The Great Book of Algebra

Wednesday, December 3, 2008
CHAPTER 1: Integer Poetry

Diamante: Adding


Sum, Augment 

Combining, Increasing, Gaining

Plus, Total -- Subtrahend, Less

Reducing, Subtracting, Decreasing

Difference, Diminish


Picture - Subtracting

Free Verse : "Rule of Multiplying Integers"

was just ecstatic to learn about   

the "Rule of Multiplying Integers".
People went in front of the class to say the rule,
I thought, when will it be my turn?

Anticipation was running through me
Just like a car driving through quickly.

I just wanted to show that I knew the rule
Minutes passing by.. it was cruel.

The teacher finally picked me

And everyone was going to see.

I said,
"When brackets kiss, you multiply.
Trust me, it's easy as pie!"

I went to sit down at my desk,
Realizing I was missing the rest.
Next thing I know,
Someone else was walking up in between the rows.

"When you multiply an odd amount of integers,
your answer is negative, Sir." 

They were still missing something
I felt like the wife of a King.
I still had a chance to show everyone what I got
I went up there again, faster than a yacht.
"When you multiply an even amount of integers,
your answer is positive and that's for sure!"

I was happy to be the last one
to say the final rule of multiplying integers and surprisingly it was fun.

Haiku: Quotative Division

Ask a division question

Say, "How many groups are in...?"

Simplicity, see?

Tanka: Partitive Division

What is partitive?

It is just like quotative

Just like dealing cards

All you have to do is share

It's easy, not hard at all

CHAPTER 2: Combining like terms and the Distributive Property


Roxanne: Hello! How have you been lately?

Joanna: Hey! I've been great, and you?

Roxanne: Just fine. Although, I have been struggling with my math lately. That's why I called you over.

Joanna: What do you need help on?

Roxanne: Well, my class and I are learning algebra.

Joanna: Algebra? Algebra is my favourite topic in math!

Roxanne: Okay, so my first question on the worksheet is n+3-5n+12. Do you think you can help me?

Joanna: Yes, I can help you. But, first of all I want you to try this question out. What do you think the answer is?

Roxanne: Uh, I think the answer is -6n+15. Am I right or wrong?

Joanna: Actually, your answer is really close. It's -4n+15.

Roxanne: How do you get the answer?

Joanna: It's quite simple. First of all, you should circle the variable so you know which goes first. Then, group like terms so it's easier. Now, simplify the question. So, it would be n-5n+3+12. Also, n just means 1. n-5n=-4. 3+12=15. Put them together and you've got -4n+15.

Roxanne: Wow, that's easy! Thanks for the help! I think I can manage on my own. You can stay if you want.

Joanna: No problem, but I still have to finish up with my chores. Just call me when you need help and I'll be here in a jiffy. Well, I'm going to go home now. Bye!

Roxanne: Wait, Joanna! The next questions has brackets.. I know I'm suppose to multiply, but what do I multiply?

Joanna: What's the question?

Roxanne: The question is 2 + 4(3n+8).

Joanna: Okay, it'll be easy just like the first question! This is called Distributive Property. It looks tricky, but once you know what to do you'll think "Boy, that was super easy!"

Roxanne: Distributive Property... Can I try this question on my own first?

Joanna: Sure, it's best to learn from your mistakes, anyway. But, tell me how'd you got the answer.

Roxanne: I think it's 12n+10. First of all, I knew the rule of multiplying integers. So, I just multiplied whatever was touching the bracket. That's how I got 12n. I didn't know what to do with the other two numbers, so I just added them together.

Joanna: Ah.. Well, I can tell you didn't know what to do with the 2. For now, just pull the 2 down. Now multiply the 4 and 3n together, which is 12n. After that, multiply the 4 and 8 together, which is 32. Now, the question is 2+12n+32. All you have to do is combine like term and simplify. So, it will be 12n+2+32. You see, I combined the integers that didn't have variables and I combined integers that did. It makes it way less confusing when you combine like terms. Now, finally... the answer is 12n+34! Very simple, like I said. Well, I probably should get going. My mom might be wondering what's taking me so long. See you later, Roxanne!

Roxanne: Oh okay and thanks! Bye, Joanna!

CHAPTER 3: One Step Equations Solving

We've been learning one step equations in addition, subtraction, division and multiplication. First, I'm going to show you how to do an additive equation. But, before we do that, there are some 'rules' you need to learn in order to be successful with one step equations.




The first question is n+9= -4. As you can see, I've isolated n by using the opposite of +9 (which is obviously -9). Like I said, what you do on one side, you have to do the same thing on the other side. So, I put -9 beside -4 to balance it out. You're left with n= -13. That is how you solve n. Now, you have to verify so you can get full marks. 


The rules are basically the same as additive equations. Isolate to get n by using the opposites, balance and verify.


The question is 2n=10. Again, the rules still apply to multiplication as well. When you're isolating n in a multiplication equation, you divide since you need to cancel them out. Do the same thing to the other side. You have to figure out what 10/2 is in order to get n. n=5. Verify.


Finally, division. In this question, there is a negative sign. You can just easily put the negative sign beside the 9 or the n. In this case, I've decided to put the negative sign beside the 9 because it's a bit easier. After that, you do the same thing again as the rest of the questions we did. You have to multiply to isolate n when you're doing a division equation. Do the same thing to the other side. Figure out what 4(-9) is. n= - 36. Verify. Now you know how to do one step equations!

CHAPTER 4: Algebra tiles


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