How I would explain Calculus to a 6th grader

[Goldhedge]

How I would explain Calculus to a 6th grader​

21m

 

[Goldhedge]

I struggled with math. Calculus ate my lunch. Moving around a lot as a kid didn't help with a solid understanding of maths.

I'm checking out this guy's channel to see if he can 'splain it to me. You're never to old to learn!

 

[CiscoKid]

I am always amused by people who say that nobody needs calculus to function in today's world. I am retired from the world of engineering and am now just a dumb dirt farmer. Yet, I am always amazed at how higher math can be used to so something as simple as farming. Take the following example. Whether it be maximizing area or minimizing cost, if you can turn it into an equation, you can use calculus to help solve the problem.

garden fence (optimization problem)

Optimization problem & solution: “Sam wants to build a garden fence to protect a rectangular … area. What dimensions minimize his cost?” See our free soln.

www.matheno.com

 

[Goldhedge]

My 'problem' with the maths is they never equate learning it to real world situations.

Calculate the slope of a curve. Why? What the hell do I care about some lines on a dry sheet of paper?

Yeah, I can figure out the area of a square, circle, triangle, but what does it matter to me what the area of some abstract shape is?

What they really need to do is equate to real life examples that would stimulate the imagination.

Something like "We're going to figure out how to fire off a rocket to the Moon. How will we be able to hit the Moon? The trajectory of the flight path?"

Then proceed to parse that bigger problem down to something piecemeal. THAT would generate curiosity as to who, what, where, when, how.

They could spend a whole semester on that 'problem' alone! Think of all the math that would entail with real life examples...!

 

[CiscoKid]

My 'problem' with the maths is they never equate learning it to real world situations.

Calculate the slope of a curve. Why? What the hell do I care about some lines on a dry sheet of paper?

Yeah, I can figure out the area of a square, circle, triangle, but what does it matter to me what the area of some abstract shape is?

What they really need to do is equate to real life examples that would stimulate the imagination.

Something like "We're going to figure out how to fire off a rocket to the Moon. How will we be able to hit the Moon? The trajectory of the flight path?"

Then proceed to parse that bigger problem down to something piecemeal. THAT would generate curiosity as to who, what, where, when, how.

They could spend a whole semester on that 'problem' alone! Think of all the math that would entail with real life examples...!

And yet the garden fence illustration in post 3 gives a very good example of a very real-world situation. I am amazed at just how much Trigonometry I still use today. Owning a farm, I occasionally have to build things. Trig helps me figure out what angles to cut on the end of rafters. Also helps me to keep the building square as I am laying out the framing. Just no end to its uses.

To this day, I still remember what my 10th grade trig teacher taught me. She was a cute thing with an amazing body and liked to wear short skirts. I know that she always had my full attention. She taught me about the great Indian chief, SOH-CAH-TOA. Sine is opposite over hypotenuse. Cosine is adjacent over hypotenuse. And tangent is opposite over adjacent. I still use that to select the correct function to this day. Bless her sexy little heart.

 

[foolsgold]

Check out the (FREE) Kahn Academy before subscribing to https://tcmathacademy.com/

whoops linky - https://www.khanacademy.org/

 

[arminius]

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[Goldhedge]

And yet the garden fence illustration in post 3 gives a very good example of a very real-world situation. I am amazed at just how much Trigonometry I still use today. Owning a farm, I occasionally have to build things. Trig helps me figure out what angles to cut on the end of rafters. Also helps me to keep the building square as I am laying out the framing. Just no end to its uses.

Yeah, agree, but that's not how I learned it. It was static. Formulas on formulas with no relation to real world projects.

 

[Newmisty]

My 'problem' with the maths is they never equate learning it to real world situations.

Calculate the slope of a curve. Why? What the hell do I care about some lines on a dry sheet of paper?

Yeah, I can figure out the area of a square, circle, triangle, but what does it matter to me what the area of some abstract shape is?

What they really need to do is equate to real life examples that would stimulate the imagination.

Something like "We're going to figure out how to fire off a rocket to the Moon. How will we be able to hit the Moon? The trajectory of the flight path?"

Then proceed to parse that bigger problem down to something piecemeal. THAT would generate curiosity as to who, what, where, when, how.

They could spend a whole semester on that 'problem' alone! Think of all the math that would entail with real life examples...!

^And this from a guy that builds precision instruments from scratch!

 

[Goldhedge]

^And this from a guy that builds precision instruments from scratch!

that's funny... however, it can be calculated... I'm merely copying what giants did before me.

In fact here is what Strad did with a compass and a ruler:



Simple geometry. Violin family is in a 5:4 ratio - aka the Golden Mean.

The distance H to I gives you the length of the violin.
To draw the above, start out with a square.
Connect the corners with straight lines ("X")
Connect the centers with straight lines ("+")
With a compass on each corner scribe an arc from the mid point of each side (H, E, I, J - makes a 'star' shape?)

What that does is assure you have a perfect square with which to draw the outline of the instrument. If any of the arcs don't line up with the + lines it's not square.


Once you have a square, you can then draw the rest of the outline.

I did this probably 10 years ago? It looks like art.

 

[Newmisty]

that's funny... however, it can be calculated... I'm merely copying what giants did before me.

In fact here is what Strad did with a compass and a ruler:

View attachment 5481

Simple geometry. Violin family is in a 5:4 ratio - aka the Golden Mean.

The distance H to I gives you the length of the violin.
To draw the above, start out with a square.
Connect the corners with straight lines ("X")
Connect the centers with straight lines ("+")
With a compass on each corner scribe an arc from the mid point of each side (H, E, I, J - makes a 'star' shape?)

What that does is assure you have a perfect square with which to draw the outline of the instrument. If any of the arcs don't line up with the + lines it's not square.


Once you have a square, you can then draw the rest of the outline.

I did this probably 10 years ago? It looks like art.

It's beautiful.
That is exactly maths equating to real world scenarios.

 

[Viking]

And yet the garden fence illustration in post 3 gives a very good example of a very real-world situation. I am amazed at just how much Trigonometry I still use today. Owning a farm, I occasionally have to build things. Trig helps me figure out what angles to cut on the end of rafters. Also helps me to keep the building square as I am laying out the framing. Just no end to its uses.

To this day, I still remember what my 10th grade trig teacher taught me. She was a cute thing with an amazing body and liked to wear short skirts. I know that she always had my full attention. She taught me about the great Indian chief, SOH-CAH-TOA. Sine is opposite over hypotenuse. Cosine is adjacent over hypotenuse. And tangent is opposite over adjacent. I still use that to select the correct function to this day. Bless her sexy little heart.

View attachment 5471

View attachment 5472

Trigonometry Calculator. Simple way to find sin, cos, tan, cot

Our trigonometry calculator can support you in finding the values of the trigonometric functions or solving the right triangle.

www.omnicalculator.com

 

[Libertas]

I am always amused by people who say that nobody needs calculus to function in today's world. I am retired from the world of engineering and am now just a dumb dirt farmer. Yet, I am always amazed at how higher math can be used to so something as simple as farming. Take the following example. Whether it be maximizing area or minimizing cost, if you can turn it into an equation, you can use calculus to help solve the problem.

garden fence (optimization problem)

Optimization problem & solution: “Sam wants to build a garden fence to protect a rectangular … area. What dimensions minimize his cost?” See our free soln.

www.matheno.com

Funny you should mention that. My Dr friend and I talk about how except for calculating medication doses we never use any of that math. However with medication those zeros and decimal points are crucial. They can kill you. But that is basic math.

 

[Libertas]

Have any of you parents or grandparents had the pleasure of trying to help your children with core math.? My granddaughter was with me on and off for a year of e-school core math during the plandemic. I have never seen anything like it. Instead of teaching them multiplication they counted tiny boxes. It is the most screwed up thing I have ever seen.

 

[Goldhedge]

Have any of you parents or grandparents had the pleasure of trying to help your children with core math.? My granddaughter was with me on and off for a year of e-school core math during the plandemic. I have never seen anything like it. Instead of teaching them multiplication they counted tiny boxes. It is the most screwed up thing I have ever seen.

That is Common Core math. Total nonsense.

You want to go to the store across the street to buy a candy bar, but first we have to hobble your legs and send you across town to get there.

 

[CiscoKid]

Have any of you parents or grandparents had the pleasure of trying to help your children with core math.? My granddaughter was with me on and off for a year of e-school core math during the plandemic. I have never seen anything like it. Instead of teaching them multiplication they counted tiny boxes. It is the most screwed up thing I have ever seen.

I used to tutor high school seniors who were in danger of not graduating. I quit when I realized that I was trying to teach them 9th grade math and that the school systems had failed them.

Common Core is the worst thing ever foisted on children. It was designed to level the playing field which basically means find the dumbest kid in the class and teach everyone to that level. It only gets the children so far and absolutely will not prepare them for higher level math classes. The people pushing this crap literally wish to create entire generations of Americans incapable of doing higher level math and, therefore, most science as well. You cannot do Thermal Dynamics, Statics and Strengths of Materials, Fluid Dynamics, or any advanced Physics classes without a strong math background. Leftists know this and they simply do not care. Private schools or home schooling is the only choice going forward if you wish your child a good education.

 

[Goldhedge]

Common core hides behind the theory that not everyone learns in the same way.

Some people are visual learners. Others are auditory. This is true, but you don't need to teach everyone to count boxes as the only solution which is what CC does. It's the same old "I want to see your work, how you got there, not just the answer... (to make sure you're learning the CC method...)."

I remember subbing in a 6th grade class. 2 of the kids were smart, the other 12 were interested in playing in the pillow fort in back of the room. I showed the 2 how to do long division. They never saw it before. They grasped the concept and how easily one could calculate a solution without boxes and unnecessary routes of addition to get there.

I didn't last as a sub for very long.

 

[CiscoKid]

Common core hides behind the theory that not everyone learns in the same way.

Some people are visual learners. Others are auditory. This is true, but you don't need to teach everyone to count boxes as the only solution which is what CC does. It's the same old "I want to see your work, how you got there, not just the answer... (to make sure you're learning the CC method...)."

I remember subbing in a 6th grade class. 2 of the kids were smart, the other 12 were interested in playing in the pillow fort in back of the room. I showed the 2 how to do long division. They never saw it before. They grasped the concept and how easily one could calculate a solution without boxes and unnecessary routes of addition to get there.

I didn't last as a sub for very long.

I play golf with a fellow who has a Masters degree in Biology. Last year he volunteered to be a sub in his local school system when they "suddenly" lost their Biology teacher. He is older than I am, owns a farm, is fairly practical, and not likely to stand any nonsense. Halfway through the semester, he's called to the principal's office because he has given several students failing grades on exams. He told the principal that he failed them because they failed the exam and also failed to turn in any of the required assignments on time. The principal told him that he could not fail any student no matter how little work they turned in or how badly they did on exams. My friend, Jeff, quit on the spot. Just got his things and walked out.

This is the state of our "education" system these days. The inmates are running the asylum. There quite literally is not enough money to make me be a teacher in this climate.

 

[Libertas]

I used to tutor high school seniors who were in danger of not graduating. I quit when I realized that I was trying to teach them 9th grade math and that the school systems had failed them.

Common Core is the worst thing ever foisted on children. It was designed to level the playing field which basically means find the dumbest kid in the class and teach everyone to that level. It only gets the children so far and absolutely will not prepare them for higher level math classes. The people pushing this crap literally wish to create entire generations of Americans incapable of doing higher level math and, therefore, most science as well. You cannot do Thermal Dynamics, Statics and Strengths of Materials, Fluid Dynamics, or any advanced Physics classes without a strong math background. Leftists know this and they simply do not care. Private schools or home schooling is the only choice going forward if you wish your child a good education.

Amen!