"New math" proposal of the day: Students should be introduced to vectors earlier, no later than 9th grade. Stop teaching distance and slope formulas written the way they are in pic related. Instead, teach them to first find the vector V between the two points. The distance is [math]\sqrt{V_x^2 + V_y^2}[/math] and the slope is [math]\frac{V_y}{V_x}[/math]. Explaining that the components are the "change in x" and the "change in y" is good but not enough, because students need practice to remember things, and what the students practice is using the formula, not your explanation of the formula.Other elementary problems students should do early on with vectors:>given a starting point, velocity vector, and time, find the ending point>repeatedly add a vector to a point to rapidly plot a line on graph paper>perform rotations by multiples of [math]90^\circ[/math] about any point, not just the origin
ok poindexter i now know to use components for slope and distance so where are those vector components for midpoint????
>>17022000Midpoint formula is fine as it is. But you can use vectors to derive it, and have students use the same argument to work out formulas for trisection points etc.
>>17022015>it's left as an exercise to the readerfuck fagmaticians
Nigga how tf dat shit gonna help me pay my taxes or budget my EBT usage and child support payments??
>>17022015>>17022022miggers are insufferable and lazy>>17022069personal finance isnt taught for a reason
>>17022015>>17022097You do have to take off the training wheels and challenge yourself if you want to learn and improve. If you don't do this you'll be in goypen forever.
>>17022022[math]M((a,b), (c,d))[/math][math]= (a,b) + \frac12 ( (c,d) - (a,b) )[/math][math]= (a,b) + \frac12 \langle c-a, d-b \rangle[/math][math]= (a + \frac12 (c-a), b + \frac12 (d-b))[/math][math]= (\frac{a+c}{2}, \frac{b+d}{2})[/math]
>>17022000>where are those vector components for midpoint????(v1+v2)/2?
>>17023443nice
Another thing that should be taught earlier is the unit circle and how to use it to find components of a vector given its length and direction. It's too useful to put off. Then [math]\sin\theta = \frac{\rm opp}{\rm hyp}[/math], [math]\cos\theta = \frac{\rm adj}{\rm hyp}[/math], and [math]\tan\theta = \frac{\rm opp}{\rm adj}[/math] would be proven as theorems. In a way, this is a return to tradition; the sine, cosine, and tangent functions were defined in terms of circles long before they were thought of as coming from right triangles.
what the fuck is this tranny talking about? They are already introduced to linear vector spaces.
>>17021993vectorscopearraythese 3 are key to human intelligence, and should be drill throughout the life, in all classroom, in all education from kinder garden to phd. every class must go over these. especially in kindergarden/elementary/middle/high schools. every single day, every single context.
>>17025597In the US, vectors are often introduced in "precalculus", which generally is taken by non-accelerated students (some of the brighter students take math classes 1-2 grades ahead) in the 12th grade and not a graduation requirement. It has become fashionable to briefly introduce vectors in geometry (10th grade for non-accelerated students), but only for the very limited purpose of describing translations, and even this is not universal. If your country does things better, then that's great. Please do some impressive space feat so the rest of my countrymen can be jealous of you.
>>17025535A way to put it to minimize the amount students have to relearn:Any vector [math]\langle \Delta x, \Delta y \rangle[/math] with nonzero length r can be scaled by [math]\frac{1}{r}[/math] to get the unit vector [math]\left\langle \frac{\Delta x}{r}, \frac{\Delta y}{r} \right\rangle[/math]. The value of this unit vector only depends on its direction [math]\theta[/math], which is measured counterclockwise from the positive x-direction. We call the functions that calculate the components of the unit vector cosine and sine:[math]\frac{\Delta x}{r} = \cos(\theta), \frac{\Delta y}{r} = \sin(\theta)[/math]And the function that calculates the slope of the vector is called the tangent:[math]\frac{\Delta y}{\Delta x} = \tan(\theta)[/math]
