The Great Big Book of Algebra

Thursday, December 4, 2008
Chapter 1: Integer Poetry

Adding Integers: Cinquain Poem

Adding
positive, negative
increasing, gaining, combining
the opposite of subtracting
Plus

Subtracting Integers: Diamonte Poem

Subtracting
different, easy
decreasing, reducing, diminishing
minus, take away-plus, increased
gaining, combining, increasing
addend, total
Adding


Partitive Division: Free Verse

"What's partitive division?" Whaat? You haven't hear it before? Well its a very simple way of showing your work and so this is how it goes... Just ask the simple question "How many equal parts are in ___ groups when you have negative/positive ___?" Think very, very hard but solve it really slow. So, then you draw the equal groups and share those positive or negative integers but make sure there equal, in equal parts of groups. Wasn't that easy?, of course it was! It's partitive division! So just remember these steps and you'll never be lost or confused!

Quotative Division: Tanka

What a simple way.
Using quotative to solve.
What goes into what?
Step by step, drawing is one.
Circle them to show your work!

The "Rule for Multiplying" or "Ron's Rule": Free Verse

Whenever your stuck on an integer question, just remember this rule and you'll be fine. When multiplied with two positive integers, remember the product is always positive. But once you multiplied a negative and positive together, uh oh, the product is now a negative. But wait, there's multiplying a negative and a another negative integer.. Guess what? The product is a positive all together! Now the last part is multiplying a positive and a negative.
Take a guess and look and see....... The product is negative! Lucky guess it may be! Now you have learned the rule of multiplying, always remember this lesson and take it everywhere you go!



Chapter 2: Combining like terms and the Distributive Property

Bella: "Hey Tina, how's it going?"
Tina: "It's been going great but I've been having trouble doing this algebra equation. I'm not sure if I did it right or wrong. Can you help me?"
Bella: "Of course I'll help you. Let's see what you did."
Tina: "Okay well our teacher gave us this equation to do, its n+3-5n+12. When I solved this equation, the answer I got was -6n+15. Did I do something wrong or is it right?"
Bella: "Well actually the real answer is 4n+15."
Tina: "Oh really? So, what did I do wrong to get -6n+15?"
Bella: "Okay well first of all, instead of adding a positive to "n" and "-5n" you added a negative to "n" and "-5n" and so that's how you got -6n+15.
Tina: "Oh, I get it now but can you go over the steps of solving this equation."
Bella: "Yeah, sure thing. Okay, first off you circle the like terms, like "n" and "-5n." Then, you regroup them and you show your two different "shopping bags." Like this: n-5n ( there's a shopping bag underneath each expression) +3+12 ( there's also a shopping bag underneath this one too.) After, you simplify it and the answer you will get is 4n+15. It's not that hard, just remember the steps.
Tina: "Oh now I get how to do it, thank you so much! If you need help, just count on me and I'll help you with anything."
Bella: " You're very welcome and you can also count on me when you need help, just call my name and I'll be right there."


Tina: "Bella, since you offered to help me, can you please tell me if I did this algebra equation wrong or right and if I did do it wrong, can you still help me do the steps right to finding the right answer?"
Bella: "Yes of course. What is the equation that you wish to talk about?"
Tina: "It is 2+4(3n+8). Once I solved this equation, the answer that I got was 12n+10. Am I right?"
Bella: "Well actually you did it wrong. The first thing you need to do is solve the brackets and the numbers beside them."
Tina: "Really? So, what do you do after?
Bella: " Okay, since +4 is touching the bracket, it gets multiplied by the numbers inside the brackets." So, what's +4 times 3n?"
Tina: " Um, is it +12n?"
Bella: "Correct! Good job Tina! So now we multiply +4 and +8. What do we get?
Tina: "We get +32!"
Bella: "Correct again! You're starting to get the hang of this. So after you have solved those in the brackets and the number beside it you bring down the answers that you've got, like +12n and +32 and you also bring down the 2."
Tina: "Okay, now what?"
Bella: "Well so far you got 2+12n+32. The next step is to group the like terms... 2+32 and then just +12n. Okay so let's solve. What do you get when you add 2+32?"
Tina: " You get +34 or 34!"
Bella: "Yes, that's right! now bring down +12n, since your not going to add anything to it. Now the answer you get is?"
Tina: "12n+34!"
Bella: "Good job! Your such a fast learner! So now, do you get how to solve algebra equations?"
Tina: "Thank you and yes now I know how to solve algebra equations because of your big help! Thank you so much! Just remember if you need help, I'm always here!"
Bella: "You're very welcome and if you need help too just call my name and I'll be there!"

Here's the video



Chapter 3: One Step Equation Solving

Here are four equations about additive, subtractive, multiplicative and divisive. I will be explaining how to solve each equation using the rules of I.C.B.V., which stands for isolate, cancel opposite, balance and verify.

Additive:
The first thing I would do to be able to solve this equation is by isolating the variable which is "n". Second, you would have to add the opposite, which is -7 to +7. You then cancel them out because they are zero pairs. After you are left with "n". Third, you need to balance it out by doing the same thing to the other side. So it would be like this.. 10-7=3. Then your left with the answer of n=3. The last step is to verify (substitute) and that is very important! You first need to rewrite the equation. Then you replace the variable to the answer you got which is n=3. So it would look like this 3+7=10. Then you would write down 10=10 to finish it off.

Subtractive:
The first thing to do to solve this subtractive equation is to isolate the variable. Second, you add the opposite, which is +2 to -2. You then cancel them out because they are zero pairs. Third, you need to balance it out by doing the same to the other side. So you add +2 to the answer 14 and you solve it. Then you are left with n=16, which is the answer. The last and important step of all is to verify! You first need to rewrite the equation. Second, you replace the variable with the answer you got, which is n=16. So it would look like this... 16-2=14. The last step is to write down 14=14 to show that you are done.

Multiplicative:
The first step for solving a multiplicative equation is to isolate the variable. You then add the opposite and cancel it by dividing 3 to 3. So you are not left with "n". Third, you balance it out by doing the same thing to the other side. So you solve 12/3 which equals to 4 and the answer your left with is n=4. The last and important step is to verify! You first need to rewrite the equation. Then you replace the variable with the answer you got, which is n=3. So it would look like this....3(4)=12. The last step is to write 12=12 to show that you are done.

Divisive:
The first thing you do to solve this equation is to isolate the variable. You then add the opposite by dividing 2 by 2. So now you are left with "n". Third, you balance it by doing the same thing to the other side. You multiply 5 by 2 and now your left with the answer 10. Now the last and important step of all is to verify! You first need to rewrite the equation. Second, you replace the variable with the answer you got, which is n=10. The last step is to write down 5=5 to show that you are now done.


Chapter 4: Algetile Video

During class, Mr.Harbeck told us to make a movie about four different equations. We had to explain how to solve each one by using algebra tiles. By the way, i'm sorry if the beginning starts of side ways and also the end when I am talking, I forgot that we had to video the whole thing landscaped. So, i'm sorry about that! Oh, and i'm also sorry if I explained it confusing!

The Great Big Book of Algebra

Chapter One:
Picture:
Subtracting Integers is easier than it seems
You don't subtract, you just add the opposites.


Free Verse: Ron's Rule
Yo, I'm about to teach you something you've never knew,
it might get complicated for you so work in a crew,
this is the Ron's proof, because I don't poof I got the proof
hey, when your multiplying an odd number of negative,
makes a negative product, so (-1)(-1)(-1) equals negative one,
but when you have something like this (-1)(-1)(-1)(-1) don't do that
because that is NOT the right route, and if your multiplying an even
number of negative integers make a product that is positive, it goes
like this (-1)(-1) equals positive one, because there's two negative ones
and Ron's proof says even numbers of negative integers make a product
of positive integers, so hey, if I were you i would come to Ron and ask him,
" hey ron what's the rule? "
Haiku; Adding Integers
Adding Integers
Having, owing integers
without training pants.


Cinquain;
Quotative Division.
groups,
scary questions and happy results
dividing, seperating, sharing
how many can you put in the number of groups?
quotative.

Haiku;
Partitive Division.
Partitive is fun,
just making numbers in groups,
its like sharing cards.



Chapter Two:


Ronnie: Hi Casey, I need some help with my math. Can you please help me?
Casey: Yes, sure Ronnie. what do you need help with?
Ronnie: Hmm, I'm having trouble doing this question in class. I really don't get it that much.
Casey: What question is it? I'll try to help you.
Ronnie: n+3-5n+12 and I got an answer of -6n+15.
Casey: No, that's it the wrong answer.You forgot to circle the variables. You didn't circle the variables which is the 'n' and '-5n'. The answer is 4n+15. After you circle the variables you have to re-write the question. n-5n+3+12 and then you do 'n-5n' is 4n then '3+12' is 15. After you put it all together and your answer is 4n+15.
Ronnie: I understand now. I'll show Mista Harbeck at school and I wonder if he'll be mad at me still.


Casey: Yes, it's that simple. Just remember to always try to remember to have 2 shopping bags to seperate your variables .


Ronnie: Casey, can I please ask one more question. This one I think you wont have trouble doing.


Casey: What is it?
Ronnie: 2+4(3n+8), I got an answer of 12n+10.


Casey: No that is wrong, you got the first part right but you added '2+8' together thats how you got 10. You were suppose to times '4 by 8' that equals 32. Then bring down the 2. If you re-write that it'll look like this '2+12n+32' then find the variables because they go first then do the rest. So you get an answer of 12n+34.
Ronnie: Oh! thank you, now I could show my teacher how to do it. He'll be very proud. Casey: Haha, yeah he will. Just tell him you worked hard to learn it and he'll be impressed.


Ronnie: Okay, thank you!
Casey: No problem, anytime hommie.

This is a video of my Xtranormal



Chapter 3:

2+n=12























12-n=8



























n/2=6















2n=12














Chapter 4:

Chapter 4 Video:
















The Great Big Book of Algebra

Tuesday, December 2, 2008
Chapter one: Integer Poetry!

Adding Integers Poem (A Diamante Poem)


Adding Integers

Adding

Easy, Fun to do,

Thinking, increasing, gaining,

Always trying your hardest,

receiving, completing, finishing..


Combining

Free Verse: Subtracting


Subtracting!

When you sutbract,

you must attack the opposite like terms.

if you do not,

you will be caught,

in a big mess returned!

Multipication Rule "Ron's Rule" (Free Verse)


Ron's Rule
Multiplying could be rough,
Need help? No problem, I'm tough!
Look for you're barn doors,
And flip to the blue side..

Open up each barn, boy these doors are wide!

Look and look until you find,

something worth a persons' mind.

Found it yet? Silly you! The answer is right infront of you!

When you multiply an even number,

with something ridiculous like a positive number,
the product is always an positive number!

When you multiply an odd number,
with something silly like a negative number,

the product is always positive!

Now go and run, and use this knowledge,
lets hope it'll make you smarter than an olive!
(Myth idea 'stolen' from Nicky D's Poem.)


Free Verse: Partitive Division

Partitive Division
Negative seven and positive four it read,

I thought really really really hard in my head.
What do you do, when you have these signs?

Do you do the grouping, or do the sharing kinds?

Oh, I know! The answer popped into my mind.

How could I forget? Negative and Postive you must always do,

something special like partitive pictures, who really knew?
You draw negative seven,
boy, that was like heaven!

You draw positive four groups,

Wow, that was like shooting hoops!
You share and share, like a deck of cards,
Until you have no more, that wasn't very hard!
Now you know, that negative and positive you must always do,

Something special like partitive pictures, who REALLY knew?!


Cinquain: Quotative Division

Quotative Division
Quotative

Negative, positive,
Drawing, writing, thinking,

Sketching and searching for pictures,

Grouping
Chapter 2: Combining Like Terms and Distributive Property


Script:
Apple - Hey Pear, how's it going?
Pear - Oh, hi Apple. Almost didn't see you there! Anyway, It's good It's good. I'm currently working on this math problem my sister gave me.. it kind of well, struck me. i'm pretty clueless right now!
Apple - Oh? Well, let's here the question! Maybe I can help.
Pear - n+3-5n+12. Think you can answer that? Look at those.. letters! I have no idea why their there..
Apple - Oh, those are variables! We use them in Alegbra to represent a number. Don't worry, Alegbra's easy. Now, tell me. What do you think the answer is?
Pear - Hm.. -6n+15.
Apple - Let's see if you're right. You group the same terms together.. which are n and 5n. And 3 and 12. Make sure you bring the operation signs with your numbers! Next we put them together.. hm, -5n+n+12+3. -5n+n=-4n, and 12+3=15! So the answer is -4n+15.
Pear -.. Oh. But I got -6n+15? Isn't that right?
Apple - Oh! No, no. Nice try there Pear, but you always, always have to look at the operation sign! Remember I told you take the operation signs with your numbers. I think you forgot the 5n was negative and added it.
Pear - Oh, thanks Apple!
Apple - Anytime, having anymore troubles?
Pear - .. I'm so sorry Apple to bother you! But I'm really not believing you when you say that Alegbra's easy. It's pretty hard to me!
Apple - Oh, don't worry about it Pear. You'll get it soon. I promise. Now, what's the next question?
Pear - 2+4(3n+8).
Apple - Oh! That's easy. For this question, we have to Distribute the Property. Here's what I mean.. well, wait. What do you think the answer is?
Pear - 12n+10.
Apple - Let's see if you're right! You first have to multiply the number that is touching the bracket with the closest number. So, for this question.. the multiplying number would be 4. And the first number TO multiply is 3n. 4x3n=12n. Then we multiply again, using 4.. but this time multiplying TO 8. So, 4x8=32. The next thing we do, so put the like terms together. 12n+32+2. The last step is to add the numbers that can... well, be added! so, 32+2=34. The answer is 12n+34.
Pear - Wow Apple, you're so smart! I think I'm starting to get it! I know why my answer was wrong! I forgot to multiply 4 with the number 8. I just added 8 and 2 together, which equalled 10. That's how I my answer, 12n+10. Whoops!
Apple - See, I told you Pear! Algebra's easy.. to everyone who tries.

(Changed some things in the movie to make script shorter)



Harbeck! I can't add Pear's mistake, my script is too long. So, I'll just
put Pear's mistake here.

Q:2 + 4(3n+8)
P'sA: 12n + 10

(4)3n=12n
(4)8=32
2+32+12n
34+12n

Oh, and I know I spelled ALGEBRA wrong. I just can't fix it, because
I already published. That's what I get for publishing without rereading.

Chapter 3: One Step Equation Solving
Here are some Additive, Subtractive, Multipicative and Divisive Equations!

RULES:
Isolate
Cancel Opposite

Balance

Verify

Additive:

I solved this equation by drawing out the question. I drew one variable, which is the long green block, 3 constants, which are the red square blocks, and 5 constants which are the red square blocks after the equal sign. To isolate the variable, I added the opposite, which was -3 to +3. I was left with n. I added -3 to the answer (6). 3 postives and 3 negatives cancelled out each other and I was left with 2. N (variable) = 2 (constant). All I had to do was verify, which is just replacing the variable with the answer. On the other side, I did the same thing, but not using pictures. I isolated, cancelled the opposite, balanced and verified.

Subtractive:

I solved this equation by drawing out the question. I drew one variable, which isthe long green blook, 4 negative constants, which are the red square blocks, and 7 constants which are the red square blocks after the equals sign. To isolate the variable, I added the opposite, which was +4 to -4. I was left with n. I added +4 to the answer 7, which gave me 10. N (variable) = 10 (constant). All I had to do was verify, which is just replacing the variable with the answer. On the other side, I did the same thing, but not using pictures. I isolated, cancelled the opposite, balanced and verified.


Multipicative:

I solved this equation by drawing out the question. I drew two variables and 6 constants. The first thing I had to do was equally distribute the contants (6) with the 2 variable (2n). I drew the 1 variable, and put 3 constants beside it. I did the same with the remaining. I soon found out that one variable equals 3 positive contants. Then I circled each group. All I had to do was verify, which is just replacing the variable with the answer. On the other side, I did the same thing, but not using pictures. I isolated, cancelled the opposite, balanced and verified.



Divisive:


I solved this equation by drawing the question. I drew one variable, and wrote down the dividing sign and numbers. After I was finished, I took the number four and multipied it with 4 and the answer, 3. This is the way you isolate. Then I took 3 and four, which had a bracket touching.. which meant they are multipying. I multipied then together and got 12. N(variable) = 12(constant). All I had to do was verify, which is just replacing the variable with the answer. On the other side, I did the same thing, but not using pictures. I isolated, cancelled the opposite, balanced and verified.



Chapter 4: Algetile Video

During class, we were told to make a video about algebra equations using aletiles. We had to work on it at lunch, because we didn't get to finish it during class. So, sorry for the background noise! Props to: Tracy, Hanbit, and Maeddah.

Scribe Post for December 2

Today in Math Class we started ALGEBRA.
We started the unit of by thinking of ALGEBRA WORDS: ADDING, SUBTRACTING, MULTIPLYING, DIVIDING, & EQUALS.
ADDING
n+6
-increase by
-combine with
-plus
-and
-add
-gains
SUBTRACTING
n-6
-subtract
-minus
-takeaway
-diminished by
MULTIPLYING
3n (means: n+n+n)
-three times a number
DIVIDING
n/3
-means a number divided by three
EQUALS
n+6=8
-equals
-gives you
-is
-makes
-results in


We also learned the difference between algebraic expressions and algebraic equations.
algebraic expression: --> pattern
n+6
- number plus six
- there are many possible answers.
What is n?
- n is a variable
What is a variable?
- a variable is a letter that represents a number
algebraic equation:
n+6=8
-a number and six equals eight
-there is only one possible answer
Well, i'm done my scribepost. I hope you liked it! I liked it because it was very colorful :) For tomorrow's scribe, I choose MICHELLE! HAHAH :D Have fun Michelle.

The Big Book Of Algbra

CHAPTER ONE: POETRY

Haiku:

Adding Integers


Adding Integers

All together, combined, plus

Increased, sum, total.


Picture:

Subtracting Integers


Subtracting Integers.


Tanka:

Partitive Division


Partitive Division

Dividing equally

How many equals

Equally separated

Many equal parts in one answer.


Haiku:

Quotative Division

How many parts are there

In quotative division

As many as there is.


Free Verse:
The Rule For Multiplying Integers

Ron's rule says
if multiplying an odd amount of negative integers
it must be a negative product

if multiplying an even amount of negative integers

it must be a positive product.

The End

Chapter Two

Combining like terms and the Distributive Property

Tiara" hi Nicole"

Nicole"Tiara can you help me with my math homework?"

Tiara"Yeah, but if I get it wrong it's because I'm only in grade 8 and you're in grade 11!"

Nicole" Well if your gonna' be mean never mind!"

Tiara" OK OK OK I'll help you but like I said. So what are the question."

Nicole"n+3-5n+12 and 2 + 4(3n+8)"

Tiara" Ok well ummm... this is hard"

Nicole" Yeah I know"

Tiara" bye"

Nicole" You said that you would help me with my homework!"

Tiara" Well........ I changed my mind."

Nicole" I hate you"

Tiara" Fine fine fine. so the first question is n+3-5n+12 right?

Nicole" yup."

Tiara" so I guess you group the veriables and then add them so n+-5n is -4n"

Nicole" right then you do this 12+3=15 so the answer is -14n+15"

Tiara" right and the second question is 2+4(3n+8)"

Nicole" yup"

Tiara"first you times the 4 by the 3n thats 12n"
Nicole"then times the 4 by the 8 that is 32"

Tiara"then 2+32=34"

Nicole" then that is 12n+34"




Nicole's Math Poetry

Monday, December 1, 2008
Addition:
She sits at her desk watching her teacher write on the board
"What is this?!" She asks.
"Addition,Math,Subtraction!!"
Addition is so easy I can even do it in my head she thought.


Subtraction, Math,Plus


ADDITION!!

Poetry Introduction - Scribe Post for December 1, 2008.

Hi. To be really honest with you, I have no idea what to blog about today. Since Harbeck wasn't here today and everything. Whoa! I'm not saying that Ms. Hay isn't a good sub, it's just that I didn't ask her. So.. yeah. But here I go! By the way, this scribe might be filled with writing.. sorry.

In Class or.. a summary for what Harbeck said on the math page.
  • Ms. Hay told us that we have to make Integer poems, which is no surprise since Harbeck told us on Wednesday.
  • 5 Integer poems. Pick any kind you want, (from the paper she gave us).
  • Poem must be about the following: Adding Integers, Subtracting Integers, Partitive Division, Quotative Division , The "Rule for Multiplying" integers (Ron's Rule, Pratts Law, Mel's Rockpile etc)
  • You need 3 different types of poetry in Chapter One. You can do the following : Haiku, Tanka, Cinquain, Free Verse Poetry, Picture, Diamante
  • ALL DUE FRIDAY!

So, during class we started our poems. But it was SOO hard, especially if you're sitting beside the most annoying..ist? boy in the world.. : CASEY. Haha, just kidding. :) Here's one of my ROUGH COPIES. It's not a FOR SURE poem, just something I tried out.

Diamante: Diamante is the Italian word for diamond. The poetic form takes the shape of a diamond when it is completed. A diamante is a seven line poem.There are two patterns to choose from. Pattern one develops one topic. Pattern two starts out with one theme and in the middle begins to move toward an opposite theme.

PATTERN ONE:
Line 1: Choose a topic (noun)
Line 2: Use two describing words (adjectives)
Line 3: Use three action words (verbs)
Line 4: Use a four-word phrase capturing some feeling about the topic
Line 5: Use three action words (verbs)
Line 6: Use two describing words (adjectives)
Line 7: Use a synonym for an ending word (noun)

Example 1: This poem expresses one theme about a pop singing star.

Star
Famous, successful
Singing, dancing, shouting
Mesmerizing the adoring audience
Performing, working, reaching
Frenzied, dazzling
Showman

My Tryout.
Adding Integers Poem

Adding,
Problem Solving, simple
Thinking, increasing, gaining,
always trying your hardest,
receiving, completing, finishing,
Easy, fun to do,
Combining

Here are some sites that might help you guys write some poems!
Tanka:http://www.edu.pe.ca/stjean/playing%20with%20poetry/Hennessey/how_to_write_a_tanka_poem.htm
Haiku:http://www.edu.pe.ca/stjean/playing%20with20poetry/Hennessey/how_to_write_a_tanka_poem.htm
Cinquain:http://www.canteach.ca/elementary/poetry5.html
Free Verse:http://www.edu.pe.ca/stjean/playing%20with%20poetry/Hickey/Free%20Verse.htm
I can't find one about Picture Poems
Diamante: http://www.franklinlakes.k12.nj.us/famsweb/curriculum/English/diamantepoems/diamante.html

So, I guess that's it. That's all I got completed, well I mean.. this was the only 'rough copy' I had for my poems. I don't want the world to see MY REAL poems yet anyway! Haha, Good luck on your poems!
oh, and the next scribe is.. Tracy.

BTW, please comment and make corrections for me! Especially you Harbeck, if this wasn't how I was suppose to do the scribe for December 1, tell me! So I can fix it as soon as possible. Thanks. Oh, and I'm not really sure if there is a math/unit test tomorrow. But you guys should still study everything that we learned for this unit (Not Poetry)!

Bye, bye.

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