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.