Solving One-Variable Linear Equations

Solving One Variable Equations: 

"Linear equations are equations with a plain old variable like "x" rather than something more complicated like "x^2"

You've probably already solved linear equations; you just didn't know it. 

When solving a one variable equation, you need to "undo" whatever has been done to the variable. 

 A solution: a solution to an equation is a value or set of values that makes the equation true. 

For Example in the Equation: 

x + 2 = 3

the solution is x = 1, because 1 + 2 = 3. 

Lets Review: Additive Inverse: 

An additive number is something you add to a number to make it equal 0. 

2 + (-2) = 0

5 + -5 = 0

Multiplicative Inverse: 

A multiplicative inverse is something you multiple by another number to equal 1. 

2 X 1/2 = 1

You do this in order to get the variable by itself; in technical terms you are "isolating the variable."

For Example: x + 6 = -3

You first want to get the x on the left side by itself. So you will subtract the 6 to the right side. So now the equation looks like x = -3 - 6. So now we solve for x. -3 - 6 = -9. So x = -9.

Whatever you do to an equation,
do the   S A M E   thing
to   B O T H   sides of that equation!

Example: x - 3 = -5

Since you want to get x by itself, so you want to add 3 to both sides. 

x - 3 = -5

+3 = +3 

x = -2

Then the solution is x = -2. 

Lets solve this equation: 3x + 6 + 4x = 13

First we need to combine like terms: those terms are the 3x + 4x = 7x. 

So now the equation look like this: 7x + 6 = 13

So now to get the variable by itself we need to subtract the 6 from both sides. 

So we get 7x = 13 - 6

7x = 7

now we divide by 7 to get x by itself to both sides. 

So x = 1. 

Now we need to check our work

3 (1) + 6 + 4 (1) = 13

3 + 6 + 4 = 13

13 = 13. 

Therefore the solution is x = 1. 

Lets solve this equation: 3 - 5x = 18.

First we need to move the 3 to the other side to get x by itself, so lets subtract the 3 from both sides.

-5x = 18 - 3

-5x = 15. 

Now we need to divide by the -5 to get x by itself. 

x = 15 / -5

x = -3.

Now we need to check our work so we plug x = -3 back into the equation. 

3 - 5(-3) = 18

3 - (-15) = 18

18 = 18. 

Therefore the solution is x = -3. 

Oder of Operations

Order of Operations: 

What is the answer to this ? 4 + 6 x 2 =

Did you get 20?

Can you see how the answer could be 16?

There are two possible ways to figure out this problem. 

          Do the addition first :                                                 Do the multiplication first: 

                4 + 6 x 2 =                                                                                  4 + 6 x 2 =

                    10 x 2 =20                                                                                  4 + 12 = 16

Which is it? 

Both answers can't be right or we would always be arguing to the answers of math problems. The nice thing about math is there is always just ONE answer. 

So a long time ago mathematicians decided to make a set of rules for what to do first in a math problem. 

The rules are called the Order of Operations!

which is abbreviated by PEMDAS.

The P in PEMDAS stands for "parenthesis"

Parenthesis in math are used to group important things together, so you always do them first. 

For example: 

 Do inside the parenthesis first:

Here's another Example: 

 In this problem we have to do paranthesis first then exponents then division.

The classic sentence that math geeks have been using for years to remember the Order of Operations (PEMDAS) is: 

Please Excuse My Dear Aunt Sally

Can you think of a sentence to go along with this acronym?

Murder Mystery- Geometry Game

After a lesson on shapes, angles and measurements i will put my students to the  test with a fun interactive game called Murder Mystery. This game will get the students up out of their seats to find clues and find who the suspect is. This game is kind of like the board game clue, students have to search through clues to find the murder.

Geometry Game- Murder Mystery: 

The Scene: The police are called to a high school, lying on the floor in the library is a dead student. As police search the library they find 5 clues written down by witness. They have sent the clues to you to decipher. They also provide a list of those present at the time of the murder. (This list is all the students in the class,  with specific details on each of the students). There are 32 suspects, each clue will eliminate half the number of suspects remaining. When all clues have been solved the suspected person will be revealed. 

Clue One: Get into Shape:

The answer to each number is a letter A=1, B=2, etc. 

1. Total number of sides of all four squares.

2. An octagon has ? sides. 

3. A square based pyramid has ? vertices. 

4. A pentagon has ? sides. 

5. A parallelogram has ? sides.

There are many more questions about 20 but I'm just giving you an example of questions you can ask. 

Clue Two: Look From a New Angle: 

I will provide the students with different kinds of angles and they will have to figure out the angle measure of each line. By the same system as above a = 10 degree, b = 20 degrees, and so on. 

For example: 

The rest of the clues also have to do with things the students learned from this particular lesson, they will have a clue on compass/directions, and also coordinating points on a plane. The last clue i will give them a story and they will have to find the error that is wrong in that story to find the suspect. 

I got this idea from another teacher but put my own spin on it, I will use my actually students as the suspects and I will let them choose if they wanna work together or not. None of the students will know who the suspect is until the game is over. This gets them up and moving around and also has them use their ipad's for clue number two. The story I also provide them with will also be available on their ipad's so they can see if they can spot what doesn't belong in the story. I have never done this game before but am looking forward to trying it in my classroom one day. I think this game can be for any grade and for any subject. The teacher just needs to have fun creating the questions, and the students need to have fun trying to figure out the clues. 

Welcome to my Technology Mathematical Educational Blog

This is a blog that I have already created to enhance students knowledge about specific topics in Discrete Mathematics (also know as Calc 4). I will be incorporating technology into my classroom also so many of my posts will be ways to incorporate technology into the mathematical classroom. I will be sharing different lesson plans, activities and my thoughts on certain math topics. Can't wait to hear feedback from my fellow classmates about incorporating technology into the classroom. At the rate technology keeps improving, we as teachers need to find new ways to keep up with the students and make learning more interesting to them.