Why does an inequality with "equal to" need a closed dot rather than an open one? If an inequality has a greater than or equal to sign then it has to have a closed dot on the number line. If it wasn't an equal to problem, then the dot would have to be open because say there is a rule for Disneyland and their tickets on how you pay. 
     The toddler tickets, which are for toddlers three and under, then there are the kids tickets which are from 3-7. There's also the adult tickets, which are 7 and older. Which means if this were on a number line then because the children tickets are from three to seven it's not including 7. The adults are ages from 7 and higher, which means children tickets are ages three and higher. 
    For example, you take the children's age tickets which only count the ages 3-6 because once your seven it counts as an adult age. There is a number line then the three would be colored in because it's counting that age and forward until 7 but seven would not be colored in because that's part of the adult age.

     What is my favorite way to solve a problem? First, I like to understand what I'm doing. Then, I follow the easiest way to solve it. After that, I do the easiest step first, then when I get to the more hard parts I take my time and make sure I do what I'm supposed to do. When, I'm done I like to check my work and make sure I got it right. Unless it's an easy problem, in that case I just solve it and move on to the next one.
     Sure once in a while I make mistakes, but it's ok. I learn from my mistakes and then with that knowledge I learn not to do it again. If I don't quite understand the problem, then I ask for help. If I still need help, then I practice until I understand the subject.

     Why is it that division never really existed? When you divide fractions, you're not actually dividing, you're multiplying. When you divide fractions, you have to change one fraction so that it's denomenator is on top and the numerator is at the bottom. Then instead of dividing, you multiply because once you divide by a fraction you are going to get a smaller number no matter what. Since, a fraction is ony part of a number you have to see how many times that part goes into the whole number, which will take a while.

      Why are there infinite numbers between 0 and 1? Between 0 and 1, there are a whole bunch of numbers that we don't even know about. The decimals and whatever comes after it are infinte and could never end. If every number had pi at the end for a decimal there would never be and ending number, which makes the numbers between 0 and 1 infinite. Of course, all numbers are rounded so there won't be such a long number. Say we have a number like 25.3269. we would round that to the tenths place and we would get 25.3. The 2 isn't bigger than 5 so that means we have to round down and leave it the same. There are numbers that just keep on going on and on and on.

    You may wonder: Why does the denominator get bigger as the decimal gets smaller? The answer is, it doesn't get bigger, it equals the same. Once you convert the fraction into a decimal it seems bigger, but it's not. Let's say we have 1/2, that's going to equal .5, 1/2 equals .5 and when there is a problem to divide and it says like 6 divided by 1/2 your going to have to divide it by .5. Once you do that then you get your answer and it would be the same as if you did it with the fraction, because half of six is three. Only the numbers are changing but they equal the same. Let's take another problem, say we have 25 divided by .5, that's going to equal 50. The .5 is only part of a number, it's not the whole, or entire thing. That's why .5 goes into 25 50 times.

     In math, we are learning how to express variables. We have an equation and we have to solve for x, the variable. We have the answer to the equation then we go backwards. Say we have (x-3)*5=25, then we would work backwards and then start off at 25 then do the associative property and divide it by 5. Then, we add three because we are still doing the associative property. We have barely started this today.
     Last week, we were doing things like how to do an equation, with patterns. Say we had a square, and it grew bigger each time. Each time, we would be adding four because a square has four corners and we have to make the shape bigger each time. So, then we would be adding four sticks or whatever the square is made of each time. Then we would have to come up with an equation like 4s=f. which would mean every time you add sticks it would equal one figure. If the pattern would continue going the next one would be 8s=2f, but since we're trying to simplify it 4s=f would be the answer.