Tissue Paper Problem

TISSUE PAPER PROBLEM

I often used this on the first day of school to let my students know that this class was going to be special. I used an ordinary piece of tissue paper (Kleenex). When you pull it out of the box, it is two-ply. That is there are two sheets together. I took those apart so I had only one sheet. I told the students that this one piece of tissue was so thin that 1024 of them stacked on top of each other, and then compressed down as far as possible, would be exactly one inch high. That is a way of telling them that the thickness or height of the one sheet was 1/1024 of an inch. I then took that one piece of tissue and folded in in half. I asked them how thick it was now compared to before I folded it. They could easily see that it was now twice as thick or, if you thought of the thickness as its height, it was now twice as high. I again folded it in half and asked them how thick or how high it was. They knew it was now four times as thick or high compared to before the folding. I continued folding and asking the same question. If you have ever tried this you know you can only fold it seven or eight times before it becomes too thick to continue. I did show them that it was ¼ of an inch high after 8 folds. I then asked them how thick or how high it would be if it could be folded in half a total of twenty times. I would say to them that even though we can't actually do that many folds that we could figure it out mathematically. I took some random answers from the students which were usually pretty far off. I then gave them another hint: after ten folds it would be one inch high. Of course that caused many of them to jump to the erroneous conclusion that after 20 folds it would be two inches high. I made sure that they knew that answer was wrong but I did not explain any further (that it would be two inches high after the 11^th fold). Their homework for the next day was to figure out the thickness or height of that one piece of tissue paper after it had been folded in half 20 times. When they came in the next day, I might have one or two kids who had figured it out. At any rate, they were all amazed that after 20 folds it would be 85 feet, four inches high. I find that most adults are amazed by that too.

When I first started using this activity, I was teaching on the third floor of a rather old building. The height of the building was about 48 feet. The building had a gym whose floor was below ground about 15 feet. It really stunned the students that a person could be down on their hands and knees on that gym floor and start folding that tissue paper and that after 20 folds it would be much higher than the top of the three story school building.

Most years I gave the students tissue paper to fold along with me. Sometimes that didn't work well because they didn't always hear the information I was giving them while they were folding. I would suggest that you try it with them folding their own tissue and if you don't like it, then just have them observe you.

(One ply of tissue paper is 1/1024 inch thick.)

0 folds – one thickness, 1 fold – two thicknesses,

2 folds – four thicknesses,3 folds- eight thicknesses,

4 folds – 16 thicknesses, 5 folds – 32 thicknesses,

6 folds – 64 thicknesses, 7 folds – 128 thicknesses,

8 folds- 256 thicknesses, 9 folds – 512 thicknesses,

10 folds – 1024 thicknesses, therefore one inch high,

11 folds – two inches high, 12 folds – four inches high,

13 folds – eight inches high, 14 folds – 16 inches high,

15 folds – 32 inches high, 16 folds – 64 inches high,

17 folds – 128 inches high, 18 folds – 256 inches high,

19 folds – 512 inches high, 20 folds – 1024 inches high.

1024 inches divided by 12 is 85 feet 4 inches.