Happy Monday! Today is the last Monday of the quarter and the last Monday of the semester. Our blog assignment for today is to name a math topic we've struggled with in the past and explain how and when we overcame it and finally began to understand it.

In years past, I've had a hard time with multiplying numbers with multiple place values. I got over it in the fifth grade, but for awhile it was seemingly impossible for me to do. 

As I stated above, it started to click for me in the fifth grade when we were doing multiplication and place value, at the beginning of the year as always. It seemed so hard and no matter who I asked -- my friends or the teacher -- it wouldn't make any sense. I'd been taught to multiply numbers with zero as one of the place values, but not with actual digits in more than one. There were places in which I didn't know whether to add or multiply. My teacher said that she'd never had a student who wasn't able to do this at the beginning of the year. I was so embarrassed that I could never learn how to use what I called the "old-fashioned" method.

I looked in the math book. The instructions all seemed like nonsense until I looked at the problem I was doing. It told me to refer back to Example 1 in the lesson article. I did, and there it was! At first the instructions looked like jumbled gray matter to me, but then I saw the step-by-step instructions and it became easy. This helped me learn to take better notes and pay more attention to the content in my textbook.

Nowadays, I use both of these methods (multiple-place multiplication and textbook referral) all the time. I've found that the math textbook often contains valuable information and easy tricks that your teacher might not explain. I've also found that the textbooks we use now are more reliable in information than the company who made my elementary school math books were. My math motto is: "always look back in the textbook". Often there will be footnotes that name a place, usually in the back of the book, where extra practice and review are available. I've also found test prep inside and outside of class helpful at the end of difficult units or chapters.

If you're reading this, I hope you have a good winter vacation and enjoy my hiatus. I've really enjoyed using this blog to write about my new experiences this half of the year. (:

Our Math Monday blog assignment was to write about the Pythagorean theorem, explain how it is used in math, and apply it to two real-life situations; one funny, one serious. The Pythagorean theorem is named after a mathematician named Pythagoras in Ancient Greece.  Pythagoras theorized that in a scalene right triangle, the two smaller measurements when squared would add up to the largest measurement squared. 

The Pythagorean theorem can be used in everyday situations, and is used by architects and engineers constantly. One example of a serious situation would be in the case of an architect who is building a modernist building in the shape of a scalene triangle. If the measurement of the shortest wall is 60 feet and the largest wall is 80 feet, what is the wall in the middle's length? We can find this by using exponents and algebra. 60^2 + x^2 = 80^2. 3600 + x^2 = 6400. The missing measurement is 2800. The measurement we need is the square root of 2800.

Our Math Monday blog assignment for today was to explain what square roots are, where we think their name comes from, and what an alternate name for them could be. 

In short, square roots are numbers that are equal factors of a large number. These large numbers are called perfect squares when their square root is a whole. Every number can be a square root and every number has a square root, but not every number is a perfect square. We use the power of 2 ("squared") in finding the areas of rectangular surfaces.

The term "perfect square" probably comes from the fact that when multiplied by the same number, the number is perfectly even in relation to these factors. The factor that creates the perfect square is a root, so it is called a "square root". This seems really confusing at first, but once it is shown to you hands-on, you'll probably start to get it a bit more. Square roots are really just a fancier way of multiplying a number by itself, the same way that multiplication is just a fancier way of repeatedly adding the same number. 

A different term for square roots could be "corners", since squares have four equal corners, or bases, to make their sides equal. Another name might be "area bases", since as mentioned above, perfect squares and the power of 2 are used to find the area of surfaces.

Square roots are not just something you have to learn in school, though. Mathematicians, architects, engineers, and scientists all use exponents and squares. Exponents and square roots might even come in handy in classes besides math. Like formulae, exponential form and square roots make long, tiring processes easier and math a little more understandable.