Square numbers you can see!

You can see, 1,4,9,16,25,36,49,64,81, & 100 all have something in common they're all square.

Child's play.

First, let's get some simple concepts down, then start using base 10 blocks to get actual numbers. And remember, all of this is just to make learning 400 multiplication facts and 45 addends fun and interesting instead of doing the same worksheets over and over again. Here we're going to deal with special numbers the pairs not to be confused with the two times table. 2x2. 3x3, 4x4... 

Base 10 blocks make algebra Childs Play. It's not hard when you can decode the symbols and see rectangles or squares which are just rectangles with equal sides. 

Building pyramids out of squares and practicing square numbers and being able to identify square numbers is the logical steppingstone to cubes but unlike every other system, we stay in to de because it's a rhythmic, not physics.  This makes second and third power, algebra easy because you can see it. It also makes 4th power algebra a breeze. On the next page, you'll see a lesson with a teenage girl where the difference of two cubes becomes visually obvious, and i even draw a picture of it for her.

Play with purpose we're playing in building pyramids, but the pyramids are made out of squares. Now, when i talk about squares and show them symbols, they know what i'm talking about because they played with it. They know 100 is square, it's not just a fact to memorize.

Square roots & radicals. Easy Peezy. 

We start out by playing with blocks and building, cool, pyramids and counting so that when we get to the allegedly advanced algebra it's easy and we don't waste our cognitive load on squares or cubes and understanding the algebra concepts are actually easy because algebra makes things simple actually, not hard. Use your module three password.

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Square roots and radicals also become visually obvious. Squares are a large part of the mathematics as it turns out, you just didn't know it because you couldn't recognize the symbols. X +1 times X +1 is a square.

This is the square number. Imagine trying to imagine a cow without ever seeing even a picture of a cow.

And then, if we want to make it (x+1)³ we can see that too. 

Now we can make an abstract square, equal to a concrete square and figure out what "x" must be.

Once you understand the squares, the cubes are just as easy and fun because bigger is funner. 

And fourth power algebra is even funnier than that.

Square root: visually obvious.

Square numbers and algebra go together like hand in glove. Square roots really are squares. We just count one side. 

Teaching littles to solve this problem so that later in the day they could intimidate their parents and impress their friends, used to be a favorite past time of mine. Little ones like six and seven year olds. Nine and 10 year olds are super easy which is usually how old they are by the time they're in third grade.  

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i have lots of free lessons regarding square numbers. Have fun watching this one if you haven't seen it already.

This is actually my very first YouTube video. i had a little wine and the woman i was with had her  video camera. Took me forever to figure out how to load up the video and so on. 16 years later, there's over 1000 videos on YouTube. And that woman is now a state representative to the State House on Oahu. Anyhow, square numbers:

There are lots of pages where you see me present these concepts to very young children.  i have many videos covering the topic.

You could do a YouTube or Google search for Crrewton Ramone square numbers. After watching a few of them, you will see why it's child's play. Then you can play with your own students and understand we aren't just piling up blocks to make pyramids. It's play with purpose...mom or dad or the teacher adds the purpose. Usually the purpose is to master multiplication, and addends. 

But certainly, square numbers, make algebra, easy and understanding. The symbols in the squares is actually fun. 

Squaring numbers that end in FIVE

Many systems just teach rules and process the Mortensen method shows you why the rules and process work, you actually SEE the math.

Fast easy lesson. Once you watch it you'll be able to square numbers that end in 5 too. If you already knew the rule, now, you know WHY the rule.

Also, check out this page where  we play with fourth power and so-called more advanced higher power algebra with x⁴, which is why i call it allegedly advanced algebra because it's actually quite easy once you can see it. 

BONUS VIDEO names of numbers:

It's always fun busting out the 10,000 square.

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"From a child, I had an inordinate desire for knowledge and especially music, painting, flowers, and the sciences, Algebra being one of my favorite studies". ~George Washington Carver

"I grew up with plenty of smart people. They would beat me at chess; they could solve brain teasers before I could, but then they would struggle in algebra. These were incredibly smart people who simply did not have the foundation in math that I had". ~Sal Khan

Can you tell it's a kinesthetic learner? She would've understood algebra if i had been the teacher.

"I have always been a practical gal. Algebra and I never got on but I could replace the oil in a Fiat Mirafiori from the age of nine. Lightbulbs and plugs were always changed with ease". ~Ulrika Jonsson

"The square is not a subconscious form. It is the creation of intuitive reason. The face of the new art. The square is a living, regal infant. The first step of pure creation in art". ~Kazimir Malevich