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I doubt even the "real world" ones will make much impression or sense for kids of that age. The farmer Bob example for the fence? Definitely real world. Minimu

I doubt even the "real world" ones will make much impression or sense for kids of that age. The farmer Bob example for the fence? Definitely real world. Minimum wage farm hand might not be the one doing the buying of fencing material that's true. 10 year old kid learning that math? Doesn't care one bit about fences, even if you make it "Your family has a dog and you just moved into a new house and there's no fence ..." Minimum wage framing crew helper. You forgot your square. Definitely real world. But you got your tape measure. Use Pythagoras to figure out if your wall is going to be square. Does the minimum wage framing guy care when he's an 11 year old kid? Nope! Figure out how high your school building is with math and without going to the roof and a loooong "tape measure"? That was cool! Especially since we actually went outside and did it. Also, and this isn't math but at least science related: gasoline fumes are flammable. Very. Real world. Minimum wage lawn mowing crew guy might want to remember. Loved the presentation our chemistry teacher did. Put some gasoline into a small can and tried to light it. Nothing happens. Had to pour it back out. Next step: let us calculate exactly how much gasoline we'd have to put in for the fumes to be ignitable. Then he did just that, lit it and man that was a nice explosion and flying can!

wink 5y ago
To be a little nitpicky about these sort of problem "How many fence posts should Farmer Bob buy"? "Farmer Bob would be pretty stupid to drive an hour to the hardware store to buy 20 fence posts and 100m of fence, because Murphy's Law and what if one happens to be bad or someone cuts wrong and we're short 2m of fence?" yes, growing up on construction sites does that to you, the problem is badly phrased if it's saying "should buy" instead of "needs" ;)
- geoduck14 5y ago
  >To be a little nitpicky about these sort of problem "How many fence posts should Farmer Bob buy"? Sure. I'll go with that. Farmer Bob can be a part of a case study. We start off simple. Farmer Bob buys exactly as many posts as necessary... then he discovers shrinkage/theft/errors The next project, Farmer Bob uses linear extrapolation from the past 5 projects and buys X% extra posts... but then he discovers new employees break things The next project Farmer Bob uses Linear Regression, broken down into key variables (like # of new employees) I think we can get a book deal with this!
  - tharkun__ 5y ago
    Hehe I like this! I don't even think it's nitpicky from your parent at all and your "progression" I would say works very well with how school should work. At first kids just learn how many fence posts and fence is gonna be there in the end. I.e. how much do you need to buy ignoring some things. Like you ignore friction losses in physics in many cases, especially in school. Extrapolation and Linear regression you learn later on to solve the same problem better! Love it! Similar thing happens (or at least happened when I was in school) in chemistry. We learned the Bohr model and it could be used to explain everything that we learned about. Towards the end we learned that there are some things that model can't explain and that there's another model that can explain those things and so we learned about that and also that it's totally fine to keep using the Bohr model for a lot of stuff as it's easier. Like ignoring friction losses in physics and the predictions/calculations come close enough in most cases that it's still useful but much easier to comprehend and calculate than if you had to take them into account.
ThePadawan 5y ago
> Figure out how high your school building is with math and without going to the roof and a loooong "tape measure"? That was cool! Especially since we actually went outside and did it. I still find it incredible that "Daumensprung" [0] is apparently not an international concept (I learned about this in Math class growing up in Germany). Unfortunately the Wikipedia link is only in German, but the short explanation is: * Extend your arm horizontally in front of you, and raise the thumb to point upwards. * Close one eye and align the thumb with the edge of a large object in the distance (e.g. a building). * Close the other eye and note how far the thumb virtually "jumped" across the large object. Now, knowing the distance between your eyes and the length of your arm, you can use trigonometry to either * knowing the distance to the object, deduce the width of it or * knowing the width of the object (e.g. using a window, doorframe, or car as a reference size), deduce the distance to it. [0] https://de.wikipedia.org/wiki/Daumensprung https://de.wikipedia.org/wiki/Daumensprung

wink 5y ago

To be a little nitpicky about these sort of problem "How many fence posts should Farmer Bob buy"? "Farmer Bob would be pretty stupid to drive an hour to the hardware store to buy 20 fence posts and 100m of fence, because Murphy's Law and what if one happens to be bad or someone cuts wrong and we're short 2m of fence?" yes, growing up on construction sites does that to you, the problem is badly phrased if it's saying "should buy" instead of "needs" ;)

geoduck14 5y ago
>To be a little nitpicky about these sort of problem "How many fence posts should Farmer Bob buy"? Sure. I'll go with that. Farmer Bob can be a part of a case study. We start off simple. Farmer Bob buys exactly as many posts as necessary... then he discovers shrinkage/theft/errors The next project, Farmer Bob uses linear extrapolation from the past 5 projects and buys X% extra posts... but then he discovers new employees break things The next project Farmer Bob uses Linear Regression, broken down into key variables (like # of new employees) I think we can get a book deal with this!
- tharkun__ 5y ago
  Hehe I like this! I don't even think it's nitpicky from your parent at all and your "progression" I would say works very well with how school should work. At first kids just learn how many fence posts and fence is gonna be there in the end. I.e. how much do you need to buy ignoring some things. Like you ignore friction losses in physics in many cases, especially in school. Extrapolation and Linear regression you learn later on to solve the same problem better! Love it! Similar thing happens (or at least happened when I was in school) in chemistry. We learned the Bohr model and it could be used to explain everything that we learned about. Towards the end we learned that there are some things that model can't explain and that there's another model that can explain those things and so we learned about that and also that it's totally fine to keep using the Bohr model for a lot of stuff as it's easier. Like ignoring friction losses in physics and the predictions/calculations come close enough in most cases that it's still useful but much easier to comprehend and calculate than if you had to take them into account.

ThePadawan 5y ago

> Figure out how high your school building is with math and without going to the roof and a loooong "tape measure"? That was cool! Especially since we actually went outside and did it. I still find it incredible that "Daumensprung" [0] is apparently not an international concept (I learned about this in Math class growing up in Germany). Unfortunately the Wikipedia link is only in German, but the short explanation is: * Extend your arm horizontally in front of you, and raise the thumb to point upwards. * Close one eye and align the thumb with the edge of a large object in the distance (e.g. a building). * Close the other eye and note how far the thumb virtually "jumped" across the large object. Now, knowing the distance between your eyes and the length of your arm, you can use trigonometry to either * knowing the distance to the object, deduce the width of it or * knowing the width of the object (e.g. using a window, doorframe, or car as a reference size), deduce the distance to it. [0] https://de.wikipedia.org/wiki/Daumensprung https://de.wikipedia.org/wiki/Daumensprung