Here you will see students as young as 4 and 5 years old doing algebra and "advanced" math, without ever knowing it's supposed to be hard.
You are invited to learn how to use this method...

Friday, February 4, 2011

Colby Completing The Square

This is a two part screencast on completing the square. This is where we are headed:

This is how we get there:

More on completing the square and making it easy by using the simple concept of degree of difficulty. Next after this is mastered we can head on to the quadratic or take a side trip into graphing them and talking about vertex form...and h and k.
But this won't be hard. And neither is this:

As I have said these are uploaded to both screencastomatic and my YouTube channel so if you can't see the screencast here look for it on YouTube.

"Colby Completes The Square Part 1"

"Colby Completes The Square Part 2"

You will find that giving them this formula isn't entirely helpful:

(x + a)2 = x2 + 2ax + a2 nor does it deepen understanding. Further when combined with this:

ax2 + bx + c = 0

with the instruction that completing the square just means replacing c with

(bx/2)2 resulting in

ax2 + bx + (bx/2)2 = -c

might actually cause some confusion as well as fear and trepidation because they don't know what the symbols mean.

Students using base ten blocks and manipulatives know what that means because they can SEE it and rather than giving them rules and process and formula to follow they get an experiential understanding of what the formula means BEFORE they ever see the formula. THEN when they do see the formula it makes sense.

“To state a theorem and then to show examples of it is literally to teach backwards.” ~E. Kim Nebeuts

When I say they don't need the symbols I mean they can hear the problems and do them in their heads...if they have paper and pencil it's even easier.

Go here to see completing the square at Crewton Ramone's House of Math. My students SEE these concepts and more right from the very start. It teaches them how to count, how to multiply and also as a by-product algebra and factoring. Math is a language teach it all at once...

The screencast mentioned in the second vid is not yet up on the password protected will cover the problems you see in green above in intricate detail...with blocks but mostly with drawing and lastly symbols. You need LOTS of practice before you move on to the quadratic formula.

“The point is to develop the childlike inclination for play and the childlike desire for recognition and to guide the child over to important fields for society. Such a school demands from the teacher that he be a kind of artist in his province.” ~Albert Einstein

“A teacher is one who makes himself progressively unnecessary.” ~Thomas Carruthers

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