Happy Final Monday of the 2012-2013 school year!!!!!!!!! I'm so excited!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I feel like I'm being discharged from prison in a way. Anyway, the Math Monday blog for today is to explain how writing about math in these blogs has helped us with learning our math standards and information, etc.
To be honest, writing about math in this blog hasn't helped me very much at all. I'm still really bad at math and the class, because these blogs can never be completely up-to-date with what we're doing, especially at this time of year. During preparation for the Math CST, I had nothing to do because I didn't take the CST itself. I can see how it would help my classmates, however, because they would be able to look back on their blogs in memory and remember what they had written about things they had learned in the past and were reviewing. I don't think writing in this blog helped me enough with my Math class as it should have. I just don't think it was very effective for me, personally.
Another part of the prompt talks about the fact that the education policy is changing. Whee. I seriously could not care any less about that itself, because it's going to change back in ten years when it no longer applies to me, but I probably should care about what's going to happen. Kids are going to hate school even more. They're going to be held behind and peered at because they didn't get the exact correct work that a different mind did and the same answer, but we do that now anyways. Teachers stress the importance of math, but in reality, most of the jobs people will have don't use things that are beyond basic. I don't think there's much of a need to know the quadratic formula and to use it step-by-step to get a ridiculously complex answer in the real world, but it's not like what any student says will be taken seriously. The only reason we need to do a lot of detailed math work is to please the people who run the education systems. I don't think we should rush a decision of a life plan on any young person, but I don't think we should stress next-to-useless things like imaginary numbers and how to use them in hypothetical situations when a very, very small percentage of students would ever need to use them in their life.
Happy Monday... just kidding, that's an oxymoron. Anyways, today's Math Monday blog assignment is to name the hardest thing we learned this year in math and tell what we did to solve it and how it affected our math learning, etc.
The hardest thing to learn in math this year was probably some of the specifics of exponents. I know how to write basic exponential form and I know what scientific notation is, but I had trouble with negative exponents. I also struggled with parentheses in this situation and distributing things that involved exponents. That was one of the few things I learned this year that I had never done before in a math class. However, using resources around me like other people's help and knowledge and my math textbook (which helped me a lot throughout the year, actually), I eventually learned somewhat how to do what I had previously had a difficult time with.
Another difficult concept I studied this year was learning how to find a slope in a graph. This tied into our study of functions and linear equations. It involved formulas and a lot of words, too, which made things very confusing for me at times. I would always get mixed up in finding what certain values on the graph were. I overcame this one, however, by taking notes on what my teacher was saying and on what the book told me. Now I don't have as hard of a time with slope when I do use it.
Things like this, which are all examples of trial-and-error, are very important to fundamental learning, especially school. Making a mistake or not understanding something specific is not the end of the world. When we make mistakes, we shouldn't dwell on them, but rather go on and look back to them as things to learn from. I think that this is why we study history. We don't want to make the mistakes of the past. All human learning has some elements of what I described above. In this way, learning things like these are more practical than we thought!
Happy Monday! Today's Math Monday blog assignment is to describe the connection(s) between science and mathematics.
Science and math are closely related, if you couldn't already tell. My dad, who is a math teacher, described them as being like "close cousins". Mostly the relationship between them depends on mathematics being used heavily in science and scientific discoveries.
For example, scientific rules and laws could not have been figured out without the use of basic mathematics. We would not know how many stars, per se, are in the Milky Way galaxy or even how many people are on the earth without the knowledge of massive, never-ending numbers. In this way, humans have used math to extend and advance our understanding and perception of the way the world works, which is what science is.
Carrying out and learning about science and math both require clear, logical thought processes, and neither are abstract. The relationship between them could be likened to that between music and art -- both require creativity and "thinking outside of the box". In the case of science and math, however, we must think outside of the box while staying inside of the box, which is where the challenge people might see in both areas comes in.
The basic map of what people know and continue to discover about the world would be very ineffective and our world very basic without the use of mathematics, and by using examples and concepts, our mathematic knowledge would be very insignificant without scientific applications. In fact, math itself is a science, just like biology, chemistry, or optics. The relations
Happy Monday! I hope you are well-rested! Today's Math Monday blog prompt is to explain what negative numbers are and give an example of where we might find them in the real world.
There are a lot of ways to explain what negative numbers are, I guess, but most people know them as being the opposites of positive numbers, or ones whose values are above zero. This makes them integers along with their opposites. Being the opposite of a number means that the absolute value as the same as its counterpart, but the sign is different. For example, -8 has the same value as 8, or +8, but the signs are different. One of them is negative and you read it as "negative eight".
Negative numbers are taught to us pretty early on because they are fairly simple to use and are more applicable to the real world than some other concepts. If you owe anyone money measured in value, then you say that you have -x dollars, unless you have more to make up for it. Adding a negative number to a value is the same as subtracting its opposite. You can do this lots of times in lots of ways. If you have a discount at a store, for example, and you find out what the rate of discount is in a number, you can add the negative value to the original price. For example, if an item was originally $30 dollars but is on sale, or discount, for 10%, you can add -3 to 30. This is the same as carrying out the equation 30-3. The item now costs $27. Easy, right?
We began learning about negative numbers in the recent years past, but they've come into play a lot in this year's math class, and we've been told before that they'll definitely be on tomorrow's CST for mathematics. Not only are they applicable in the real world, but they can also be used within the field of mathematics too. We've used them in a lot of other units this year. They really are one of the basics of math we've learned about.
Good morning, and Happy Monday! Today's Math Monday blog assignment is to explain the steps we would use to find the answer to the equation 2x - 7 = 15. - The first step you'd carry out to do the problem, if you were to do it on paper, would be to draw a line down the equals sign, just for the sake of organization. This makes it easier for us to keep track cognitively of what we've done.
- Next you would look at the left-hand side of the problem. You would find out what operation is involved between 2x and the constant 7. You'd do the inverse of this operation -- since the equation says to subtract 7, we'd do the opposite and add 7. Cross out the 7, we don't need it.
- Now we do the same thing to the other side. Add 7 to 15. This makes 22. Our equation now says 2x = 22.
- Do another inverse operation. Divide both sides by the constant 2. Our first digit's value is canceled out, so now our problem reads x = 22/2.
- Do as the problem says. Divide by 22 by 2. You'll get 11. x = 11!
- You can also check your work by plugging in the variable to the equation. 2(11) - 7 = 15 --> 22 - 7 = 15. This is a valid equation.
By learning how to use inverse operations and dividing our equations into parts that correspond with each other, we simplify algebraic expressions. We learned how to do this at the beginning of the year, and it's one of the most memorable things I've learned in my math class this
Good morning! Today's Math Monday blog assignment is the opposite of last week's. This week we are to explain two ways we can convert a decimal into a fraction. There are two similar ways to do this that I can think of. I'll tell you which one I prefer and why.
- The first method we can use is the exact opposite of one I named last week, and it's to set up a proportion. In last week's blog, I explained that you can equate a number that divides evenly into 100 with 100. You can do this this time, too. All decimals are really fractions of 10 and therefore 100. You could make .4 into 40 over 100. This is a fraction, but when reduced it's 2/5. You can check your answer by dividing 2 by 5, which you'll see makes .4.
- The second method, which is more specific to decimals such as .74 that aren't evenly divisible into 100, is very similar to the last one, only it has an extra step at the beginning. The number 100 has two zeroes after the 1, so you would need to move your decimal point two places to the right. This changes .740 into 74.0, or 74. When you insert 100 as a numerator like you did previously, it becomes 74/100. This would need to be reduced. It reduces to 37/50. You should reduce all fractions whenever you use them, and that's especially important here.
Like I pointed out last week, both of these methods are somewhat specific, and both are easier to use in certain contexts. The former is more applicable in easier things where the numerator is easily divisible into 100 to make an even fraction that can be reduced. The latter can be used in this situation or mor
Happy Earth Day! Since we did not write a Math Monday blog last week, we're making up for it here. The Math Monday blog assignment for today is to name two ways we can turn a fraction into a decimal and tell which method we prefer and why.
One of the ways you can turn a fraction into a decimal is to make a proportion. This takes longer than the other method. It is also where a percentage would come in. For example, if the fraction is 2/5, you could equate it with another fraction -- 40/100. This is 40%, which can also be written as .40 or .4.
The other way that fractions can be made into decimals will probably be easier to use if the denominator of the fraction is not a factor of 100. You can divide the top number by the bottom number. If you divide 2 by 5, you'd get .4, or 4/10 of the number "1".
As for which method I prefer to use, I'd say that it depends on the context and value of the fraction. If the denominator is a factor of 100, then I'd set up a proportion, more likely. However, the second one is more applicable and easier to use in places where the denominator is prime or cannot be multiplied to get 100. The latter, though, can also be used in that context, and the former can also be applied even when a proportion could also be easily used.
In my opinion, fractions and decimals are both really easy to learn and apply to real-world situations.
Happy Monday! Our Math Monday blog assignment for today is to explain which method would be better to use in purchasing food for sale at a restaurant, ratio or percentage?
My answer for this is pretty clear, but confusing at the same time. I think that in purchasing food to sell again, you'd need to use both the ratio and percentage to find out a price. I'd probably use percentage more, though. When you find out how much of the original price you are going to sell any retail item for, most people would use a percent method. However, the proportion would make your answer and thought process more clear. Some people would find it easier and more suitable to use a proportion over 100 and cross multiply for the correct price. I don't think this would be the case here, though. Setting up a proportion takes longer. Overall, the methods will give you the same result if you carry them out correctly, which is why there is no true correct answer to the question.
When I first got the blog prompt, I was kind of confused by it, because right now in Math we're studying geometry and circles. However, today Ms. Moon taught us that percentage can be used in finding the degrees of certain parts of circles. For example, to find out the measure degree of an area that encompasses 40% of a circle, you need to multiply 360 (since there are 360 degrees total in a circle) by .40 or .4. This, however, is a real-world problem that uses the same basic principles and knowledge. Percentages and ratios are two of the most useful and applicable things to learn in Math this year. I hope we can find other ways to use them and learn about them even in other classes.
Happy Monday! Our Math Monday blog assignment for today is to explain how to find the circumference of an object with a radius of 3 feet using pi.
- Use the formula of area = pi x r^2.
- When we substitute our values, we get area = pi x 3^2, or area = pi x 9.
- Multiply pi, which is roughly 3.14, by 3^2, which is 9.
- Your result is roughly 28.27. This is the circumference of the object.
Happy Monday. Today's blog assignment for today is to write everything we know about pi. This is because pi day, or March 14, is coming up soon, on Thursday.
Pi is the name of a Greek letter that is given to a very famous irrational number. The number can be expressed as an improper fraction 7/22, or as a decimal that is very long but is typically shortened to 3.14. The actual pi decimal has more than a million places and is non-terminating, or goes on forever.
Pi is fun to recite, but it can also be useful outside of school. Architects and civil engineers use pi to find the circumference of an object. They use only 3.14 since pi goes on endlessly. This is why there is no such thing as a perfect circle, only very close optical illusions. In this way pi is sort of like a mathematical paradox. Like I said previously, pi is represented as the Greek letter of the same name. This is what it looks like.
Click image to enlarge
We celebrate Pi Day on March 14 because in American dating, it looks like 3/14. If we were to properly use pi's fraction form, the day would be celebrated on 22/7, but there is no 22nd month! The actual exact Pi Day, when the date matches the places in the number, will be on March 14, 2015 at a certain time in the morning (the 9:00 hour). I don't know pi to very many places, but a lot of people memorize it for fun and around the country and world pi-reciting contests are held. Kind of a useless skill to learn, but it would be fun to show people, I imagine.
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