301 cm ~ 12 feet), bracket-style, so the most fun, safe jump moved on to the next round.

```
```@MrVaudrey be careful!! #barbiebungee day 2 pic.twitter.com/fUFJ1Dze9o

— Claire Verti (@ClaireVerti) May 27, 2015

```
```2nd opinion please. Who won? #barbiebungee @MrVaudrey pic.twitter.com/7PyKB31q6C

— Claire Verti (@ClaireVerti) May 27, 2015

With the remaining time in class, we discussed possible improvements, then showed this video:

Verti: That’s what we’re doing tomorrow. Tomorrow, Barbie jumps off the back of the visitor side of the bleachers. Start thinking about what you’ll do.

### Day Two Student Quotes

We should get the average, like find how much one bungee gives us, then divide.

Whoa! We figured out a way to do a half-bungee!

What do we do if we have one point that’s like… out there?

Let’s set up a proportion!

It shouldn’t be this hard. If Algebra kids can do it, we should be able to figure it out.

I told you to add an extra bungee, but you said, “Noooo, we gotta be saaaafe.” Safety’s for losers!

I don’t like technology; I’d rather do a worksheet.

## Day Three – The Big Jump

Students got right to work, grabbing iPads, opening Safari^{1}, navigating to the link on the board, and awaiting instructions.

Vaudrey: Today is the day. You have a new graph where you may enter your data, AND you have the option of checking your line against the data from other classes by clicking the folder for your doll’s weight class.

NOTE: Claire and I realized that we didn’t actually tell students to input their 301 cm jump from Day Two, which might have helped their data a bit.

Next year.

After building their long bungee, we began the seven minute trek past the fence from Day One (yellow ellipse) to the back of the visitor’s bleachers.

Then, the fun part.

Bad Idea: attempt to have a conversation about bungee length from 32 feet in the air.

Good idea: Have the discussion *in class* before walking outside. It allows the meticulous teams some more time to build their 61.5-bungee cord^{2} while the rest of the class can be validated or made nervous by their classmate’s calculations.

Our graphs all had… um… all intersected at different spots, so we took the smallest number because we wanna be safe.

Claire and I got more and more excited hearing the variety of reasoning skills, the students got less and less certain that theirs was the “right answer”.

### Day Three Student Quotes

*(points to a data point at the bottom of the cluster) This*group was playing it safe, they probably just took the first jump and didn’t see how close to the ground they could get.

Keep the head on, if we take it off, it’ll mess up our whole calculation.

S: Is he a real teacher?

Verti: Yes, he’s a real math teacher.

S: He is?!

S2:We have 37 bungees, that feels like a stupid lot of them.

V: Someone last period used 33 and it was a safe jump.

S1: But was it fun?

V: I don’t know.

S2: Uhhhhh, I don’t like this uncertainty! This is stressful!

## Day Four – Exit Ticket

This is the first year that I haven’t given the Teacher Report Card to students, so I welcomed some student feedback. We didn’t use the Exit Ticket on Day One, so we tweaked it and Claire gave a voluntary link for students to complete on Friday.

We then color-coded it; Green for Great, Yellow for Next Year, Red for Ouch.

If you so desire, have a look and mourn the students clinging tightly to final exams and grades.

## Comments

Barbie Bungee is a yearly staple in Fawn’s class, and she bundled the rubber bands in groups of seven so students can’t keep any (I assume). I gave out rubber bands like Oprah and–of course–had a couple freshmen shoot each other on Day One.

Vaudrey: Come here.

Freshman: It was an accident!

Vaudrey: … you’re a freshman, right?

Freshman: Yeah.

Vaudrey: … hm. [Deliberate, silent eye contact] Don’t do that again.

Day two had no issues.

Here’s a YouTube Playlist with all the uploaded videos.

## Resources

For the first time ever, I planned a lesson in Google Docs. I missed my spiral notebook, but for Claire and I to co-plan, we needed something collaborative, so this worked okay.

Here’s the folder with everything in it *except *the pictures. Some of Claire’s students haven’t signed media releases.

## Confessions

On Day Two, I was beat. My throat hurt from using my teacher voice and I was fried from plowing six periods through the gym to do bungees *for a mathematical purpose that was unclear*. This was the second-last week of school and it felt like it: disjointed. We got some great feedback here on how to improve it for next year.

Stacy’s head popped off years ago. This year, Grace and Sparkles lost heads, too.

Before tossing them from the top of the bleachers, I loosened all three of their heads so they’d pop off, prompting an “Ohhh!” from the students below.

I regret nothing.

~Matt “Please, Can I Borrow Your Classroom?” Vaudrey

P.S. Attendees at Twitter Math Camp this summer can come experience Barbie Bungee firsthand, featuring Fawn Nguyen.

^{1. Desmos in Chrome on the iPad was glitchy to the point of unusable. More points in the “Buy Chromebooks for Secondary Students” basket. ↩}

^{2. One group figured out a way to tie the bungee so it’s only half as long. I asked how they knew it was exactly half. Could it be 0.6 bungees? How much of a difference does that make?↩}

Hi Matt,

Stumbling across your blog I have realized your way of teaching math resembles my idea of being a teacher.

I am currently studying pedagogy in Germany and I am going to be math teacher soon. This semester I have the opportunity to test my skills in teaching at one of our seminar classes on the fellow students. Since my topic is explorative learning I thought of your Barbie Bungee and hope

you can answer me some questions.

Because of my audiences higher age there could occur some problems, like the lack of motivation or the inexperience of the students with explorative learning in contrast to heavily instruction based classes.

Motivating them with the help of videos (of Bungee Jumps, etc.) could work. For them to know the right steps I thought of step by step instructions.

Do you have any experience dealing with these specific problems and what would you recommend?

I would be happy about all kind of ideas.

Greetings from Germany

Hi, Mattias.

I advise

againststep-by-step instructions; if your goal is to get students to explore, the path should be clear, but the steps to get there should be murky. That’s the teaching challenge that you’re describing.Feel free to email me to continue this conversation.