**In Pre-Algebra, we did...**

## Tessellations

Tessellations are a kind of art style that deals with shapes. I think that Mr. Dorman chose us to do this because it relates to shapes or geometry. He had us make a stencil out of a rectangle, and then we had to trace it over and over on a blank sheet of white paper, and had us color it in 2-3 colors.

Although it looks fun (and it is), you had to make a shape that can fit with one another. Look at the picture. Notice how the shape repeats itself and there are no gaps? We needed to make it fit like a puzzle, so that it creates a pattern that seems to go on continuously. The process in making this was not really hard. Like I said before, the only thing you needed to worry about was making sure the shape fits like a puzzle to one another, no gaps or open spaces. This project was a success, and it was something that I really enjoyed.

Although it looks fun (and it is), you had to make a shape that can fit with one another. Look at the picture. Notice how the shape repeats itself and there are no gaps? We needed to make it fit like a puzzle, so that it creates a pattern that seems to go on continuously. The process in making this was not really hard. Like I said before, the only thing you needed to worry about was making sure the shape fits like a puzzle to one another, no gaps or open spaces. This project was a success, and it was something that I really enjoyed.

## Solving Inequalities

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Solving inequalities is one of the hardest math units I've ever learned. I was always confused about it, not sure when or where to divide or multiply. Funny thing is, when I explain it, I feel like I know it all.

The first step is to multiply or divide the equation. For example, "4x > 8." Since we need the variable by itself, we need to divide 4x by 4x and 8 by 4x. 4x divided by 4x is 0, so then cross it out. However, 8 divided by 4 is 2. So now your equation is "x > 2." When you graph it, make sure that the dot is a closed dot, since ">" means greater than.

The first step is to multiply or divide the equation. For example, "4x > 8." Since we need the variable by itself, we need to divide 4x by 4x and 8 by 4x. 4x divided by 4x is 0, so then cross it out. However, 8 divided by 4 is 2. So now your equation is "x > 2." When you graph it, make sure that the dot is a closed dot, since ">" means greater than.

## Equations with Variables.

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In Mr. Dorman's class, right now we are learning about solving equations with variables in both sides. For example, 34n-6h=?. We are also learning about greater than, less than, greater or equal to, less or equal to, and equal to. We've already learned about decimals, and adding up fractions, which are pretty easy to me, but the problem for me is learning about solving equations with both variables on each side.

What I mean is, equations with variables on both sides, for example 3+4n=5n-4. The first step is to get rid of the variable. So in this case, subtract 4n on each side. On the left it should be 4n-4n, and on the right it should be 5n-4n. Since 4n-4n is 0, you cross it out because it isn't any of good use. Since 5n-4n equals 1n, then you use 1n. Second, you turn the problem into an equation. Since you no longer have 4n, the equation should be 3=1n-4. Then you subtract 4 on each side. On the left, 4-4. On the right, 3-4. 4-4 is 0, so you cancel it out. However, 3-4 is -1, so you keep it. Now you only have -1=5n. Here is where you use the basics. Divide 5 by 5n and -1, then after that, your answer should be -0.2. Then check your answer to see if it's correct, and when your done, congratulations! So this is how you solve equations with variables on both sides.

What I mean is, equations with variables on both sides, for example 3+4n=5n-4. The first step is to get rid of the variable. So in this case, subtract 4n on each side. On the left it should be 4n-4n, and on the right it should be 5n-4n. Since 4n-4n is 0, you cross it out because it isn't any of good use. Since 5n-4n equals 1n, then you use 1n. Second, you turn the problem into an equation. Since you no longer have 4n, the equation should be 3=1n-4. Then you subtract 4 on each side. On the left, 4-4. On the right, 3-4. 4-4 is 0, so you cancel it out. However, 3-4 is -1, so you keep it. Now you only have -1=5n. Here is where you use the basics. Divide 5 by 5n and -1, then after that, your answer should be -0.2. Then check your answer to see if it's correct, and when your done, congratulations! So this is how you solve equations with variables on both sides.