Welcome To My Blog (This is the blog of Scholar Sedariest Hammond.)

I would like to welcome all students, teacher, parents,and others to my blog. This blog gives you help on certain topics of 8th grade pre-algebra and other topics of 8th grade math. Here is a list of Georgia performance standards that I have addressed: M8AN1 Elements: g.,j.
M8A2 Element: c.
M8A3 Element: c.
M8A4 Elements: c.,d.
M8A5 Elements: b.,c.
M8G1 Element: a.,b.
You can also find this list in the archive to your right, but they are not in the order that I have just given you. I advise everyone to take notes, frequently.
Now, 8th grade math can be a challenge for you and others but with a little practice you can conquer it.
 The creators drive:
This was a math project that I thougt went well. I believe my explanations went well. Also I heavily encouraged the students. My math teacher, Ms. Crew, was the foundation in order for me to greatly explain to you. So I hope you enjoy. Oh, and please post comments about the blog under an element.   (If you want to learn alittle about me read my short autobiography.)

M8A5 Element c.

This states graph the solution set of linear inequalities in two variables. Now in inequalities all you have to do is choose a test point or a pair of coordinates and plug them into the inequality. If the final statement is false then shade the opposite region but if it is true shade that region. Here is a video explaining: http://www.youtube.com/watch?v=7sInE5tGJX4&feature=player_detailpage.

M8N1 Element j.

This states express and use numbers in scientific notation. This is a pretty simple topic of pre-algebra. If they give you a big number that number is in standard notation. All you have to do is move the decimal. The decimal is on the end. What you do is count the spaces until you get to the first number and the decimal should be after the first number. Then you put that decimal number times ten to the your exponent. Now your exponent will be the number of spaces that you counted. Here are some laws of scientific notation:
1. The number in front of the decimal should be one or greater no less than and it should be LESS than ten
2. The base of the exponent should always be ten and the exponent should be the number of spaces that you counted.
3. The exponent should be positive if the numbers are in the back and the exponent should be negative if the numbers are in the front.  Here is a video explaining more: http://www.youtube.com/watch?v=QZW39OTQEg8&feature=player_detailpage. Here is a video explaining how to put the number back into standard notation: http://www.youtube.com/watch?v=Hqok8UyyUXA&feature=player_detailpage. Here is a final video on negative scientific notation exponents: http://www.youtube.com/watch?v=iOPRM0VXo08&feature=player_detailpage.

M8N1 Element g.

This states simplify, add, subtract, multiply, and divide expressions containing square roots.
Now this is simple first you need to know how to break down a radical. All you have to do is use the factor tree and  give two multiples and break those down until they can't be simplified any more then you circle your pairs. If their is one pair you bring one number from the pair out and then multiply it by the number that was originally out side the radical If their is no number their then we know it represents an invisible one. After that you put the paired number outside the radical then the one that did not pair up it goes inside the radical. If theirs more than one number that did not pair up then you multiple those together and put the product inside the radical. Now if their more than one pair then one number from each pair drops out those are multiplied and by the number that was originally outside the radical. Here's a video explain more:  http://www.youtube.com/watch?v=ucnKcrg5TrQ&feature=player_detailpage.
Here is a video explaining radical expressions: http://www.youtube.com/watch?v=fHAO7xkXz6k&feature=player_detailpage. After you have watched the video you have just seen another way to break it down it does not matter whether you do it that way or the way you just saw in the previous video.

M8G1 Element b.

This states apply properties of angle pairs formed by parallel lines cut by a transversal.
There is some vocabulary to remember here, so here is a video explaining it: http://www.youtube.com/watch?v=mMIP1d3nnSc&feature=player_detailpage.

Now finding the measurements is simple as well just watch this video: http://www.youtube.com/watch?feature=player_detailpage&v=Ij8AotZHfzU. After you have watched that I wanted to state something not all questions will give you the measures some will only give you one angle measure but based on the info. you just learned you can figure out the other measures. In some cases they will give you  equations to find the angle measures. All you have to do is solve this like you would solve two equations in y-intercept form. Then when you got your answer you would substitute back in the original equations to find the measures and from your prior knowledge you would find the others.  

M8A3 Element c.

This states distinguish between relations that are functions and those that are not functions.
Okay their is major vocab. dealing with this subject. Like domain the first number in the ordered pair otherwise known as x or independent variable. Then theirs range or the second number in the ordered pair otherwise known as y or the dependent variable.
When they say relation in pre-algebra terms they mean a set of numbers with repeating domains.
Function- the domain does not repeat.
Look at this {(9,2),(9,7),(9,3),(9,1)} This is a relation because what is repeating the x right which is 9.
Now it does not matter if the y repeats itself, only the x. If the set of coordinates uses the same number for a the x more than ONCE  it is a relation.
Now look at this {(0,1),(1,2),(3,4),(5,8)} This is a function because the domain does not repeat.
In other words if we were to graph the coordinates and do a vertical line test and if the vertical line hits that figure more than once its a relation, but if it hits the figure once its a function.
ex.:   This is a relation because the vertical line hits the figure more than once, and the coordinates domains repeats.
This is a function because the vertical line hits the figure only once and it coordinates domains do not repeat. (Don't let linear and non-linear lines confuse you.)

M8G1 Element a.

This states Investigate characteristics of parallel and perpendicular both algebraically and geometrically.

First I will show you geometrically:

Now the one to your left is perpendicular and the one to your right is parallel.

The perpendicular one has only one solution that is the point of intersection or where they meet. Also their slopes are negative reciprocals of each other. So lets say the slope is 6 the negative reciprocal of that is -1/6, because 6 is like saying 6/1.

The parallel lines have no solutions but their slopes are identical or the same.

Remember these things as I am about to explain this algebraically.

Say for instance you have your system and they are in slope y-intercept form:

y=5x-2,y=5x+3 The lines will be parallel because their slopes are the same AND THEIR Y-INTERCEPTS ARE DIFFERENT.  For if they have the same slope and y-intercept it is one line and the solution set is infinite, but this does not apply for perpendicular lines. Okay, you have

y=-5x-9, y=1/5x-9 it is perpendicular because the slopes are negative reciprocals of each other, and making one solution. In some cases you with have to rewrite to figure out what they are.

M8A4 Element d.

This element states graph equation from standard or ax+by=c.
The main thing that you want to remember is you can't graph from standard or ax+by=c form. To graph you would have to rewrite the equation to slope y-intercept form  and then graph. So lets say they give you
2x-2y=10, you would subtract 2x from itself and ten to get y alone. After that your left with-2y=-2x+10, then you would divide -2 by all sides to finally isolate y and to get into your final answer y=x-5.
 2x-2y=10
-2x           -2x 

-2y=-2x+10

-2    -2   -2
y=x-5              The x represents an invisible one when you divided negative two into negative two.
                       We did not subtract -2x from 10 because they are not like terms. Now we graph starting at out y-intercept and rise 1 and over 1 because the x is like saying 1/1 or 1 over 1. (Note: When you graph make sure the direction of the line is correct. If the slope is positive it should come down from the first quadrant or from your right. If its negative it should come down from the second quadrant or your left.)

M8A2 Element c.

This states graph the solution of an inequality on a number line. When we talk about the solution we're talking about what satisfies that statement. Here is a vedio explaining how to do it:  http://www.youtube.com/watch?v=y81YtBL1Q40&feature=player_detailpage. Sometimes the statements have and or the word or in it this is called a compound inequality. http://www.youtube.com/watch?v=xOPFNDmBCKU&feature=player_detailpage. Now what yo have just seen is an example using or and is much different as I will show you. Say if they give you x<3 and x>o here's how you do it:


We  connected them because the any where that we shaded satisfies the statements. We have a dark circle over zero because it has an equal to sign under it. There is a open circle over 3 because it does not have and equal sign and to show it is not part of the solution set.

M8A5 Element b.

This element states solve systems of linear equations algebraically and graphically.
Now when they say a system of linear equations were talking about two or more equations. In both equations what ever two variables are given we have to solve for both either using elimination w/multiplication or plain elimination or substitution. Then when we get those solutions those are the coordinates and we just substitute back in to find out weather those coordinates are correct. When they give you a choices of coordinates on a test instead of going through a lenghty process just substitute back in to figure out which one is right. Here is how you solve with just plain elimination, Watch this: http://www.youtube.com/watch?v=xB-oXaCoJoc&feature=player_detailpage. Here is how you do it with substitution: http://www.youtube.com/watch?v=KNwwu5wjcaA&feature=player_detailpage. Now after you have watched that listen to this if the first equation is not in y or x intercept for you have to rewrite to get it there.
Say for instance you have  10x-5y=5 well this is simple all you have to do: 10x-5y+5
                                                                                                                -10x      -10x
                                                                                                                -5y=-10x+5        
                                                                                                              -5        -5    -5
                                                                                                               y=2x-1
We subtracted 10x because we wanted to isolate or get y alone. We can't subtract -10x from five because
they are not like terms. Then we divide -5 by all sides to finally isolate the y. Now check out solving with muliplication: http://www.youtube.com/watch?v=Q37XBPSgisM&feature=player_detailpage