Math Blogs

06/10/2013

Writing about math was a mixed experience for me. On one hand, I like math, and writing helped me further define my understanding. On the other, some of the math posts were much too easy and I couldn't write the required amount without being redundant. Some posts even didn't apply to me, such as struggles in math. For those, I just picked a topic at random and explained it. Math blogs are a good thing, but I think the blogs should be better designed to suit the requirements.

I did know that the standards are changing to what is known as Common Core. In my CORE class, we took a practice version of what the CST's may look like next year. In my Algebra class, we talked about how geometry may be replaced with "Source 1" or something else like that. I hope that the Common Core writing will help me as much as the blogs did, but I hope the subject will be more in touch with the requirements.

Challenges

06/10/2013

In math this year, there weren't very many challenges. The one time was when our teacher asked us to solve a combined work problem. A combined work problem is like this: if I can do the work in 5 hours, and you can do it in 2 hours, how fast can we do it together? My group and I had no idea, and so we came up with a complication, random solution. The actual way to do it is to say, well if I can do all of the work in five hours, in 1 hour I can do 1/5 of the work, and in 1 hour you can do half the work. Then you can write the equation 1/5*h+1/2*h=1. You multiple the whole equation by the LCM, which is ten. 2h+5h=10. 7h=10.   h=10/7. h=1 and 3/7. h= 1 hour and about 25 minutes.

Other than that, I really had no problem with math. By far, my biggest challenge was finding something to do when I was finished. My problems were solved when I went to a math competition and the school's geometry teacher instructed us in paper football. First, someone flicks the football to the other side in a "kickoff." Players then flick the football back and forth, alternating turns, and a touchdown is scored when part of the football is hanging off of the edge of the table. If the football falls off the table, the player that flicked it off is scored an "off." When a player reaches 3 offs, their opponent is awarded a field goal attempt, and they shoot it through the classic paper football literally handmade goal posts. An extra point is scored in the same way. After any scoring or kick attempt, all offs are reset to zero. That is what I did when I was done with my work in Algebra.

Math and Science

05/23/2013

Math and science are connect in one main way. In complex science, math is used to test theories and hypotheses. Since much of science is theoretical and cannot yet be tested in the real world, math plays a big role. For example, Einstein's theories were in the category of physical science. But his arguably most famous contribution, the equation E=MC^2, is nothing more than variables and exponents that have real life counterparts. Isaac Newton, who developed the theory of gravity and the three laws of motion, also created a complex form of math known as calculus, which he used to help him in his work.

Much of math is learned ultimately for science. After years of test-taking and busy work, many of the math concept can be used in everyday science. From balancing an equation; for example, accurately doubling a recipe; to using a radical equation to find the perimeter of your fence, math plays a big part. Math is used in business, to measure profits, debts, and income. As can be seen, math is used in many things, even more than mentioned here.

Negative Numbers

05/23/2013

Negative numbers are used a lot in higher level math, but they also appear in the real world. One way they can appear is in finances. For example, if someone owes someone else five dollars, they can be said to possess negative five dollars (\$-5). Negatives can also be used to combine debts, or be used in addition with positives to eliminate them. If someone owes five dollars and borrows five more, then the expression -5+(-5) can be used to find the overall debt of -10 dollars. If someone owes -5 dollars and earns 20 dollars, the expression -5+20 can be used to find the amount of money the person has with all debts paid.

Negatives are also present in the stock market, where they shows the rise or fall of the value of the stocks. If a stock has a difference from the previous day of -\$5, the it has fallen five dollars in value. If it has a difference of +\$5, then it has risen five dollars. Negatives can be used along with positives to show margin of error. If efficiency rating is 5.6 +/-.5, then the efficiency can go anywhere from 5.1 to 6.1. If the rating of another system is 6.6 +/-.7, then the rating can go anywhere from 5.9 to 7.3. It is possible for the first macine to be more

2x-7=15

05/23/2013

When solving an equation such as the one above, the ultimate goal is to isolate the variable. That is, to get the variable all alone on one side of the equal sign. This is necessary to solve the equation because solving the equation means knowing the value of x. Currently the value of 2x-7 is known, but that's not the correct answer because it's not simplified. Another important fact is to remember that any operation can be done, but it must be done to the equation as a whole, not to just one side. Combining "isolating the variable" and "both sides of the equation" will provide a clear path to finding the solution.

The first step in isolating the variable is to add 7, so the -7 is gone, and there is less on the side of the variable. However, this must be done to both sides. The result is 2x=22. Now the x side only has one more thing on it: 2x, or 2 times x. To undo multiplication, you divide. 2x/2 is x; and 22/2 is 11. The equation is now x=11.

Decimal to a fraction

05/22/2013

One way to convert a decimal to a fraction has many steps. The first step is to count the number of places after the decimal. For example, .002 has 3. The next step is to put the digits over a number that starts with a one, and then has as many zeros as the decimal has place numbers. For example, 002/1000 or 2/1000. The final step is to simplify the fraction. For example, 2/1000 is 1/500. That is one way to convert decimals into fractions.

Another way is this. Multiply the decimal by ten until it isn't a decimal anymore. For example, .216*10=2.16; 2.16*10=21.6; 21.6*10=216. Then multiply the number of 10's together. For example, 10*10*10=1000. Put the non-decimal over the product of the tens: 216/1000. Now simplify. 108/500, 54/250, 27/125. The answer is 27/125. Those are two ways to transform decimals into fractions. They are both wim

Fractions to Decimals

04/15/2013

There are two official ways to convert fractions to decimals, and an alternate of one of the ways. The first way is to convert the fraction to an equivalent multiple of ten. After that, the conversion is easy: 3/10=.3, 55/100=.55, etc. However, the first step is often hard to do. For example, if one has the fraction 3/4 and wants to use the first way, then they would first multiply the fraction by 10/10, or 1 in a different form. The fraction 30/40 could then be multiplied by .25/.25, still one. This would then make the decimal over ten. But the number thirty doesn't quarter as easily. Long division, extensive mental math, or a calculator would be required to make the fraction equivalent, and many problems are more complex.

However, there is a second way. The second way also requires long division, extensive mental math, or a calculator, but it doesn't have any of the extra "multiple of 10" steps. This method is to simply divide the denominator into the numerator, or divide the numerator by the denominator. This method always works, but is sometimes complicated. Nevertheless, it is often easier than the multiples of 10 method, except when the fraction is already in that form.

Restaurant Supplies: Ratios Or percentages?

04/08/2013

When deciding between ratios and percents to find the amount of food necessary to restock a restaurant,  ratios would be the better choice. Let's say that a restaurant has a popular dish, and a less popular dish. It restocks ingredients for both those dishes, but wants to have twice as much of the popular dish (D1) than the less popular one (D2), or have the ratio 2:1. Now, let's say that D1 requires fish (I1) and salt (I2), and D2 requires bacon (I3) and pepper (I4). If the restaurant is left with 20 units of I1 and 10 units of I2, and knows they want to restock fully to 100 units of I1 and 50 of I2, but lost the information about D2, then the ratio 2:1 can be used to come up with the solution of 50 units of I3 and 25 of I4.

That can be done like this. For I1, 100 is the one that is going to be larger, so we'll put it over the unknown: 100/?. Two is greater than one, so: 2/1. Then a proportion can be written: 100/?=2/1. Using cross-multiplication, which in this case says that the product of the outside numbers must be equal to the product of the inside. So, 100*1=100, but what times two equals 100? 50, of course. So, 100/50=2/1. From that, it can be discovered that 50 units of I3 are needed. Also, the same process can be used to find the answer of 25 units of I4.

The same ratio could also be used in a different situation. Let's say that everything is the same, except for the fact that the restaurant lost the information on D1, instead of D2. Then, the proportion would have to be set up like this: ?/50=2/1. Since 50*2=100, ?*1 must equal 100. Because anything times one is itself, ?, and the number of I1, must be 100. The same can be done to find the

Using Pi

03/18/2013

The formula for area of a circle is r^2*pi=a. If you know that the radius is three, then you can find the area of at 9*pi, or 9*3.141592653589793238462643383279502884197169399375105820974944592307816406286208... This can be simplified to about 27. The formula for circumference is diameter times pi. The diameter is the same as two radii, so the formula can also be two times radius times pi. If the radius is three, then the diameter is six. Six times pi can simplify to about 18.

3.14159265358979323846263382379502284197169399375105820

03/18/2013

Pi is an interesting number. For one thing, it is an irrational number, which means that it goes on forever and never repeats. Pi can be used for a number of things, although most have to do with circles. For example, if you multiply pi by the radius squared of a circle, you get the area. Pi is usually not written out like it is in the title. It is simplified to the pi symbol or 3.14,. An example of the area of a circle formula could be the following. if the radius of a circle is 2, then square it (4), and multiply it by the pi substitute of you choice: Either 4 (pi symbol) or 4*3.14=12.56. The formula can also be done in reverse. The square root of the area of a circle divided by pi is the radius.

Another thing that can be found with pi is the circumference, or the length around a circle. That can be found by the diameter times the value of pi, or diameter times two times radius. For example, if the radius is two, then the diameter is 4, and the circumference is  Either 4 (pi symbol) or 4*3.14=12.56.

JJ s.

These are requests given by the Computech math teachers that I respond to every Monday.