So Long day at work. The 2nd Monday this week. Technical issues that have wrecked havoc on my productivity.
I get home late and have not had lunch so hangry. One kid sick wife is doing everything and I wish I could do a fraction of all she can do. The other daughter needs help with homework. Well it’s math right we use it everyday no problem. I look at the problem of X,Y coords and man I get excited. Go grab a pad my pocket scale and glasses. Start drawing the quadrants plotting to scale the X,Y values show her how to replace the X,Y for east and north. I am just as happy as a puppy with well you holder the point. Then daughter said dad that’s all great but I need to compute the slope of the line from these pairs. Yep there went my brain. I could not think of the formula for at least 30 minutes while I was eating and finally remembered the y=mx+b. Then I could not get it in my head how to explain it to her in the terminology she was being taught. My brain wanted rise to rune or percent slope . I was about to get on here and see if I could hire @mathteacher because my brain would just not function. Finally after a few glasses of sweet tea and such I was able to get back to the drawing board. Tell me I am not the only one that has had this happen. lol
Definitely incurred such dilemmas while assisting with homework. Their textbook approach to a problem was different from MY textbook approach to a problem.
Slope equal rise over run.
>Slope equal rise over run.
Except for earth grading. That always seems strange. Why shouldn't a graph, roof, and embankment use the same way of expressing it? Humans are weird.
Well y’all make me feel better about myself now. lol. I used the rise to run and also took her out to see the roof on house. She had helped me lay the shingles on a shed and so I said remember how I took the 4’ level as I was building the rafters and checking it every so often. She had helped with taping the rise to my 4’ level as I held it level. That’s was a couple years ago. But she remembered. Yes they teach how to do the math not the application or understanding as much. But once I wrapped my head around it I hopefully got her pointed in the right direction. I did feel like an idiot for a while last night though.
Well, thanks for the shout out. I work for free after working for almost nothing for 40 years.
To start from a somewhat advanced point of view, the slope of a line is the tangent of an angle. Remembering that is a good way to remember the formula.
In the picture below, AB is the line whose slope we want to find. In mathematics, that slope is the tangent of angle A. which is the length of BC divided by the length of AC. The length of BC is the difference between the y-coordinates of B and C, while the length of AC is the difference between the x-coordinates of A and C. There's a great teaching/reteaching moment here about the lengths of horizontal and vertical lines. Note that in surveying and ground-work, it's the slope of angle B that's used.
The slope of AB is (y at B - y at C)/(x at C- x at A), which is the tangent of angle A.
In early algebra, we teach the formula (y2 - y1)/(x2 - x1) and emphasize that it is "rise over run." Good teachers also introduce the term "rate of change" and, using methods of their choice, ask that if we go horizontally 8 units from A, how far up will we have to go to get to B?
I used to use the elevation difference between North Wilkesboro, NC and Boone, NC as the "rise" and the measured horizontal distance on a map (I know, I know!) as the "run," calculate the slope and ask why the road between the two cities had to be curvy.
The key thing now is to memorize the formula. It will be key to the slope-intercept form of an equation, y = mx + b which, in turn, will be the basis for the fundamentals of differential calculus.
Thank you. I will show this to my daughter tonight for sure. That y intercept of several x,y values was where my brain to the momentary dump lol. Rise to run of course is what is stuck in my brain. But also that rate of change. She did say she took in my miniature to scale drawings of several problems I made up to her teacher. Now I have been volunteered to meet him and give some of those real world app for him to use. For the upper grade level classes. Although once I was able to wrap my head around everything I did use the roof and slope between man hole structures from the difference in elevation etc. I made some copies of a few sections of profiles on from some storm plans to give her for extra practice.
It's great that you're supplying real-world problems. Math classes are starved for those.
