Well from what I've searched, I think that the canned Mountain Dew is a better deal than the liter Mountain Dew. I used the "percent of changes" method to solve this.
        In my search, the canned Mountain Dews were worth $15.99, while a liter Mountain Dew is worth $21.99. First , all I did was decide if it was a decrease or an increase, and in this situation, it is a decrease. Next you have to subtract $21.99 - $15.99, which equals $6.00. Then you have to create a ratio from the difference and the original amount, which is the bigger number. so the ratio would be $6.00/$21.00. Then you divide $6.00 by $21.00 to find the percent. When you find the answer, if it's reaches over 3 decimals, then stop at the third decimal (Example: .789). Then you have to skip two numbers to make it a percent (Example; 78.9). After that, you should round to the nearest whole number, which makes it an official percent, or you can just leave it as it is so it can be an extended percent. 
         There are also many non-mathematical reasons why you should prefer canned Mountain Dews over a liter Mountain Dew, but thinking mathematically could help a lot too.

     It's a new quarter. and also a new year! Many things have happened last year and during Winter break, which means that it's all in the past now. However, that doesn't mean that we can just forget the struggles from last year, because some how in some way, they can be useful for anything and anytime.
     The thing that I remember most about math is mostly all my mistakes. I remember that I had trouble with the Pythagorean Theorem, and also had trouble with remembering the properties. I remembered only the Commutative Property. It was a very big mistake, because since I forgot, my scores for my test weren't very well. Once, I asked Mr. Dorman for a hint, and he said, "Think Distributive Property." I was in a very big pinch, because  I couldn't remember what Distributive Property was. I ended up getting a "B" on that test because I missed two out of a total of 10 questions. I know that a "B" isn't really that bad, but I wanted to improve myself better, and to get a straight "A" instead of a "B." 
     That taught me to not forget the basics, and instead, to practice and study them, because you never know when there's a moment where you will need to review them. This goes out to all the things you've learned.

          I'm not sure if this is a concept, but I've struggled a lot with math word problems. When I was little, I understood math problems easy, because the teacher had a chart on the wall that shows key words to figure out the operation. However, now since I'm in 7th grade, I've been having trouble on figuring out how to find the missing variables and the property and operation.
         Today, word problems are starting to get easier, and I've been getting it little by little, however I'm still getting stumped. My dad helped me out a bit, and thanks to him I get it a bit more. I notice that I've been only paying attention to the numbers instead of the words, but many people say that it's a common thing. I think I could improve by highlighting or circling the key words and numbers, and reading it thoroughly instead of just skimming through it for numbers. I should also mentally ask myself what is it that I need, and what should I use for it. Word problems aren't always easy a you get older, so I think that I should act now before I get really mixed up.

      The Pythagorean Theorem is a way of finding different sides of a right triangle. The theorem will not work on anything else. It can be used for many reasons, whether it's funny or whether it's serious.  
        One serious situation can be when you want to know the distance. For example, you are on a beach and you want to know how many miles will it take on sand or sidewalk to walk to the nearest restaurant. The sidewalk is a few yards in front of you, and you're on the sand. Both lead to the nearest restaurant. Which way will be quicker?
         The only funny thing I could think of using the Pythagorean theorem is having your favorite cartoon, celebrities, or characters in it. It's not very funny, but it makes it bit more enjoyable. For example, Bugs Bunny wants to visit Donald Duck at the park. Bugs Bunny is thinking of taking the taxi or the bus. The bus travels vertically to the park while the taxi travels diagonally. We already know that the bus takes about 3 miles per hour, and the park is 8 miles away from Bugs' house. How many miles does the taxi take?
       The Pythagorean theorem has many situations where it can be used seriously, or jokingly. Even though mine weren't great, you could make your own situation for a brother or sister. Have a good Monday!
      

    The reason why a positive raised to a negative is less than one, is because..well it's negative. Negative numbers are always before 1, which is why there is -9 or -3. Positive numbers and negative numbers are opposites of each other, and they have difference and similiarities. 
      In pre-algebra, we learned 2 forms. Standard and Scientific. The exponents' power were negative numbers, which made a big difference, because this time, we had to move the decimal to the right, and when the power is positive, then we move it to the left. I realized that the problems always used the number "10." I asked Mr. Dorman why, and he said that it was because in Science, they mostly focused on the number 10. It was a bit odd for me, but I'll accept it.
      Raising positives to negatives can be confusing for a lot of people, especially for me. However, when you think about it, it's really easy.

        Exponents are numbers that shorten numbers. Like 45. 45 means 4x4x4x4x4. So basically, it's a shortened version of that kind of equation.Exponents can be used to speak mathematically. It would sort of be annoying to say, "Four times four times four," all over. So instead, use an exponent. People usually say an exponent like, "Four to the fifth power." 
          I've seen exponents everywhere at least once math sheet ever since 3rd or 4th grade. At first, they were pretty tricky, but then after a while, it got easier. These days, I almost never see an exponent anymore. All I see on my math sheet are variables, inequalities, fractions, word problems, and decimals. 
         I'm not very sure when an exponent should be used, because the only thing I can think of that it should be used is math. There are definitely many ways to use them, but I guess I will just have to figure out on my own.

   

    Square roots are another word for exponents with a 2 (Example: 3 to the 2nd power). Now what makes square roots, square roots? That's what we're going to find out. 
       In my opinion, square roots are the easiest exponents. All you have to do is just multiply the same number together. So if the problem is 3 to the 2nd power, then all you have to do is multiply 3 times 3, which equals 9. I think square roots are called square roots because when you do the math, it's similar to finding an area of a square. A square has four equal sides, so if two sides of a square is four, then that means that all sides of the square is four. So when you multiply 4 x 4, which equals 16, then the shortened version is 4 to the 2nd power. 
        A possible name for a square root is "double time." I chose that because since 4 to the 2nd power means 4 x 4, then it basically is a double being multiplied. It's not the best name, but it is a possible name. 
        Square roots are very easy to figure out if you know exponents well. If you keep on working on exponents, then you can probably figure out more than square roots!

     To be honest, this game wasn't hard at all. Sure, it needed work to be shown, but it was just basic math. I played the game 3 times with decimals, integers, and money. If I had to choose which one was more difficult, it would be integers. 
      With decimals, all you had to do was just line them up and subtract, same with money. Decimals and money are basically the same thing. Integers, however, require more work. You have to change the operation to its opposite, same with negative or positive integers. If it had a bit algebra, then I would've used more time to work it out and solve it. The game was a bit fun and entertaining, but I think it's suited more for 5th and 6th graders rather than 7th graders.

       There are 2 different dots in inequalities. A closed dot and an open dot. Some people wonder why we have them. Well now here's the answer!
        A closed dot is used when it doesn't include that value. For example, if you have  "4 > x" we would use an open dot at 4 because 4 can not be included since it is greater than or equal to. We use a close dot when something is greater. lesser, or equal to somthing. Like "4 > x." Basically. you use a closed dot when it's just less than, greater than, or equal to, and open dot when it's just less than or greater than.

   Everybody has their different ways of solving math. Some count their fingers, others use calculators, and some people can even do it all in their head! Here are some ways of how I solve math.
         For me, it depends on the problem. If the problem is big, then I show my work. However, if the problem is small or basic, then I can do it in my head. For example, 39,874x234 is a big problem, but 6x9 is basic. You should  know right away that 6x9 is 54, since you learned it ever since 3rd grade. However, you can't just do 39,874x234 in your head, and even if you did, your mind will feel jumbled and get it wrong. Unless your a super smart person like Albert Einsten. Most equations like variables include doing your work. For example 3n-5=21. It's possible that you can do it in your head, but a better idea is to show/do your work.