The Great Big Book of Algebra

Wednesday, December 3, 2008
CHAPTER 1 INTEGER POETRY
Addition-Haiku
Adding Integers,
Plus, increase, greater than, add,
Adding is so fun!

Subtracting Integers-Free Verse Poetry
Subtracting integers is just mad...
In the world of integers,
We never subtract, we add!
Adding integers is so fun!
Lets get to it! And get the job done,

Subtracting Integers does not exist,
But there's a twist
If you do subtract, you must add instead,
Adding is very much easy like
watching tv or sleeping in bed!

Partitive Division- Tanka Poem
You give to everyone,
Called sharing division too,
Share your yummy cookies,
Give until you have none left,
Remember to share cookies!!

Quotative Division-Haiku
Groups of Integers,
Group them in equal parts now,
It is so easy.

Rule of Multiplying Integers-Free Verse Poem
In the world of integers
There is only 2 rules
When you multiply an even amount of negative integers the product is always positive
Isn't that just cool!

Other rule is when you multiply an odd number of negative integers
the product is always negative
With our rules multiplying integers is a breeze
Multiplying Integers is easy like 1,2,3!
Easy as eating cheese!

CHAPTER 2
Xtranormal
Combining like terms and the Distributive Property
Billy Bob Jones: Hey Mike! I need your help with my homework.
Mike Hawk Jones: Sure let me see.
Billy Bob Jones: My last question asks what is combining like terms.
Mike Hawk Jones: Oh that's easy. It's like going shopping, you group the apples with the apples and the oranges with the oranges. But this time you group the variables(letters) with the constants(numbers).
Billy Bob Jones: Oh! I get it, so if there's 2a+1a+2+1. I just combine them so it's 3a+3?
Mike Hawk Jones: Yep just like that. It's like simplifying your answer so it's more easier to solve.
Billy Bob Jones: Thanks Mike!
Mike Hawk Jones: No problem Billy! Glad to help.

Questions:
Cosmo: I need help with homework! Is N+3-5N+12 is -6N+15??
Wonda: That's not right, lets go over this question.
Cosmo: Ok... How do we do this?
Wonda: First lets change the way we look at it. N-5N+3+12 is much better for your eyes. Now we have to simplify.
Cosmo: How do we simplify Wonda?
Wonda: We add the variables with the constants so there's only 1 variable and 1 constant left.
Cosmo: Ok N-5N is -4N and +3+12 is +15 so the answer is -4n+15 Wonda?
Wonda: Yep! Way to go Cosmo.
Cosmo: Thanks Wonda(:

Patrick: Hey Spongebob how's it going?
Spongebob Squarepants: I have homework from boarding school...
Patrick: What's your homework?
Spongebob: A question is 2+4(3N+8) I think it's dealing with combining like terms and the distributive property. I think the answer is 12N+10.
Patrick: No that's wrong! I think the answer is 12N+34 because we are dealing with the distributive property so we multiply the 4 with 3n+8 which is 12N+34. Then we add the 2 so we get 2+12N+32. Now we combine like terms so 2+32 is 34 and there is only 1 variable and 1 constant now. So our answer is 12N+34.
Spongebob: Oh! I'm sooooooo stupid, I should of known we had to do that. Thanks Patrick and how did you get so smart at this?
Patrick: Hahaha I guessed
Spongebob: Now that's my best friend right there!


Chapter 3!
1 Step Equations



When your doing additive. You just have to balance each side, so at the end you have n=? or in this case (2). Or in other words you have to isolate the variable by canceling using the opposite. When your done finding what the variable is, you need to do one last step, verify. Verify is very easy, you just substitute to check. You write down the question again and replace the N with your number. You will know if its balanced by verifying.
When your doing Subtractive, its just the same as Additive. First you isolate the variable by canceling using the opposite. Then you'll find what your variable is and then you just verify to check if its right. You rewrite the question and replace your N with your number. At then end, you should know if its balanced or not.
Multiplicative now. Its just the same but this time your multiplying. First you need to isolate by canceling using the opposite, don't forget to balance. After you need to verify(substitute to check). You rewrite the questions and replace N with your number.

Division now. Division is just the same as Multiplicative but instead of dividing to cancel, you need to multiply to cancel. First isolate the variable by canceling using the opposite. After Verify but rewriting your answer and replacing the N with your number. By verifying you can check if your answer is right!


Chapter 4!



The Great Book of Algebra

CHAPTER 1: Integer Poetry

Diamante: Adding

Add

Sum, Augment 

Combining, Increasing, Gaining

Plus, Total -- Subtrahend, Less

Reducing, Subtracting, Decreasing

Difference, Diminish

Subtract

Picture - Subtracting


Free Verse : "Rule of Multiplying Integers"

I 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

Script:

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.

                                              


ADDITIVE

     

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. 


SUBTRACTIVE

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


MULTIPLICATION


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.


DIVISION


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




The Great Big Book Of Algebra

Chapter 1: Integer Poetry


Adding Integers [Free Verse Poem]

I had come to my math class with my binder in my hands,
to learn the lesson that Mr. Harbeck had planned.
We had just finished probabilty,
I just hoped that the next lesson was within my ability.
So, I sat in my chair with an anxious look on my face,
I was wondering what unit would take probability's place.
Then Mr. Harbeck Shouted,"The next thing we are doing is..."
I thought, Oh no! We might be having a pop quiz!
Then he continued on with his talk about what we are doing today,
"Integers! We are doing integers! Hurray!"
I wondered what we were doing with integers this morning,
Mr Harbeck then said,"Guess what kind of equations I've been forming!"
Everyone waited for his important annoncement,
Then he began," We are doing addition in integers! Isn't adding integers an enjoyment?"
Then I wispered, 'yes!'
I loved addition in integers. I think that they're the best!
No need to pretend,
But I wish that it didnt come to an end!


Subracting Integers [Tanka Poem]
Subracting is hard
Additon is what to do
When you can't get through
in the question you change signs
to understand the question

Partitive [Haiku Poem]

The Partitive way,
Is easy when you get it,
If not it is hard.


Quotative [Free Verse Poem]

The quotative way,
The only way to get some types division done,
Without hurting your head.


Joysie's Joy-ful Rule of Multiplying Integers [Free Verse Poem]

Multiplying or Dividing
the rules are the same
If you have an even amount of negative integers,
your answer is always positve,
but if you have an odd amount of negatives,
then your answer will be negative.
Multiplying or Dividing,
The rules will always be the same.

Chapter 2: Combining like terms and the Distributive Property
XtraNormal


Nuki: Hey, Yuki.
Yuki: Hi, Nuki
Nuki: Is something the matter? You look kind of puzzled.
Yuki: It's just that I cant get the math problem that we were supposed to do in class.
Nuki: What's the question?
Yuki:The question is N + 3 - 5n + 12 n.
Nuki: What so hard about that? It's just algebra.
Yuki: Yea , I know but this question is pretty tricky...
Nuki: Let me have a go at it. My teacher says that i'm the best in math.
Yuki: Okay. But you have got to be careful. It's pretty confusing.
Nuki: Got it! The answer is 4n + 15.
Yuki: 4n + 15??? Is that really the answer? When I solved it , My answer was negative 6n+15. Can you show me how to simplify it?
Nuki: Sure. First you have to re write the question. You have to put the constants together and the variables together. But remember to bring the signs that are in front of the variable or the constant. Then you add the variables together. And add the contants together. And there's your answer.
Yuki: Wow, Nuki. You sure are good at simplifying algebra questions.
Nuki: Don't mention it. That's what friends are for.
Yuki: And since your so good at math, do you mind helping me with one more question?
Nuki: Sure, Yuki. What's the question?
Yuki: The question is 2 + 4(3n+8)
Nuki: I remember how to do these kinds of questions! I'll have it done right away. 'Pauses' Done! And the answer is 34 + 12n.
Yuki: I thought that the answer was 12n + 10. I guess I dont know my algebra. Want to show me how to do it?
Nuki: You bet ya. In this question, you have to multiply. The the constant is beside the letter without any thing in between it, meaning only one thing.. multiplying! You have to multiply the outside constant with the constants in the middle. One at a time of course. You start with the one on the left then go to the right. After multiplying, you have rewrite the question without the brackets and the constant that in front of it. After doing that, you have to add the constants. And then you get your answer.
Yuki: Wow. Thanks Nuki. You really helped me understand better algebra.
Nuki: No problem. I'm always happy to help you.





Chapter 3 : One Step Equation Solving
In this chapter you will learn how to solve one step equations. First you have to learn I COB V:
Isolate the Variable by
Canceling using the
Opposite
Balance and
Verify

Here how to do it:

Addition
Subtraction
Multiplication
Division

The Great Big Book Of Algebra Chapter Two

Haiku: adding integers
with two integers,
if you are deciding to add
put them together

Tanka:subtracting integers
subtracting, the myth
it is a total mirage
what you must create,
is to add the opposite
it is quite easy

Partitive: haiku
twelve apples, three bags
how many apples in each?
you can use your toes

Qoutative: haiku
twelve grapes,three per bag
how many bags were in there?
it is four of course!

multiplucation rules: free verse
how do you multiply?
i will tell you.
if it is two positives,the product will be positive.
like five times four.
if you multiply a positive by a negative, the product will be negative
if you multiply a negative by a negative, the product will be positive
if you multiply a negative by a positive the product will be negative

Chapter 2 Combining like terms and the Distributive Property












Tuesday, December 2, 2008
Today in math we started ALGEBRA so to start off the unit we thought of words for ADDING SUBTRACTING MULTIPLYING DIVIDING EQUALS and finally ALGEBRA WORDS and this is what we came up with

Adding
plus , greater than, larger, add, and increase

Subtracting
subtract, minus, negative, decrease, less than, reduce, diminish

Multiplying
times, multiply

Dividing
goes into, divided, a certain number of parts

Equals
resulting, equal, equal to, is, gives you, makes

AND FINALLY

Algebra words
variables- are letters that are substituted for numbers

N+6 - many answers
N+6 = 12 equation 1 possible answer

N+6 says a number plus 6 and
N+6 = 12 says what number plus 12 equals six
I pick uhh tanner

The Great Big Book of Algebra

Monday, December 1, 2008
Chapter One: Integer Poetry

Cinquan: Adding Integers
Adding integers,
big, great,
adding, combining, gaining,
Two numbers coming together,
Plus.

Free Verse: Subtracting Integers
In the world of integers,
subtraction does not exist.
In the world of integers,
subtraction is not missed.
When there is a subtracting sign,
I change it all the time.
Addition now,
I'm almost done.
Adding is more fun!

Haiku: Partitive Division
How many equal parts?
Asks Partitive Division.
What is your answer?

Free Verse: Quotitive Division
How many of a number is in a group?
Do you count all, or count in twos?
Of course you count,
one by one!
Do this and the game shall be won!
Fear not,
this is not repetitive.
It does not work for negative, negative.

Free Verse: The "Rule of Multiplying" integers.
Every odd amount of negatives,
is a negative product.
Every even amount of negatives,
is a positive product.
Know this,
and be free.

Chapter Two: Combining like terms and the Distributive Property

MASON: BOBBY! BOBBY! Guess what!

BOBBY: What now Mason?!

MASON: I learned how to do algebra in school today!

BOBBY: So?

MASON: What do you mean "so"! Now, I'm not only super fly, but smart too!

BOBBY: Really now?!

MASON: Yup.

BOBBY: Want to help me with my homework then?

MASON: Sure. Let's check it out.

BOBBY: What is n+3-5n+12? I think it's -6n+15.

MASON: Hm . . . how did you come to that conclusion?

BOBBY: First of all I write down the question. The second thing I did was re-group so it looked
like this -5n+n+3+12. Third, I put them together which came to -6+15.

MASON: You did all the right steps, but your error is in -5n+n. The n by itself is a positive. Think of it as -5+(+1)=-4. The correct answer to n+3-5n+12 is -4n+15.

BOBBY: Oh! I get it now!

MASON: Got any other questions? I want to train my skills.

BOBBY: Ha ha, whatever you say. Well, there is another question that I don't get.

MASON: Which one?

BOBBY: 2 + 4(3n+8), I think the answer is 12n + 10, but I'm not sure.

MASON: Wow. You are so wrong dude.

BOBBY: Well then, you teach me "oh great one"!

MASON: With pleasure! It's like this young one. First you multiply the 4 with 3n whi-

BOBBY: BUT, what about the 2 in front of the 4?

MASON: DON'T INTERRUPT THE MASTER!

BOBBY: . . .

MASON: As I was saying, 4x3=12n. Then you take the 4 and multiply it with 32. Right now you should have 12n + 32. You taking notes?

BOBBY: Yes sir!

MASON: Good. Now you take the 2 in front of the 4 and add it to 32. You should now have 34 and the answer is 12n+34.

BOBBY: But I don't understand, where did I go wrong?

MASON: I think you got mixed up when you did 4x3n then you did 2+8.

BOBBY: Oh . . . well . . . thanks for helping me.

MASON: No problem.

BOBBY: I guess you really are are pretty smart.

MASON: Thank you!

BOBBY: *looks at camera* and remember folks, drive safely!

PART ONE




PART TWO




Chapter Three: One step equation solving

ADDITION: First of all, you need to Isolate the variable (n) by Canceling with the Opposite. The opposite of +2 is -2. You must Balance, which means whatever you do to the left side, you must do to the right side. Last, but not least, don't forget to Verify!


SUBTRACTION: is very much like Addition. Isolate the variable (n) by Canceling with the Opposite. The opposite of -3 is +3. You must Balance and Verify.


MULTIPLICATION: Isolate the variable (n) by Canceling with the Opposite. The opposite of multiplication is division. So you will have to divide 3n by 3.
Balance and Verify.


DIVISION: Isolate the variable (n) by Canceling with the Opposite. The opposite of division is multiplication. So you will have to multiply (n) divided by 2 with 2.
 Balance and Verify.

Chapter Four: Algetiles

Scribe Post, December 1

Today in class, we did Poetry! We had a sub. because Mr. Harbeck was away. Her name was Mrs. Hay!
We started our poems on the five topics that we are suppose to write about. This will be due this Friday (December 5). The five topics that we were suppose to make poems on were:
-Adding Integers
-Subtracting Integers
-Partitive Division
-Quotative Division
-The "Rule of Multiplying" Integers

Mr. Harbeck also gave us a few types of poetry forms that we could use to make up our poetry. This was also posted on the Sargent Park Math Zone site.
The different types of poetry forms are:

Haiku
The haiku consists of 3 lines. 1st line should have 5 syllables, 2nd line having 7 syllables, last line having 5 syllables
Tanka
The tanka has 5 lines. The first three lines, start off the same has the Haiku. The 4th and 5th line has 7 syllables
Cinquain
There are two ways to write a cinquain. They are 5 lines in length. The first form of cinquain, starts with a one word topic (noun). The second line has two adjectives describing the noun, the third line has three action words (verbs), the fourth line should have a four word phrase, then the last line should end with a word that has the same meaning as the topic word or another word that is equivalent.
The second way to write a cinquain, is to start the first line with words, or a two-syllable word. The second line would have to have anything that is 4 syllables describing the topic. The third line should have anything that is 6 syllables expressing an action. The fourth line will have anything that is 8 syllables expressing feeling. The final line should have anything that is two-syllables, and must be a synonym to the topic.
Free Verse Poem
This type of poetry does not have to follow any rules, you can make it anyway as long as it stays on topic. You can include sentences, but you do not have to, you can instead just write a page of words. For this to be a good poem, you should use strong vocabulary and colourful words.
Diamante
For an easier way to explain on how to write diamantes, here is an interactive website that can teach, and give you examples on how to make diamante poetry, CLICK HERE
Picture
A picture poem can be made up of letters, words or sentences. The finished poem should end up looking like a picture, that is related to your topic that you are writing about. There is an example near the bottom of this post.

You must use at least 3 different types of poetry. You must make at least one poem for each of the five topics.
Here are some examples of poetry, you can try and guess what type of poetry it is:

Green and speckled legs,
Hop on logs and lily pads
Splash in cool water.



School.
Teacher.
Jail, boring.
Learning, playing, eating.
Stupid, strange, tired, grumpy.
Torture.

I didn't create any of these poems, so I do not take credit.

Well, that's all for today, I pick the next scribe to be... Braden.
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