Summer project (3 of 3)

We went to the State Fair last week.

Having wondered about the height of the Giant Slide, and having developed a technique for measuring things, we needed to collect the information required to answer our original question.

The only problem? No one but me wanted to ride the slide. This is a big change from previous years.

I went up alone in the name of mathematics.

There are 104 steps to the top.

I asked a young woman employee how many steps she thought there were. She said 108. I told her my count and she was ready to believe it. I asked a young man employee how many steps he thought there were. He had no idea.

How can you work at the top of that thing and not be curious how many steps there are?

In any case, should someone wish to check my work next year, I got 1 set of 20 and 3 sets of 28.

I also took a kebab stick from Griffin’s dinner along with me. I broke it off at the height of one step partway up. I checked it against another step further up. Then I taped the stick into my notebook when we got home.

May not be actual size on your screen.

So then Griffin and I sat down one morning to finish this off. Recall our guesses of 40 and 45 feet.

It was a fairly conventional conversation, so I’ll just list the bullet points instead of trying to reconstruct our exact words.

• I asked him to estimate the length of the stick, which he did—4 inches.
• He measured the stick with a ruler—$4\frac{1}{2}$ inches.
• He suggested a calculator was in order.
• I suggested that this would not be happening.
• We sought to find $104\cdot4\frac{1}{2}$.
• He naturally subdivided this into $104\cdot4+104\cdot\frac{1}{2}$.
• His first answer to $104\cdot4$ was 408; on further reflection he got 416.
• I was a useful resource for remembering intermediate results (such as the 116).
• Half of 104 was easy for him.
• We ended up with 468 inches.
• He knew we needed to divide this by 12.
• I modeled an intelligent guess-and-check strategy for doing this by asking him to guess. I did the multiplication. You can see the results below.

For the record, I spoke aloud while doing these. E.g. “Two 45s is 90; ten 45s is 450, so 540” Et cetera

Upon completion of our analysis, Griffin wanted to know how high the Sky Ride is.

Success.