Guess And Check Discovery: discovering the math within

Guess, Check, Discover

Practice fundamentals.  Practice again and realize there's some kind of higher level connection.  Practice again and discover a "shortcut."  Practice again and move to a higher level of thinking.  Discover higher order thinking skills such as Algebra and realize that now you know your math facts!

For a simple example, spz. you want to solve for x in 3x + 2 = 17.  Obviously, because this is simple you know the answer is x = 5.  By guess and check one would guess a value, then check to see if it works:

3(guess) + 2 =?=17

To get 17, one might try guessing x = 9 to start:

3(    9    ) + 2   =  29.  Checking, we see 29 higher than 17 so guess lower than 9.  Try 3.

3(    3    ) + 2   =  11.  Checking, we see11 is to  low  so guess more than 3.  Try 5.

3(    5    ) + 2   =  17.  Discover the answer is x = 5.

There is more to discover. There is a pattern.  The 3, (), +, 2 and = are all repeated, we never know what 3 is going to be multiplied by.  When we don't know what a number is going to be, we use a "?" or a variable such as "x."

Now we may write:  

3(    ?    ) + 2   =  17,  or

3(    x    ) + 2   =  17.  After all the guessing we have done, something tells us there is an easier way and we ultimately discover that we could have subtracted 2 and divided by 3.

We subtract 2 from 17 on the left (which is in the form of 3x+2) and subtract 2 from 17 on the right.  Both sides of the equal sign now equal 15:  3x = 15.  Finally we realize that 3x can only be 15 if x = 5.

So that's just one example of using guess and check to give the idea.  There are many applications of guess and check discovery that help develop the mindset. 

Ok, big deal - now what?

Well, now we practice algebra.  Practice algebra again and realize there is some kind of higher level connection.  Practice again and discover a "shortcut."  Practice again and move to a higher level of thinking.  Discover higher order thinking skills such as calculus and realize that now you know algebra!

The really big deal is calculus.  It is reveals worlds beyond imagination.  Yet these creations are indeed connected to our application of simple math to our visual, audible, and physical sensory experiences.

In algebra we learn the slope of a straight line.  In calculus we learn the slope of a curve. 

This is how you learn with Guess And Check Discovery.  To download and purchase go to the PayPal page.

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