Our Math Monday blog assignment for today was to click on the link to a math game we were given, play a few rounds, and then reflect on it. The game was called "Diffy" and the actual game objective was to find the differences between certain numbers -- certain kinds of numbers, too, depending on how and if we adjusted the game. Once a "frame" of numbers was completed, we progressed to a smaller one until the level was complete. 

The game seemed really simple at first, but as the levels progressed, more mental math was required to solve it. It was, as expected, easiest in the whole number stages as well as the integer stages, with some frames being much harder than others. The most challenging number frames were probably the ones that dealt with negative integers. Those ones needed the most effort and mental math. I was successful in figuring all of them out using the formulas and skills I've been taught so far this year. For example, when finding the difference between -16 and 11, one can simply leave out the negative sign on the -16 and add 16 + 11 in your head. Your answer is 27, which is the difference between their absolute values, but there's a negative sign on the 16 and it's said that "the darkness rules". The final answer is -27. -16 - 11 = 27.

One of the most unseen challenging things was the fact that we could not refer to any sort of number line or other reference point. All of the work was to be done in our heads and tricks and formulas were to be used. I think it was a nice way to tie in all of our reflective math skills and knowledge of rational numbers including wholes, fractions, and integers. 

Our Math Monday assignment for today is to explain why when graphing inequalities, the circle for one with an equal in the inequality must be closed.

Most obviously, this is what separates inequalities that could potentially be equations from regular ones that use "greater than" and "less than" signs. It also helps to show that the line below the regular inequal sign actually means something. In addition, it shows on the graphing line that the given numeral is grounded because it may be equal to the variable that we have graphed, but the arrow rising from it shows that the variable could very well be inequal to the numeral. In normal graphing, there is no differentiation or indication of differentiation between open circles and closed circles because we are already sure of the value of our numbers.

This lesson ties in with our current Math unit of solving inequalities. This is quite easy for me so far because it ties in to many of our other units and we can use the skills we learned in the past. Last year my teacher would tell us that in our Math curriculum, lessons and skills were layered on top of one another. This is why the basic skills come first. Sometimes we have to combine like terms when solving equations. Other times we have to simplify inequalities. Sometimes we have to find precise values of variables and use inverse operations to solve algebraic equations.

I am, however, looking forward to doing more advanced things in my Math class and combining all of the skills I've learned so far. Math can be hard, but oftentimes it's useful in the real world and with grown-up matters like jobs and marketing. It's also pretty interesting as well as annoying sometimes.

There are a lot of ways to make solving problems in math easier. These can include simplification and reduction, finding common denominators, combining like terms, changing forms, etc. I've never really put much thought into what my favorite was, but we've been learning lots of new ones in math class.

We've recently learned how to combine like terms. This is another way to make algebraic equations easier to solve. For example, the expression 2a - 3b + 7a x 4 contains the variable a more than once. To make the problem easier, we can use reverse PEMDAS and combination. 

First we find the like terms. We have 2a and 7a. The sign directly to the left of 7a signifies addition, so we add. 2a + 7a. Since our variable is the same, we get 9a. We also have 3b and a constant, 4. Our problem right now looks like 9a - 3b x 4. Since there are no like terms left in the equation, our problem is simplified enough.

I think algebra is a really interesting form of math. It also ties directly into our Core unit, which is on Islam. Arabic scholars invented algebra.  I also think real-world connections make math a lot more interesting.

To put it simply, there is no such thing as division because it is just the inverse of multiplication. You can not really divide numbers by other numbers but only multiply. For example 16 divided by 2 is 8. This process can not really be executed or shown. We can only multiply 8 by 2 to get 16 and "divide" that by 2 to make 8.

In Math class, we recently learned about one-and-two-step equations. We learned what an inverse operation was. We had to use the inverse operation principle to both sides to finalize our answer, which was always a variable. The same rule applies to the simplest of problems involving "division". Division is the inverse of multiplication because while multiplication is adding groups of the same number repeatedly, division is cutting up the number in even groups and counting them; this is also why in elementary school and even now most of our division word problems involve someone sharing, dividing, and distributing.

There is an infinite amount of numbers between 0 and 1 due to the principles of decimals and fractions. A decimal or a fraction (they are equivalent) is a number that is between two whole numbers but is not whole and only represents part of a number, such as .5 and 1/2. Decimals can be as simple as .5 and as complex as 4.5437534583495834908534908390584395... and so on. Fraction equivalents to decimals can be found by counting the number of places in the decimals, making a fraction, and reducing. Any number that is either whole, mixed, a decimal, etc. is called a rational number, whether it is infinite or not. The amount of numbers between the simple counting numbers 0 and 1 is infinite and can go on forever. One common number, pi, is written as the fraction 22/7 but contains an infinite amount of decimal places. Usually we round this decimal to 3.14. We acquire this decimal by dividing 22 by 7. In the same manner, there is an infinite amount of numbers between 1 and 2, 2 and 3, and so on, thanks to the decimals and fractions principal. if a decimal begins with a whole number, it can be turned into a mixed number (i.e. 6.5 to 6 1/2) and then into an improper fraction by multiplying the denominator of the fraction in the mixed number by the whole number (2 x 6 is 12) and adding the numerator (12 = 1 = 13). The denominator remains the same, so your improper fraction is 13/2. To find the decimal version of this number we divide the numerator by the denominator. This is why, in proper fractions like 3/4, the outcome is smaller, since the outcome of 3 divided by 4 is not a whole number. 

I know, all this math seems really hard, but when it comes down to basics, it's easy as pi.

Happy Math Monday! Today's pressing question concerns fractions and denominator: as the denominator grows smaller, why do the numbers following the decimal point increase?

     The answer to this question has to do with the basic principles of division. Divide the denominator by the numerator and you get a decimal. If the number following the decimal point is large, then the actual number, or fraction, is smaller. For example, 1/2 and 1/8. The denominator is smaller in 1/2, but when you find their decimal equivalents (.500 and .125, respectively), .500 seems larger, which it is. .500 can also be written as .5 whereas .125 will always stay the same, and adding the same number of decimals that follow the first place in .125 gives a large number. So it does indeed have to do with the division of the numerator by the denominator. For improper fractions like 48/12, which reduces to 4/1 or 4, the decimal is written as 4.0 because 1 divides evenly into 4. The exact same value is found in multiples of that same fraction, like 96/24, or reductions of it like 24/6. This is actually one of my favorite math tricks. If you divide 1 by a number larger than it, you are certain to get a decimal number. 

1 divided by 1 is 1
1 divided by 2 (or as the fraction 1/2) is .5
1 divided by 3 (1/3) is .33333...
1 divided by 4 is .25

and so on and so forth!

 If you are observant and pay attention, you will notice that a few days ago, in the week before last, I wrote a blog entry on science and what I have learned in that class. Today I am doing the same thing, but for a different class: Period 4 Math.

     So far in math we have learned about positive and negative integers, how to write equations using them, and we are now begining Unit 2: Rational Numbers. This inclides fractions, decimals, rational numbers themselves, and irrational ones. Periods 2 and 4 have already begun deployment from Mrs. Pope's class to Mr. Dorman's room, but we stuck in Mrs. Pope's room today. I have Math before Computers, so I have already gotten my daily math lesson. Today it was 2-1: Rational Numbers. I will write about it today.

     The first thing we do in Math is take out our agendas and write down our homework, which usually consists of a few scattered problems across one or two pages that focus on today's lesson. On Fridays, when there is no homework, we just hold out our agendas for Mrs. Pope to see. We also do a quick warm-up in our math graph books. Today after this we did equations from the SmartBoard to our notebooks. Usually we use our whiteboards for this, but we needed these equations as notes today. We practiced decimal gimmicks for changing fractions into decimals, and vice versa. There is a long gimmick involving repeating decimals and the number "9". Mrs. Pope took a long time to show this to us today, even though you can just put the number of 9s as there are repeating digits in the number and have your fractions! Things like this are the reasons I like Mrs. Pope. She's one of my favorite teachers so far. 

     I sit by Camille, Rebecca, and Tatum in Math. Camille is my partner and usually we work together, but Rebecca and I used to sit elsewhere, so she usually corrects my work while Camille and Tatum do this in Homework Review, which my dad usually helps me at home with. Recently we turned in our TMR #1, a worksheet of 30 problems spanned over several weeks as something to do in addition to our nightly homework. We also have an Extra Credit paper assigned after Friday's lesson that we have not collected yet.

     As you can see, I quite like Math so far this year. I think I will do well in Math this year as I usually do, because my dad is a high school Mathematics teacher (Statistics and CAHSEE Review). I am thankful for all of the tools I am given in Math that make such a normally difficult subject easy here at Computech.