Hahahaha . . . . I busted 2 of my students last week for failing to label their work. With 18 students . . spending ann hour to grade papers each week . . . .well, you can do the math. . . . . . but, when you do. . . LABEL YOUR WORK!
IF was fun to give a mid-term in the famous Havermeyer Hall . . .
Had to go see my lad's math teacher last year, was whining because the boy wasn't doing the work the way the system said he should but the way I'd shown him, simple straightforward, clear, & he was getting marked down for it. I'd already told him about looking for the 3-4-5 relationship & that was what was creating the problem in class. When I told the teacher that it was something I used regularly & had daily practical use, he replied that perhaps I ought to be teaching the class then.
This doesn't inspire great confidence in your offspring's education I can tell you. They don't teach the practical useful part of math, but they spend ages learning how to multiply & divide negative fractions. I despair.
Funny grumpy, I first rattled through all the sine / cosine / tangent equations in my head for that triangle, decided I didn't want to be bothered getting out the calculator then had a little harder think, then remembered the a squared plus b squared equals c squared thing, rattled them off in my head and got the "5" answer, then thought to my self "Duh! It's a 3 4 5 triangle stupid!".
All in a few seconds mind you, but it's still funny how complicated a path I took to get to the simple and obvious solution.
Makes me look like an idiot when the problems are simple. But it pays off when the problems get hairy or when a proper derivation will yield a superior but non obvious answer to the problem.
Then I forget to show the units and loose 10% anyway.
If they don't want you to make the leap of the 3-4-5 triangle, then they shouldn't be using a 3-4-5 triangle. You would think that you would get a better grade for finding the answer in the easiest possible way, not the hardest. How do you show you're work when the answer is staring you right in the face? I guess we're training kids for a government job.
No, we're not training kids any more at all, we're just keeping them busy at school, the answer to everything is online so why bother any more than that.
Everyone who's ever laid out a string line for a foundation knows the 3-4-5 rule for establishing 90° angles. One guy I worked with could do subtractions amazingly fast (i.e. 84¼ minus 29¾ = 54½) until he showed me how he did it with a tape measure folded over. Pretty cool trick.
For those that haven’t seen it, you fold the end of your tape measure so that the hook lines up with 84¼” and then read any number along the tape below that. The number opposite the one you’ve chosen will be the difference. I don’t suggest letting your kid take a tape measure into class.
I'll bet the 3 4 5 trick was used in layout of the Pyramids.
I heard a story in my youth about a famous mathematician being given a busywork assignment as a kid to add up 1 through 100. He thought a moment then wrote down 5050 and got in trouble with the teacher. He explained that he visualized folding the string of numbers over and got 50 sets of 101 - 1+100, 2+99, etc.
Uranus isn't just gassy, it's also tilted completely sideways, such that instead of rotating like a spinning top, it rolls around the plane of the solar system more like a giant ball. Now astronomers think they know how this happened, and it means that Uranus has been pounded really, really hard not once, but twice.