Index Card Tower CHALLENGE

After teaching the Mathletes how to measure the height of tall objects, or any object for that matter, including trees, buildings, etc., I wanted to challenge them to engineer their own tall structures. We spent considerable time discussing engineering best practices: which structures had the most integrity and how to increase height without risking instability. 
I used seven of my favorite engineering marvels to illustrate best practices in building:
  1. Burj Khalifa in Dubai
  2. Petronas Towers in Kuala Lampur
  3. One World Trade Center in New York
  4. Capital Gate Building in Abu Dhabi
  5. Eiffel Tower in Paris
  6. Great Wall of China
  7. Roman Aqueducts in Italy
They noticed that with one exception (the Capital Gate Building), that all of these structures had a wide base tapering off as it rose into the sky. So when they built their first index card towers with a small base, they found that it fell after 20 inches or so. Then they went to work fortifying a larger base, and tapering in only when they had to. This created towers of 40 to 68 inches just in a short period of time. Imagine what they could accomplish with more planning and optimizing their designs.
The shape of the base before each horizontal floor was also at issue. They tried to use the hotdog fold (the long way on a 3x5inch card) but this proved to be unstable. The short hamburger fold only provided 3 inches per floor, but significantly more stability.
Please have them create their own at home working with friends, siblings, parents, etc. and then take pictures with a tape measure in the background and bring those pictures to class.
Here are the rules I gave them in class and the pictures of the seven engineering marvels are in the attached pdf.
I did a similar challenge a number of years ago and it fell short of teach engineering best practices since it allowed them to use tape. This tower construction is much more challenging and forces students to think strategically. Finally, the collaboration among groups was astounding. No-one in a group was excluded and each member brought a set of specific skills to the party. 
Task: C​reate the tallest index card tower that remains self-supporting for 10 seconds after time ends.
Materials:​ Index cards, scissors, and yardstick (no additional materials allowed, including tape or staples)
  • each pair or group will have ____ minutes to build the tower
  • the cards MAY be cut or folded as desired
  • the tower will be declared successful only if it can remain standing for a minimum of 10 seconds when time ends
  • height is determined by measuring the perpendicular distance from the base of the tower (table) to the highest point of the tower
  • if your tower stands for 10 seconds, but it falls before you have a chance to measure it, it will be disqualified. 
Measure it quickly and record the height.
During the week, after you measure your tower, take a picture and print it out for class.
Record your tower heights: 


3. ________________

4. ________________


 Home project tonight - over 7’ tall - 85” and we ran out of cards!