Algebra

Welcome to Algebra.  Algebra is basically split into two parts.  The Equations and Graphs.  

 Part I:  Vocabulary, Expressions and Equations.

Vocabulary

 Remember -- Math is like a whole other language.  You have to know the vocabulary to be able to make your way around the problems.  I sent you home with the Vocabulary Quad sheet.  I hope you put it in a place where you look at it daily.


Order of Operations (PEMDAS) :

 Here are some videos and sites that might help you with Order of Operations (PEMDAS):


Don't forget to also check out the "Helpful Math Sites" box on the Home page.  Khan Academy also has some great videos you can watch and replay as much as you need to.
  

Solving Equations

 Remember, the difference between the expressions we have been working with and the equations we are just now beginning is that equations have an equal sign (expressions don't) and must stay balanced on both sides (of the equal sign).  

 To solve equations, remember that you must:  

 1.  Use the opposite operation to isolate the variable.     

 2.  keep both sides of the equal sign balanced (equal).  This is often done by:         

 3.  "If you do something to one side, you must do it to the other side."

 One step equations:

Two Step Equations

 Inequalities:  the steps to solving inequalities are exactly the same as the ones for solving equations. 
  • Only two things change between equations and inequalities:  
      1.  the symbol  -    > , < , > , < ) --- not an = sign.
      2.  the variable you are solving for is no longer just ONE number, it is a range of numbers           

 Remember:  
the  >   and  <   will mean an open circle on a numberline
the   <   and   >   will mean a closed circle on a numberline

 Here are some examples of how inequalities are graphed on a numberline.  (scoll down a bit when you click on the link)

Reading Graphs.  Vocabulary to know:  concrete, discrete, increasing, decreasing, constant, rapidly, slowly, gradually.  

 This link has examples of Discrete and Concrete graphs.  It also has graphs with matching situations.  The pictures are small but the info is good so I would increase the magnification on your computer.
Part II:  Graphs.

All numbers have relationships.  One way to show these relationships is to use functions to create ordered pairs (x, y).  Then, those ordered pairs can be placed in a table, mapped or graphed.

***  The Domain is always the x value.  The Range is always the y value.***

 Functions:  Vocabulary to know -- domain(x), range(y), input(x), output(y), independent(x) and dependent(y), ordered pairs (x, y)




Here is what Math Is Fun has to show you about Functions.  And some more here too.

 This link has an example of taking input(s), putting them through a process (function machine), to create outputs.  And here is another one from Pearson.

 Here is a video by Pearson modeling a function 3 ways.

 How to tell if the ordered pairs really make a function by using the Vertical Line Test

This a video that shows you another way you can be asked to find the Domain(x) and Range (y) by evaluating a function.  


Graphing Quadratic Functions
Here are some good examples of what "Systems of Equations" is and some examples of how to find a solution to given systems in a variety of ways.  The two we will focus on in class are Solutions by Graphing and Solutions by Substitution.
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