Since this is my last Math Mondays Blog for this school year, I have asked myself this question: Has blogging about math really helped me this year in math class? Or has it all just been a waste of time? I just realized the answer to that question after some really hard thinking. And the answer is........ Yes, Math Mondays Blogs have helped me with my math class and just my general math knowledge. One way Math Mondays Blogs have helped me this year is: Since I'm in Algebra class, there are some things that we don't learn or go over that the PreAlgebra kids do. And since most of our Math Mondays Blogs are topics given to us by the PreAlgebra teachers, I don't necessarily know the answer to every single Math Mondays blog post. That's what gives me a challenge and makes me Google a question or ask my teacher and friends how to do a certain math problem. Without this challenge, Math Mondays Blogs would be very easy to complete.
Another way Math Mondays Blogs have helped me this year is: They're great review. Sometimes in Algebra class, we learn something a few months before the PreAlgebra students do. For example: Slopeintercept form, or y=mx+b. We learned this early in the year, and the PreAlgebra students learned it, I believe, right before Winter Break. When the teachers decided a good topic would be about y=mx+b, PreAlgebra students had it fresh in their head, but we Algebra students needed a small review so that we could blog about this topic. This is how Math Mondays Blogs have helped me throughout this
You own a restaurant. I know you that most of you really don't, but just bear with me. To start you're business you, have to buy the correct amount of food for the restaurant. How much do you buy? Would you use a ratio or a percentage?
Answer #1. I would use a percentage because you know what percentage of that food you use for each plate. So if you use 2% of the whole each time you serve that dish, and the whole is 100 lbs. of meat, then you know that you are using 2 lbs. of meat for each dish. That is how I would calculate it.
Answer #2. I would us a ratio when ordering for items with more than one ingredient, such as a pancake. If I need 3 cups of milk, and 2 cups of flour to make one plate of pancakes, the ratio for milk to flour would be 3:2. So if I wanted to order ingredients for pancakes that would allow me to serve 10 plates, I would multiply each part of the ratio by 10, which is 30:20. This shows that I need 30 cups of milk and 20 cups of flour to be able to make 10 plates of pancakes
What was the hardest math subject of the year for me? Well, I understood almost everything we learned in Algebra, but there is probably one thing that took me a while to understand. And that was the quadratic formula. I know it by heart know: b+/the square root of b^2 4ac/2a. It's difficult to type the quadratic formula, but just bear with me. I'm sure why you can see I was pretty confused with this equation. We were working with the equation of parabolas, ax^2+bx+c. I understood this equation, but when Mr. Erickson introduced the quadratic formula, I didn't really understand why we had to use it. It was a long while until Mr. Erickson showed us exactly why we needed this equation. This is why:
When you have an equation like x^2+4x+4, you can easily factor this to (x+2)^2=0. This gives you x=2 . But, if you have an equation like x^2+4x+3, you would have to complete the square, meaning you would have to add 1 to both sides of the equation. So now the equation is x^2+4x+4=1. Now you factor, and you get (x+2)^2=1. Now square root both sides so that you get x+2=+/ 1 ( The square root of one gives you 1 ). So you solve both equations, and you get x=3 and x=2. Pretty easy, right? Now for the fun part. And when I say fun, I mean hard. So what happens when you get a problem with no complete square? Let's do the problem x^2+11x+5=0. Well, you can't factor it just like that, and you can't create a perfect square for it. So let's see what we get by plugging in the quadratic formula. a=1, b=11, and c=5. 11+/ the square root of (11)^2 4(1)(5)/2(1). 11^2 is 121, so 12120=101, and the square root of 101 is 10.0498... but we'll round it to 10. So now we have 11+/ 10/2=x. 11+10=1, divided by 2 is .5. 1110=21, and divided by two is 10.5. So now you know that x=10.5 and x=.5. It seems very complicated, but after doing problems like this and seeking help from Mr.Erickson and friends, I was finally able to understand the quadratic formula.
From years of science and math classes, I've realized that without math, there would not be science. There are so many mathematical equations and estimations done in science, and sometimes you don't even realize it. Almost every scientific experiment includes math. Here are a few examples:
Mixing Solutions: When you mix two solutions together, you can't put mix too much, or else it will have a very large chemical reaction, and you can't put too little, or else you won't have a large enough chemical reaction. So what do you need to do? You need to use Algebra, and more specifically, solving systems. Without math, this would be virtually impossible to complete.
Measurement: I'm sure you have used a beaker to measure the amount of some liquid, or measure the length of something, so that you could record it for whatever reason. You may have even weighed things with a scale. Well, I sure have. You even need mathematical equations for volume and circumference of objects. Without math, you would not have a number system or different measuring tools to do these measurements. Without measurements, no data. No data, no knowledge. Do you see why math is needed for science? Here's one more example:
Equations: One of the most famous scientific equations ever is e=mc^2. But, you need math to understand this equation. If you substitute numbers for m and c, you would have to square c, and then multiply it by m. This number is e. If you don't understand math and the order of operations, you wouldn't be able to read this equation correctly. There are also many other equations for science, like D=RT, C=D*PI, and A=1/2bh. By demonstrating these three examples, I have just
There are two ways to change a fraction into a decimal. The first way is something that I usually use when converting a fraction into a decimal. Most of the time it would be a lot easier if you have a calculator with you for long decimals. So this is how you convert it. You divide the numerator by the denominator, or top divided by bottom. I'm sure you already know this, but let's practice just in case you forgot. So let's say I have 1/3 on this big math test, and I'm supposed to convert it into a decimal, and it's multiple choice. You have: A. .5 B. .3 C. .6 D. .333... Which one do you choose? Well, if this was an actual test, I would do the work to see what is correct. Remember, numerator divided by denominator. So it would be 1 divided by 3, which is what? Well, we know that it is not C or A, but is it B or D? Ask this question to yourself: Does 3 go into 10 evenly? No, it doesn't, you get 3.333... So what do you now know about 1 divided by 3? Right! It doesn't divide evenly, so the answer
So, if you are not in the fourth grade yet, you may wonder what negative numbers are. Well, what are they? Negative numbers are numbers that come before zero. The way you would get a negative number is by subtracting from a number larger than the number. You may get it by multiplying a positive number by a negative number. You may also get it by dividing a positive number by a negative number. There are many ways you can get a negative number. But, negative numbers don't just apply to math, but to real life, too.
These are ways negative numbers could be applied to real life. Let's say you have a friend next to you, and you need some money for that delicious ice cream right there. What happens? Of course, you ask the friend for some money, and ( if he's a nice friend) he gives you the 2 dollars. You buy the ice cream, and !BAM! There was just an instance of negative numbers in real life. You now OWE your friend, meaning you now have 2 dollars, because the next time you get an allowance or earn some money, you need to first pay your friend, meaning you do not get the full amount because you borrowed that money. Another instance: If you live somewhere cold like Alaska, I'm sure you already thought of this negative number instance in everyday life. The weather man just forecasted weather for north Alaska, and it's cold. Below zero cold. !BAM! There's another instance! Below zero. What does that really mean? It means a negative temperature, because it is below zero. Do you now see how common negative numbers are in our life? Hopefully you can now spot a negative number instance in your daily life, now.
If you take PreAlgebra or Algebra class, then you are probably going to have to study for your CST testing. Mine starts tomorrow. For some help studying, I'm going to go through a stepbystep process of solving the following equation: 2x7 = 15. For some of you, this is a simple Algebra problem, and for others ( Shame on you if you are one of these people) this is a very difficult equation. Let's get started!
Alright, the equation is 2x7 = 15. What does your gut feeling tell you to do? Get the x by itself! The first thing to do is to get rid of anything that is not directly effecting the x. What number is that? It's 7. So how are you going to put this number on the other side of the equation. You can't put 7 on the other side, so you just add 7 to both sides of the equation. 7+7=0, and 15+7=22. What do you do next? Well you have 2x=22. You have to do the opposite of what is happening to the x, so if it is being multiplied by 2, you're going to.... divide it by 2. You now have x by itself, and x=11! Good job! Now you're partially prepared for your CST's!
Let's say you need to find the area of a circle with a radius of 3 feet. Well, first you need to find the circumference of a circle by doubling the radius. This would give a diameter of 9 feet. You then multiply the 9 ft. by pi, which comes out to about 28 feet^2. That's the approximate area of that circle with a radius of 3 feet.
Let's try one more circle. We're going to do this a little differently. Let's say that the radius is 10 feet. Remember, you first find the circumference. So 10^2 = 100. Then what do you do? You multiply 100 ft. by pi to get the circumference. You can pull your calculator out and do this, or if you know the first few decimals of pi, you know that the circumference comes out as 314.159265... but let's just round to 314 to make this a little easier. So know what? You already know what the diameter is, 100 ft., so know you just multiply 314 ft. by 100 ft. which equals 31,400 ft.^2. That's how you get the area of a circle.
In our last blog we covered how to convert a fraction into a decimal. Know we will be discussing how to convert a decimal to a fraction. Let's say you have you have to convert .5 to a fraction on that big math test. First of all, this problem is a piece of cake. I already memorized what the answer to this problem is, but if you're having a bad day and you totally forgot to study, this is how you find the answer. You take .5 and automatically drop the decimal. Then you just put the 5 as a numerator, and 10 as the denominator. Know you have 5/10. But you're not done.You usually have to simplify to get full credit, so you would divide both top and bottom by 5, so you get 1/2.
Here's the second way. Let's say you have .68, and you have to convert it to a fraction. You can't put 68 over 10, because when you simplify you'll end up with 6.8 as your answer. So you have to put 68 over 100. You then end up with 68/100. But remember, you have to simplify. Divide both sides by 2, and you get 34/50. Now we're done. Just kidding! We could still simplify, so let's divide this by 2 one more time. Now you have 17/25. That's it, you're done! You are now a decimal to fraction master!!!
No, not that delicious pie that you eat, but pi. You know,
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679... The one that goes on forever and ever. Yes that one. Pi is used for two things, finding the circumference of a circle, and for small competitions to see who could recite the most numbers and get a prize. The way you use pi is by multiplying it by the circle's diameter, giving you the circumference of the circle, which is impossible to measure without pi. Pi was invented by Sir Isaac Newton, who calculated the number 3.1416 to get the circumference of a circle. Later on ,after computers were invented, the number was actually calculated to be longer, than as later and later computers came out, the number just kept going and going, turning out to be much longer than first anticipated. Pi goes on forever, never stopping. The number above is just a mere piece of pi (Hahahaha, pi pun!). Thanks to Sir Isaac Newton, we found a way to entertain ourselves and figure the circumference of a circle.
