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.
There are some really big doors around Halifax. The door on Irving Shipbuilding's Halifax Shipyard Assembly and Ultra Hall facility is big enough for large "mega-blocks" of ships under construction to pass through. The doors at IMP Aerospace's Hangar #9 at the Stanfield International airport is big enough for large aircraft to pass through. Which door do you think is the largest?
What Do You Mean by Largest?
The first thing you might want to do is settle on what you mean by "largest". Do you mean width, height, area, mass or some other measurement? Each of these doors might be the largest for a specific measurement. For example, the aircraft hangar door is made of metal and quite probably has more mass than the shipyard door which is constructed of a polyester fabric.
The shipyard door is really tall but the aircraft hangar door is really wide. Below are pictures of the two facilities from Google earth with the same scale so that you can compare the buildings that these doors are on.
Door Dimensions and Surface Area
So the shipyard door has the largest height and the largest area but the hangar door has the largest width and the largest mass. Would you call this a tie? How would you determine the winner?
More Big Doors
Do you know of other big doors around Halifax? Have you seen bigger doors in other parts of Nova Scotia or the rest of Canada? What is your definition of door?
Note of Thanks: I want to say thank you to the people at both Irving Shipyard and IMP Aerospace who were very helpful providing information for this post.
The sign reads "No Vehicles Over 3200 kg." I realized that I have no idea what the mass of my car is nor what type of vehicles would have masses greater than 3200 kg. I have personal referents for smaller masses such as 1 gram (such as a jellybean or a paperclip) and 1 kilogram (like a bag of sugar). I also know that my son weighs about 20 kg but I have no similar reference for 1000 kg. 1000 kg is also known as 1 megagram (Mg) and 1 metric ton (t). I know that a cubic metre of water has a mass of 1000 kg but that doesn't really seem to be helpful to me because I have no experience with an actual cubic metre of water.
This made me realize the importance of personal referents when teaching students about SI units of measurement. Students are introduced to grams and kilograms in Grade 3. The curriculum guides states that, "as with all measurement units, it is important that students have a personal referent for a gram and a kilogram. Students should recognize which mass unit (gram or kilogram) is appropriate for measuring the mass of a specific item." The curriculum guide also states that as they begin to estimate and measure masses using the gram (g) and kilogram (kg), they should develop a sense of what a kilogram feels like, "by lifting and holding a variety of objects that have a mass of 1 kg." One activity that the curriculum guide suggests is for students to make a kilogram mass of their own. "Provide students with materials such as sand, flour, sugar, and small cubes from base-ten materials to fill a container until it exactly balances with a 1 kg mass on a balance scale. Using this kilogram container they can now compare its mass to items in the classroom to help them find a personal referent for 1 kg."
Unfortunately, it is not feasible for me to fill a container with 3 200 000 jellybeans in order to compare its mass to a car ( ...but maybe you could use Skittles). I'm going to have to find my own reference for this mass. I found that a subcompact car, such as a Toyota Yaris hatchback has a curb weight of approximately 1000 kg. On the opposite end of the passenger vehicle size spectrum, a full size luxury SUV, such as a Cadillac Escalade, has a curb weight of about 2600 kg (I had to read up on the difference between curb weight and gross vehicle weight). Once students have an general sense of vehicle weight, it might be help solidify this understanding (and be a bit of fun) to challenge them to estimate the mass of a number of different vehicles... from motorcycles to truck cranes (similar to Dan Meyer's "How Old is Tiger Woods?" activity but with mass instead of age). I made a public Google Sides document with some photos and weights of various vehicles (still a work in progress).
Now, when I'm crossing the bridge, I'm constantly estimating the size of the different vehicles around me. I keep my distance from really big vehicles on the bridge... just in case.
Nova Scotia Mathematics Curriculum Outcomes
Mathematics 3 - M04 Students will be expected to demonstrate an understanding of measuring mass (g, kg) by: selecting and justifying referents for the units gram and kilogram (g, kg); modelling and describing the relationship between the units gram and kilogram (g, kg); estimating mass using referents; and measuring and recording mass.
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.