Yet More Factoring With Positive 3rd Power Polynomials

Here is a session with an 11 year old, I tacked a short segment on the end of if with a 15 ear old high school student so there can be no question it's basically the same stuff...the textbook problem at the end uses M's instead of X as if that makes it more interesting...

Again if you want to see negatives you need a password...




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Crewton Ramone Start In The Concrete!

Start in the concrete, there's no better way to cement the facts into their heads than to start with hands on experience of the math...

Some people find it amusing that kids who have trouble with addends and multiplication can factor third power polynomials...that's because they fail to understand proper application of the 5 basic concepts. Math is just counting. Multiplication and addition as well as 3rd power algebra are just counting.

The main idea here though is start in the concrete and watch your success rate go up...

Here is a short screencast covering this lesson.



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It's Not Magic It's Math

I like this screencast for several reasons, one it has a lovely shot of powerlines at the beginning but even more than that it shows how you can go from working on simple subtraction to third power algebra all in the same lesson, and even more than that, once the student understands the concepts he can make up his own problems and start making discoveries about algebra and the distributive theory of multiplication and what factors end up where, and more. Don't be fooled this student DEFINITELY hasn't recovered his joy of learning when it comes to mathematics but at leaste he doesn't hate it (as much) anymore. Sometimes he has fun in spite of himself.

Now with regard to rules an process when it comes to subtraction, and making change...it is important to make sure students of all ages but especially very young children get the concept of subtraction, that we are "taking away" or "minus-ing" in kid speak. The algorithm make nines and a ten make subtraction easy but it's not magic or a trick and they can see that and get a hold of that concept IF you start in the concrete with the blocks. They can see that the "difference" and the "subtrahend" are the same as the "minuend", in other words if you add the difference to the subtrahend you get the minuend. The minuend is the number you are subtracting from and the subtrahend is the number you are subtracting and the difference is what's left AND my students have never even heard these math terms because they are not important for conceptual understanding.

That's why I refrain from calling this magic traingles because it's not magic IT'S MATH. So I call them math triangles. You can find more on my subtraction page and even download a 10 page pdf with practice problems for making change. A one page math worksheet is FREE access to a lot of pdfs including the 10 pager and fractions and algebra vids using negatives costs a whole buck. Get a password here. Where it says multi-page password.


For more on math with Playing Cards check out this page cleverly called teach math with playing cards.

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Higher Powers of X

Math is just counting. Here we count a bigger rectangle than just "x squared".

60 seconds ought to give you an inkling of how cool this is...note I say "x-squared" but I meant "x-cubed" or "x to the third."

The students are 4 and 5 years old.

Here we factor x³ + 6x² + 12x + 16!



Here is a longer explanation/demonstration:



At the end they look like geniuses


Here we play with

x³ + 7x² + 14x + 8



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