MTBoS Mission #3 Collaboration

This week we were asked to blog about one of a list of MTBoS collaborative pages. I've chosen Estimation 180, a cool collection of short estimation exercises by Andrew Stadel to help students build number sense. The mission was to share some ideas on how to incorporate estimation into my (so far imaginary) classroom, but I wanted to do a little more. Since this mission was about collaboration in the MTBoS, I wanted to create something that others could share if they so wished (but give credit where it's due).

While scanning through some of the Estimation 180 archives, I noticed that I would have to modify quite a few for my (imaginary) classroom, since I'm in Australia. Asking my students off the bat to estimate the distance from NYC to San Diego (or similar) seems a bit mean. We also have a different currency, so I'm not too keen to use the nickels, pennies and dimes estimations either. I'd prefer to change it and have students estimate how many 5, 10, 20, 50 cent pieces, but then I'd need a bunch of coins and a camera, neither of which I have. With this in mind, I decided to make one of my own Estimation 180 questions, from an Aussie perspective.

Sydney NSW to Perth WA

Sydney NSW to Perth WA by air

Sydney NSW to Perth WA by car

The 'by air' image was from Google maps edited by me to add the red line. I then found out using this website that the correct answer was 3,293km. The units of measurement from miles to kilometres is another change I'd need to make for Aussie students.

The 'by road' image is a bit different to the general Estimation 180 questions, but I thought it might be interesting to see students estimates of how much extra distance the winding road makes to the distance between two cities. The image was straight from Google maps which also told me that the distance by road was 3,935km and should take 40 hours by car.

One thing I'd love for students to ask is "Why is the red line curved?" Or upon seeing one of the US examples, "Why is the red line curved the other way?"

I'd like to get the chance to mention, as a tangent, that the curvature of the earth actually has implications for stuff in 'real life'. For example, most Aussies know that driving across the Nullabor from Sydney to Perth is long and straight and flat (and some say boring), check it out and decide for yourself. Yet in the 1960's when the trans-Nullabor microwave communications link was being built between Adelaide and Perth, one thing that influenced the distance between the towers was, if I remember my physics lecturers correctly, the curvature of the earth (aha, so flat isn't always flat) since microwaves travel linearly, whereas radio waves are reflected by the ionosphere and follow the earth's curvature.

However, I have one little issue with this estimation exercise. I have some answers, given to me with no uncertainties. If one student guessed 3,290km and and another guessed 3,295km it would be unfair to say that the latter was closer than the former. It also depends where the measurements were taken. I'd like to demonstrate correct practice/convention to students when dealing with measurements. Considering this, I'd probably give the answer as 3,300 ± 50km by air and 3,900 ± 100km by road. I simply couldn't sleep at night if I just gave my students the answer with no uncertainties.

Big thank you to Andrew Stadel for his Estimation 180 exercises and website, to Google for their maps and road measurements and to Daft Logic for their 'by air' measurements.