The Great Big Book of Algebra

Thursday, December 4, 2008
Chapter One: Integer Poetry


Haiku – Adding
You add negatives
And positives too
The answer is sum

Tanka – Subtracting
Although we subtract
We never really ‘subtract’
Know the difference
Subtracting is quite easy
If you know how to subtract

Cinquain – Partitive Division
Calculate
Quick, simple
Dividing, splitting evenly, sharing
One way of dividing
Equal groups

Free Verse – Quotative Division
This is about quotative division
It all comes down to the right decision
First, know should how to group
It’s not hard, don’t send in the troops!


Free Verse – Multiplying Rules
You want to know the multiplying rule?
I guess you don’t know, you fool.
I learned the rule because I go to school!
You mainly need to know a few main facts
So now you know you can relax!




Chapter Two: Combining Like Terms and The Distributive Property



Script:

Podgy: Hello!

Cappie: Hi. Who are you?

Podgy: Well, I'm Podgy, and I'm a student! I want to learn about destructive properties, and mining bike germs!

Cappie: Destructive properties and miming germs? Don't you mean distributive property, and Combining like terms?

Podgy: Oh, yes. Those things... Say... You wouldn't happen to know about distributive property and combining like terms .. would you?

Cappie: Oh, yes. I do. Would you like to learn, Podge meister?

Podgy: Oh, ah. Sure. I mean. I wouldn't mind... I mean. Learning about those things woudn't be too bad... I mean... If you don't mind teaching ... me, Podgy... That is. Hehe...

Cappie: Calm down Podge meister. I'll teach you, in one condition, though.

Podgy: So, uh. Cappie... Dude, guy, mister, sir... I mean, teacher... Sea foo... You know, they call the teachers Sea Foo in Japan that... I think it'd be okay to call you that.

Cappie: Quiet Down! The condition is for you to stop being a blubbering fool, you've been rambling all this time! So, there! I'll start off teaching you about combining like terms. It is more simple..

Podgy: OKAY THEN! Combining like terms it is!

Cappie: I have a practice question. n+3-5n+12 . First, look at the question.
n+3-5n+12.
Now, identify the constants (integers that won't change), and variables (letters).

n +3 -5n +12
So now, you need to group them together. Or "combine like terms"! Once you know that, you know all you need to know about combining like terms!

Podgy: OK! I'll start with the variables... There are n and -5n. So... If I add another n to it, it should be -6n. Now for the consanants. All positives, woot woot! 3 and 12, make 15. So, is it -6n+15 ?

Cappie: No, it is not. Think about the steps! You made a little error in your thinking process. Remember that when you add a positive to a negative, the digit decreases. Think about a number line, that should help you a lot.

Podgy: Gee, thanks Cappie! I'll try it once more! Starting off with the variables... n, and -5n ... should be -4n! And, and the 3 and the 12 still make 15, so it must be -4n+15! Aren't I right, sir?

Cappie: Right!

Podgy: Hot dog, am I ever glad! What do you know about Distributive Property?

Cappie: Well, here's an example to work with. 2 + 4(3n+8). You need to multiply the 4 with 3n, and +8, because 4 is touching the brackets. Once you have done that, combine the like terms.

Podgy: Oh, okay! Hmm. 4 multiplied by 3n is 12n. 8 and 2 equals 10 ... So, we add them together. Combine like terms! So the answer must be 12n+10!

Cappie: Podge meister, I'm quite proud of you. But your answer is incorrect. Your flaw was that you forgot to multiply the 4 by 8. Try again.

Podgy: Ok, then. 4 multiplied by 3n is 12n. 4 multiplied by 8 is 32. So, I'm left with 12n+32+2. Combine like terms! 32+4=34. So the answer must be12n+34! I get it! Thanks so much for teaching me Cappie, sir!

Cappie: Oh gosh, you're making me blush. Call me Cappie!

Podgy: Ok! Cappie it is!



Here is my XTRANORMAL movie, Combining Like Terms and Distributive Property (Part One)




Here is my XTRANORMAL movie, Combining Like Terms and Distributive Property (Part Two)





Chapter Three: One Step Equation Solving



Above is a picture example of how to do addition algebra. A very important part of algebra is knowing I.C.O.B.V, which is an acronym for...



I - Isolate the variable by
C - Cancelling using the
O - Opposite
B - Balance
V - Verify

Now, when confronted with a question such as the one provided, your objective is to isolate the variable. In doing so, you need to cancel out, using the opposite. But, you need to remember that you need to keep things balanced; so what to you do one side, you do to the other side. Once you understand this, you merely simplify to N equals whatever N equals. In this case (referring to the example above) N=3.
So, in the example above, N+3=5 your objective is to isolate the variable. To do that, you need to cancel using oppposites. Remember to keep it balanced; what you do on one side, you do to the other side. N+3-3=5-3 Simplify that. N=2. Now that tells you what N equals. In order to get full marks, you need to verify. Just copy out the question, and substitute N with what N equals.
N+3=5
2+3=5
5=5
Understand it?

In many ways, subtracting and adding are alike, like how you solve algebra questions. Above is an example of a subtracting algebra question. Like adding, you need to isolate the variable by cancelling out using opposites. Do not forget to balance by doing what you do to one side, do to the other side, and verify.
The question is N-5=1. Isolate by cancelling out, using the opposite. Don't forget to balance out!
N-5+5=1+5
Once you have that, you need to simplify it.
N=6
Once the question has been simplified, you need to verify.
N-5=1
6-5=1
1=1
Easy-peasy.


Now multiplicative type is a bit different, but no harder, no easier. Above is an example: 2N=10. What you need to do still has to do with I.C.O.B.V. Isolate, cancel, oppositve, balance, verify. Ask yourself, what is the opposite of multiplying? Well, the answer is as simple as the question itself! Division, of course! So, to isolate N, (or, to get it by itself) you divide 2N by 2. But since you've divided 2 on one side, you must do the same to the otherside, leaving you with N=5. Since you know what N equals, you must verify.

2N=10
2(5)=10
10=10

If you don't understand something, feel free to comment! Or perhaps I've made an error, and you'd like to point it out, please comment all the same! :)

As I've said, adding and subtracting are in someways similar, but they're also opposite. Well, since multiplying and dividing are opposite they're also similar is some ways. They're alike because they use eachother to do algebra. Above is an example of how to do dividing type algebra.
N = 6
--
2

With a question like this you need to isolate the variable by cancelling using the opposite. Don't forget to balance it out!
(2) N = 6(2)

------
2

Now simplify.

N=12

Now that it is simplified, verify!

N = 6
--
2

12 = 6
--
2

6=6


Please feel free to comment on this!

Chapter Four: Algetiles Movie

(I'm not exactly sure what the title and tags are... So, I guessed)





Here is Giselle's, Nikki's, and my movie for Adding, Subtracting, Multiplying, and Dividing with Algebra Tiles.

13 comments:

  1. Joysie 817 said...

    Good job, Linda!
    I liked how you made the titles big and orange. It made it stand out more. I liked how easily your poems flowed. It all came together.
    I think it looked like it took a while for you to do because it was so well done.

    I can't see any mistakes at all when I am reading through it.

    Great Job, Linda! Keep up the great work! ☺

    December 4, 2008 at 9:08 PM  

  2. linda 8-17 said...

    WOOOH! Thanks Joysie (: Your comment is appreciated (YY)

    December 4, 2008 at 9:18 PM  

  3. Kevin 8-17 said...

    Woah, nice poems LINDA! It took me forever to think of each poem on mine, I'm so bad at poetry. Anyway, really nice poems!!

    December 4, 2008 at 10:08 PM  

  4. Karen 8-17 said...

    WOW mang! Your poems are like wow ( I know I have to think of better adjectives). I really like the multiplying one it's good and funny--you fool! LOL:D. All of your poems are so interesting and it's just so good to read. I don't see any errors I'll even double-check for you;)..well reporter DUCKIE KOODOS for you;)
    -Kayue;]
    y the way..I am loving the orange and the way you made things bigger.

    December 4, 2008 at 10:23 PM  

  5. courtneyc 8-17 said...

    DUCK! (:
    good job, your poems are so good. I enjoyed reading your poems, you put 100% in all of your work (:

    - good job again.

    December 5, 2008 at 10:41 AM  

  6. camille817 said...

    DUCKIE!!!

    Awesome poems!:) I like the "fool" one and I liked how you rhymed Subtraction with subtraction! ;p anyway good job. keep up the good work!

    December 5, 2008 at 5:10 PM  

  7. Vincent 8-17 said...

    whoa nice rhyemes lol =p

    December 5, 2008 at 11:46 PM  

  8. sharmayne8.17 said...

    Duckiee (:
    Good Job Duckiee ! haa i really liked your last poem."I learned the rule because I go to school!" I like that line alot, ha it got me laughing. Thanks for the comment on my poetry also, You helped me alot with minor errors.
    K3 Shaaar.

    December 6, 2008 at 11:18 AM  

  9. Kevin 8-17 said...

    hahah, that movie was great. Podge-myster, haha. Great video!!!!!

    December 16, 2008 at 11:30 PM  

  10. nikki 8-17 said...

    Great job Linda! I liked your poems! I also like your math movie. I didn't see any mistakes. I liked how you explained so well of how to combine like terms and the distributive property. Good job!

    December 18, 2008 at 9:53 AM  

  11. camille817 said...

    DUCK!
    Hey duck good job on your movie I LOVED it! and and I liked how you mixed in Japanese that was pretty awesome! " sea foo " :) anyway I Loved the back round music as well! keep up the good work! :D

    December 18, 2008 at 8:50 PM  

  12. Kevin 8-17 said...

    Hey Linda!,
    Wow, that's an awesome explanation you did on chapter 3! You must've spent a long time on that! Great video too, you guys are awesome!
    Keep it up!

    January 15, 2009 at 8:08 PM  

  13. nikki 8-17 said...

    Awesome job Linda! You had a really great explanations for chapter 3. You explained everything step by step and I didn't see any mistakes. We did a pretty good job on the algetiles movie. Keep up the good work!

    January 18, 2009 at 10:21 AM  

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