I'm marking my students last TMAs before their exam next week and I'm a bit swamped so I wanted to get this down and I'll be brief and this may not make any sense to anyone but me, sorry.
I've had so many students get questions wrong because they're messing up their conversions between km and mm and back. Now I'm lazy and I use my calculator to help me (thanks to a former A level student of mine for pointing out this feature). A scientific calculator has an ENG button for Engineering notation. In SM123 we use scientific notation so we might say 1.982 m where a carpenter would say 1982 mm. It turns out that engineering notation is pretty much the same as astronomical notation. In an astronomy paper you'd say 567 Mpc (567 megaparsecs) you wouldn't say 5.67 x 102 Mpc - you work (in astronomy) in powers of 103. So lots of kilo, Mega, etc.
Now the nice thing my Engineering A level student showed me was that you can have a random number and press the ENG button and it will move up and down in 103 steps. Very handy when you want to convert a measurement in km to a measurement in mm or visa versa.
Also, keeping my astronomer's head on, every time I see milli I think 10-3, kilo is 103, Mega is 106.
So if you have a measurement, that 1982 mm I mentioned before, I see 1982 x 10-3 m. If you type 1982 and then x10x and -3, you get 1.982, which is the value in metres.
Anyway, I used to use Vizualisers (or at least attempt to) at school so I think it's probably not a bad idea to show students some tricks to minimise the errors using techniques in real time in my next tutorial.
Visualizers and Calculators
I'm marking my students last TMAs before their exam next week and I'm a bit swamped so I wanted to get this down and I'll be brief and this may not make any sense to anyone but me, sorry.
I've had so many students get questions wrong because they're messing up their conversions between km and mm and back. Now I'm lazy and I use my calculator to help me (thanks to a former A level student of mine for pointing out this feature). A scientific calculator has an ENG button for Engineering notation. In SM123 we use scientific notation so we might say 1.982 m where a carpenter would say 1982 mm. It turns out that engineering notation is pretty much the same as astronomical notation. In an astronomy paper you'd say 567 Mpc (567 megaparsecs) you wouldn't say 5.67 x 102 Mpc - you work (in astronomy) in powers of 103. So lots of kilo, Mega, etc.
Now the nice thing my Engineering A level student showed me was that you can have a random number and press the ENG button and it will move up and down in 103 steps. Very handy when you want to convert a measurement in km to a measurement in mm or visa versa.
Also, keeping my astronomer's head on, every time I see milli I think 10-3, kilo is 103, Mega is 106.
So if you have a measurement, that 1982 mm I mentioned before, I see 1982 x 10-3 m. If you type 1982 and then x10x and -3, you get 1.982, which is the value in metres.
Anyway, I used to use Vizualisers (or at least attempt to) at school so I think it's probably not a bad idea to show students some tricks to minimise the errors using techniques in real time in my next tutorial.