This blog post could easily have been titled, "A Long Wait in a Really Long Line" but I like to be positive. I focus on the silver lining instead of the grey cloud. That's why I took a wait in a long long as an opportunity to practice estimation instead of a tedious and boring waste of time.
I spent a sunny Canada Day afternoon at the Halifax Commons. I went with my family to watch the SkyHawks, the Canadian Armed Forces Parachute Team. After the SkyHawks finished their jumps, we headed to the end of a a really long line so that my son could take a turn on a giant inflatable slide. Instead of dwelling on the length of the wait, we decided to focus on some fun estimation questions. How many people do you think are in this line? My son says he thinks it's more than 100 and I agree. How long will it take to get to the front of the line? I feel like we're in for a long wait. My initial estimate is at least 30 minutes. (Note: in order to answer this last question, I took a look at my watch to check the time... 12:06 pm).
Have we gotten any closer? It's 12:27 now (21 minutes in line) and it still feels like we've got a long way to go. There appears to be a strong correlation between the age of a child and the likelihood that they will have second thoughts at the top of the slide. This slows the line down dramatically as parents try to coax and cajole their child to make the leap. How many people in this line are kids waiting to slide and how many are parents/guardians? What is the average age of the kids going down the slide?
It's 12:40 now and we've been in line for over a half an hour. How many steps do you estimate their are to the top of the slide? I estimate that we're about half the distance to the slide from where we started. I realize that my initial estimate for how long we will be waiting was way off. At this point, I notice a group of upper elementary age students in front of us playing a hand clapping game called Concentration. After a bit, they shift to playing Chopsticks. This is a game I really like and I've used to introduce students to modular arithmetic so I watched their game to check out their strategy. It kept me entertained for a bit.
So close now I can taste it. It is 1:10 and we've been in line for over an hour. How tall do you estimate that slide is? I'd say it is about as tall as my house (a two story foursquare) which has a height of about 26 ft. (Note that the internet says this inflatable structure, called the 'Freestyle Combo', is 30 ft tall so my estimate seems pretty close).
We finally make it! It is 1:17 pm and we stood in line for 71 minutes. My son seems to think that this was a reasonable investment for such an awesome slide but I have my doubts. At least we got to do a lot of estimation while we waited in line. We definitely won't be heading to the back of the line for a second slide.
Swimming in the hotel pool I saw these depth markers. As a math teacher, they made me a bit uneasy. What do you notice in the photos below? What do you wonder?
Just look at those significant digits. They look so precise. I first thought... going from the shallow end to the deep end, it gets 1 foot / 0.2 metres deeper. That must mean that 1 ft = 0.2 m right? But then if 1 ft is 0.2 m then shouldn't 3 ft in the shallow end be 0.6 m instead of 1.0 m?
So I looked at it another way... 1 m is the same as 3 ft... So 1 ft must be about 0.33 m. Which would make 4 ft equal to about 1.33 m not the 1.2 m as shown. But I know that a meter stick is shorter than a yard stick so this is just an approximation. No problem, they just rounded off both values.
Then I had a moment of doubt... in the shallow end the values are in a ratio of 1/3 and in the deep end the values are in a ratio of 4/12 which is also 1/3 so shouldn't this work out? Then I realized the errors and misconceptions in this line of thinking.
Other Linear Conversions
Today, as I was driving around, I looked more closely at the clearance signs that I passed under. There doesn't seem to be much consistency in the units used or precision. Do people with tall cars know the height of their car? I just know that I'm about 6 ft tall and my car is shorter than I am. Of course you can always just wing it. If you clear the warning bar, you're good to go. Anyway, I know for sure that my car is less than 11 foot 8 if I ever end up in North Carolina.
I saw this relatively accurate sign at a parking garage today so I took a photo. 6'0" is approximately 1.8288 metres so these values are the closest I've seen.
Nova Scotia Mathematics Curriculum Outcomes
Mathematics 10 M02 - Students will be expected to apply proportional reasoning to problems that involve conversions between SI and imperial units of measure.
Mathematics at Work 10 M01 - Students will be expected to demonstrate an understanding of the International System of Units (SI) by describing the relationships of the units for length, area, volume, capacity, mass, and temperature and applying strategies to convert SI units to imperial units.
Mathematics Essentials 10 D1 - Demonstrate a working knowledge of the metric system and imperial system.