
INTRODUCTION TO GEOGEBRA

In order to play with these interactive GeoGebra modules you will need to make sure that you have the Java Plugin installed. If you don't have the plugin installed you will not see the interactive module below. If you don't see the interactive module below download the Java Plugin here. Once the Java plugin is installed restart your browser and come back to this page and will see the GeoGebra module below.
PLEASE READ THE FOLLOWING:
To see some of the features that you can control in a GeoGebra module see my video here. Even though the video deals with the toolkit functions there is plenty to learn about how to interact with any GeoGebra module.

DEFINITIONS AND IMPORTANT IDEAS

PEMDAS is an acronym that represents the order in which an arithmetic expression is to be evaluated. When evaluating an arithmetic expression you evaluate parentheses first, exponents second, multiplication third, division fourth, addition fifth and finally subtraction. If you have multiple operations of the same type you are to work from left to right until you complete all the operations of the same type.
Variable_{defintion}: in the game of mathematics it is a letter of the alphabet that can be replaced by a number.
Monomial_{defintion}: a number, a variable, or a number times one or more variables.
ex. 1) 2 is a momomial since 2 is a number 
ex. 2) x would be called a monomial since x is a variable. 
ex. 3) 5x would be called a monomial since 5x is a number times a variable 
ex. 4) 2x^{2} would be called a monomial since 2x^{2} = 2xx and 2xx is a number times one or more variables. 

ex. 5) 2xyz would be called a monomial since 2xyz is a number times one or more variables. 
Coefficient_{}_{defintion}: a number that is multiplied by one or more variables.
ex. 1) 5x
5 is the coefficient
nj 
`ex. 2) 7xy
7 is the coefficient

ex. 3) (2/3)x^{2}y^{5}z

2/3 is the coefficient

Term_{defintion}: any "part" of a "math expression" that is being added or subtracted.
ex. 1) 2 + 5
2 is a term
and 5 is a term. 
ex. 2) 7  11
7 is a term
and 11 is a term.

ex. 3) 4x  3y
4x is a term
and 3y is a term.

ex. 4) 3x  6x + 5f
3x is a term
and 6x is a term and 5f is a term. 

ex. 5) 3x + 2y  8f + 2n
3x is a term
and 2y is a term and 8f is a term and 2n is a term.

Like Terms_{defintion}: two or more terms that contain the same variables raised to the same power. Only the numerical coefficients can be different though they could be the same.
comment:
Pure numbers are considered like terms.
ex. 1) 2 + 5
2 and 5 are like terms because they are both pure numbers. 
ex. 2) 7x  11x
7x and 11x are like terms beause the variables are the same and the powers of the variables are the same.

ex. 3) 4x^{2}  3x^{3}
4x^{2} and 3x^{3} are not like terms.
The variable x is the same in each term but the powers are different.

ex. 4) 3f^{2}  6f^{2} + 5f^{5}
3f^{2} and 6f^{2} are like terms. 

ex. 5) 3x^{3} + 2y^{2} + 1x^{3} + 5y^{2}
3x^{3} and 1x^{3} are like terms and 2y^{2} and 5y^{2} ^{} are like terms.

SUBTRACTION TO ADDITION RULE
ALL SUBTRACTION CAN BE REWRITTEN AS ADDITION
a  b = a + 1b
IN ENGLISH
Change the operation of subtraction to addition
then multiply the term that followed the subtraction by 1. 
ex. 1) 5  3
can be rewritten as
5 + 1(3)
which means
5 + 3 

ex. 2) 3  8
can be rewritten as
3 + 1(8)
which means
3 + 8 

ex. 3) 7x  18x
can be rewritten as
7x + 1(18x)
which means
7x + 18x 
ex. 4) 7x  18y  9x  10y
can be rewritten as
7x + 1(18y) + 1(9x) + 1(10y)
which means
7x + 18y + 9x + 10y) 


ADDING AND SUBTRACTING TERMS RULE
LIKE TERMS CAN BE ADDED AND SUBTRACTED 
HOW TO ADD OR SUBTRACT LIKE TERMS
step 1) Add or subtract, depending on the operation between the like terms, the coefficients of the like terms
step 2) Multiply that result in step 1) by the VARIABLE PART of the like terms 

HOW TO USE THIS MODULE

Step 1) On the first line of your paper, write down the algebraic expression ax + bx + cx on a piece of paper
Step 2) Choose values for the variables a, b and c by moving the sliders for a, b and c in the GeoGebra module.
Step 3) On the second line of your paper, write down the values of the variables a, b and c on your paper.
Step 4) On the third line of your paper substitute the numbers into the variables
of your algebraic expression. You will now have 3 like terms!
Step 5)
On the next line of your paper, start adding the like terms using PEMDAS. ONLY DO ONE STEP OF PEMDAS AT A TIME!
Step 6) After each step click your mouse in the "check box" to reveal whether you did the process correctly.
Step 7) If you make an error and cannot understand WHY you have an error ask you teacher WHY you did PEMDAS improperly.
Step 8) Once you finish, click the reset button, , in the upper right hand of the GeoGebra module and the module will be set to the original state. Now you can choose new numbers for your variables and go through the process once again.
Comment: Make sure you number each problem that you do. The first problem that you do is to be labeled 1, the next problem 2, so on and so forth.
MODULE BELOW:
