### The Great Big Book of Algebra

Thursday, December 4, 2008
Chapter 1: Integer Poetry

Adding Integers: Cinquain Poem

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

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. 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!