Don’t mean to burst your bubble

via Colossal, an art, design, and photography blog:

stress-4While waiting for a train, commuters can help themselves to square sheets of bubble wrap labelled with how long it would take to pop them.

stress-5

I love this idea. The world is a better place because of it. I hestitate to bring this up, but …

the math is wrong.

Bubble Wrap Length

It looks like the approximate times are based on length. Above, the ratio of side lengths is 3 to 5 to 10, or 1 to 1.67 to 3.33. Let’s assume that the small sheet does, in fact, take 3 minutes to pop, one bubble at a time. The large sheet does not have 3.33 times more bubbles; it has 3.33 times as many rows and 3.33 times as many columns. Therefore, it has 3.33^2, or 11.11, times as many bubbles. A better approximation for the large sheet would be 30 minutes. If we base the approximate times on area, the ratio of sides lengths would be 3 to √(5/3) to √(10/3), or 1 to 1.29 to 1.83, as shown below.

Bubble Wrap Area

I’m thinking about how I could use this image or idea in class. Some possibilities:

1. As-Is

Display the photos. Ask students, “Are the times accurate?” Have students apply their understanding of the relationship between scale factor and area. M’eh.

2. Hands-On

Display the photos. In pairs, have students record how long it takes to pop a small square sheet of bubble wrap. Pose the problem, “A square sheet takes twice as long. What are its dimensions?” Have students test their predictions. In this activity, students develop their understanding between scale factor and area. They poke holes in the common misconception that when dimensions are doubled, area is doubled, too.

3. Three-Act

Play a video of a small square sheet of bubble wrap being popped. Include a timer. Maybe a soundtrack, too. Play the beginning of a video showing a large square sheet of bubble wrap being popped. Have students guess how long it will take. Ask, “What information would be useful?” Show the dimensions of the squares. Play the answer video.

I see this task being similar to Dan’s Penny Circle. Dan filmed himself filling a circle with 663 pennies so that the rest of us wouldn’t have to. I have a roll of bubble wrap measuring 24″ by 30′. Before I take one for the team and spend a ridiculous amount of time enjoying bubble wrap, any suggestions?