Posts on the "Why math?" series
- Why are we learning math?
- How math is an efficient language
- Math language is entirely logical - The "rules" make sense
- Math equations are not magic! - You can see for yourself
_____________________________________________
With what we just saw above, you can reason for yourself:
Teachers might give you these 4 different "rules" to remember and use when you can just reason it through yourself!
++1 = 1 is like: Do do blink, = Do Blink
- - 1 = 1 is like: Don't NOT blink, = Do Blink
- +1 = -1 is like: Don't do blink, = Don't blink
+ -1 = -1 is like: Do NOT blink, = Don't blink
Another good example of this is the...
Think of the area of anything as just this:
Click to jump to a section on this post:
Why it's just a logical language
If I tell you: Do take your shoe off. - You will take off your shoe.
What about: Do NOT take your shoe off - It is the same as saying Do keep your shoe on.
Do Not = Negative, (-ve)
Do = Positive, (+ve)
Off = Negative, (-ve)
Do = Positive, (+ve)
Off = Negative, (-ve)
On = Positive, (+ve)
So,
Do not take your shoe off → Do (-ve) take your shoe (-ve)
= Do keep your shoe on → (+ve) keep your shoe (+ve)
= Do keep your shoe on → (+ve) keep your shoe (+ve)
A negative on a negative have the same result as a positive! By saying "Don't NOT blink" I'm telling you to just "blink", as you're NOT going to: Not blink. = You're going to blink.
Just like in English language we just say "Do Blink" instead of "Don't not blink", in math:
-(-1) = +1. which is written as just 1.
Or you can think of this way...
If you take AWAY a negative, you're moving that number one step AWAY from the negative, which is towards what? The positive side! So taking away a negative [10 - (-1) ] = [10 + 1]
This is only logical, right? So should be all of math. I don't teach my students to remember any rules but to just understand these things logically.
Teachers might give you these 4 different "rules" to remember and use when you can just reason it through yourself!
++1 = 1 is like: Do do blink, = Do Blink
- - 1 = 1 is like: Don't NOT blink, = Do Blink
- +1 = -1 is like: Don't do blink, = Don't blink
+ -1 = -1 is like: Do NOT blink, = Don't blink
Another good example of this is the...
Area of shapes
If you understand what the CONCEPT of the area means in the first place, you can reason through getting the area of something instead of remembering so many different rules for areas.Think of the area of anything as just this:
The rectangle is 3 by 4. To find it's area means to just think of each 1 by 1 little square as having an area of "1"
So 3 of them by 4 = 3 * 4 = 12 of them.
You can also look at these balls. To get the area is to get the amount of balls in there!
Therefore, if you cut that rectangle in half, the area is still 3*4, but you divided it into 2.
What's a right-angled triangle? It's literally just a rectangle cut in half:
Therefore, the area of the triangle is: Base * height = bh, but cut in half:
1/2 bh
We can deduce the area of every shape with this one understanding of what area even is. It's one idea / concept that can derive many different rules / facts/ formulas.
What I always do in math is to understand this one fundamental logic then apply it, instead of remembering many different things and getting confused with using them all separately.
