Completing The Square Fun and EASY!

Completing the square for fun and profit watch this video at two times speed it takes you behind the pay wall.

Watch at 2x speed and the tour takes 8 minutes.

The basic concept is a square is equal to a square. The problem is you see all the symbols and you don't see any squares or recognize square numbers. In fact, when you do see the symbols, they may even cause consternation or fear.

But the concept is so simple little eight--year-olds can tell me what x is the same as.  Using our super duper math skills, we reduce difficult problems into child's play as you can SEE with just a little bit of conceptual mathematics suddenly this allegedly advanced algebra  became a simple game of what's under the cup...with one very obvious answer and one that takes just a little more work

There are some really fun videos on the other side of the paywall.

The symbols can be daunting to some students, especially girls who have had a bad experience with algebra.

This introductory page to completing the square shows you how to use your base ten blocks to make this algebra concept EASY to understand. On the other side you will see little boys and girls having fun figuring out what makes the squares the same...you can go there first or if you don't have a password here is more instruction. 

But there's nothing like watching me teach it so you can see the theory in practice and you can also see that, yes: it works. The young ones understand what's going on it's not just memorization, they can see it. When you can see it the symbols make sense. 

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Module III

"Algebra is nothing more than geometry, in words;
geometry is nothing more than algebra, in pictures".
~Sophie Germain

Part learning how to complete squares is learning how to square numbers that end in 5.

Gain a better understanding of completing the square and how to apply it all in one simple series of videos. This page will take you from the very basic to the "advanced" applications of vertex form and graphing.  Basic completing the square with positive numbers and expressions is easy but what about expressions with negative numbers or more than one x²? And how is it useful for graphing polynomials.

The next page shows you how with videos that show you theory in practice.  Watch this for a better idea of what you get although it is already outdated as you can see if you watched the first one up there.

Spoiler alert, i give you the blog post that's buried on the blog in this video so you could get a lot of information and understanding for FREE, but of course this page has quite a bit more on it than what you'll see on the blog.  If you liked that you get even more explanation and lessons on how to put it together for your students on the other side of the paywall. If you don't have a password there is more explanation for free here.

This page is now part of Module Three.  i charge $60.00 pr hour for lessons; these are videos of actual lessons with actual students: quite a bit more than an hour's worth...i used to sell this page all by itself but now you get this and a whole lot more in module three. 

i also have algebra courses for students and for teachers. i don't just teach you algebra, i teach you how to teach algebra. You will see why i call it allegedly advanced algebra. Because allegedly, advanced algebra is hard but once you can see it, it's simple.

x² + 4x + 4 = 49 Easy and fun. Learn how to teach it and have fun doing it.

As you can see, these concepts are readily accessible to even very young students. They certainly don't have to be in high school or their first year of college before being introduced to algebra concepts like completing the square or factoring polynomials. Once this concept is mastered, the quadratic equation will also become obvious. It's just a little more complicated but it's not hard: bigger is funner..

In fact you will se a very young student ask to do

5x² + 10x - 75 = 45 

The last one on this PDF.

We had FUN using no one get back to one... The last of the basic concepts.

The major problem with the way this concept is taught traditionally is you don't see any pictures when you look at all those symbols but what you're doing is making a square equal to a square one is an abstract square using a red x square, some blue x's and some units and the other is square made up of units...1,4,9,16, etc...

Your job is to discover what x is to make this statement true.

You can SEE many of these problems, and then do a bunch of them yourself when you get across the pay wall. You can also see McCrae doing problems like this on his page, McCrae eight. Specifically: lesson 39. 

Want to see behind the paywall? Here's a little more in depth video on how to use these pages to best effect. This video is already outdated because i have added even more stuff. 

Videos make it visually obvious that the basic concept is just building squares.basic, completing the square page

There is plenty of explanation and free video on this page basic completing the square page too. If you don't have a password, be sure to visit that link. 

Use your module three password and you're about to be astounded, especially if you've never seen math this way before.

ENTER

For $250.00 you can have a Mod III Pass. You get this page and many others.  Check out module three. Hours of detailed instruction await the curious learner.  Pay once, and you're in for life.  

If you haven't already, sign up to get AMAZING ADDENDS for free as an added bonus just for visiting the house of math. Don't forget the algebra is just along for the ride were using completing the square to teach counting, 45 at ends in 400 math facts for multiplication.

If you like that the addends book, you love my division book, and if you have young children you will like the Curious Counters' Compendium too. i am told this was a child's favorite book growing up and many have told me they got good use out of it.  Get ALL my books with the purchase of any password. The password you need for these paywalls is the Module III, Sitewide password. 

Bonus Video:

Use the five basic concepts to make algebra and completing the square easy. Here is a video where i comment on my own video.

If you haven't already seen it, this video should demystify the concepts for you. If you watch it on YouTube, be sure to give it a like.

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Do you see how Mortensen math turns all of this on its head?

"I was the happiest in English class, and algebra was where I cried."~Shelley Hennig

"When I was in fifth grade, there were many girls who were good at math, but when I was in junior high school, I was taking intermediate algebra and I looked around the class and realized I was the only girl". ~Judith Love Cohen

"I'm a visual thinker, really bad at algebra. There's others that are a pattern thinker. These are the music and math minds. They think in patterns instead of pictures. Then there's another type that's not a visual thinker at all, and they're the ones that memorize all of the sports statistics, all of the weather statistics". ~Temple Grandin

"As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection". ~Joseph-Louis Lagrange

"An ounce of algebra is worth a ton of verbal argument". ~John B. S. Haldane

"Algebra is generous; she often gives more than is asked of her". ~Jean le Rond d'Alembert