Today I'm going to look in the chapter about factoring. This chapter doesn't scare me as much as quadratic equations, but I'm still going to have my pen and paper handy.
This chapter begins with the description of terms for algebraic expressions. After naming the expressions "a one-term expression a monomial, a two-term expression a binomial, and a three-term expression a trinomial," the professor describes the roots of the terms, mono=one, bi=two and tri= three. He also gives examples of the roots, like monorail (one rail), bicylce (two wheels) and tricycle (three wheels). These examples remind me of a Greek and Latin root class I took in college, the roots of the words can help you figure out the meaning, this applies to math as well as English.
As I keep reading, I'm having trouble keeping up with all the terminology, "multiply a monomial by a binomial." I stopped, read it over and went back to my notes. Then I thought of writing out an example of a monomial by a binomial. I wrote: 3 x (4x + 7) which I solved = 12x + 21. Now that I had numbers to visualize the words, I understood what they were talking about.
Next, we came across multiplying two binomials. This lead to the FOIL method. I was reminded of my last blog, and how I had to look up the FOIL method to help me with quadratic equations. I think this would have been a helpful chapter to review before doing quadratic equations.
Now to do some practice with factoring.
Tuesday, October 20, 2009
Monday, October 19, 2009
Quadratic Equations (Part 2)
Today I decided to try something different while reading. I took the book and a piece of paper and pencil and wrote down the numbers from the problems on the blank piece of paper.
The narrative that explains the math makes me think of educational computer games I used to play when I was younger. There would be characters and they would seem to just do math equations for fun.
When Recordis suggested using the FOIL method I was reminded of my 8th grade class. I remember solving problems using this method, however I forgot what the letters stood for. After writing the problem down, I looked up "FOIL."
I tried it myself and got x^2- x - 30= 0, just like the next step in the book.
However, the next paragraph said to go back to the original equation, even though I was frustrated and confused, I decided it would be best to just keep reading.
I understood the next few sections on how to solve for 0 and get the two answers -5 and 6.
Then we were brought back to the quadratic equation. This really confused me, I thought we had the answer and that was it, what's the point in going back to the beginning? I kept reading hoping to find out.
The narrative about the King and his court was really starting to confuse me. I just didn't understand the point of all this assuming and guessing they did to solve problems. I was reminded of my 8th grade teacher telling me that I would have to keep plugging in numbers to find the two answers. I remember hating this explanation because to me guessing does not seem like a mathematical way of solving problems.
I kept reading until I got to a point that was clear to me. "You will never be able to solve every quadratic equation this way! Your trial-and-error factoring method will soon become helpless when you meet the equations I shall give you." I made a personal connection here, because this is how I felt when I was reading the earlier passages.
After a lot of trial-and-error, the King and his court determine the answer and create an equation to solve future problems quicker: The Quadratic Formula.
The narrative that explains the math makes me think of educational computer games I used to play when I was younger. There would be characters and they would seem to just do math equations for fun.
When Recordis suggested using the FOIL method I was reminded of my 8th grade class. I remember solving problems using this method, however I forgot what the letters stood for. After writing the problem down, I looked up "FOIL."
First - multiply the first term in each set of parenthesis: 4x * x = 4x^2
Outside - multiply the two terms on the outside: 4x * 2 = 8x
Inside - multiply both of the inside terms: 6 * x = 6x
Last - multiply the last term in each set of parenthesis: 6 * 2 = 12
I used this to help me look at the problem (x + 5)(x - 6) = 0
I tried it myself and got x^2- x - 30= 0, just like the next step in the book.
However, the next paragraph said to go back to the original equation, even though I was frustrated and confused, I decided it would be best to just keep reading.
I understood the next few sections on how to solve for 0 and get the two answers -5 and 6.
Then we were brought back to the quadratic equation. This really confused me, I thought we had the answer and that was it, what's the point in going back to the beginning? I kept reading hoping to find out.
The narrative about the King and his court was really starting to confuse me. I just didn't understand the point of all this assuming and guessing they did to solve problems. I was reminded of my 8th grade teacher telling me that I would have to keep plugging in numbers to find the two answers. I remember hating this explanation because to me guessing does not seem like a mathematical way of solving problems.
I kept reading until I got to a point that was clear to me. "You will never be able to solve every quadratic equation this way! Your trial-and-error factoring method will soon become helpless when you meet the equations I shall give you." I made a personal connection here, because this is how I felt when I was reading the earlier passages.
After a lot of trial-and-error, the King and his court determine the answer and create an equation to solve future problems quicker: The Quadratic Formula.
My only problem with this is, why all the explanation in the beginning of the chapter? All that back-story to the formula just confused me. Is that ever going to come in handy? Why couldn't they say: this is the formula, plug in the numbers to solve.
The rest of the chapter is practice problems, I'm going to go try a few of them now that I'm equipped with the formula.
Tuesday, October 6, 2009
Quadratic Equations (Part 1)
On page 162, in the first word problem, the professor says that Pal can only catch the ball when it is exactly 10 units about the ground. I wonder why does it have to be exactly 10 units? What if he bent down to get the ball, or if he jumped up? When I've seen baseball games, the outfielder uses different strategies to try to catch the ball at different heights, so I wonder why Pal can only catch the ball at exactly 10 units.
When the king described the function for the ball, that x is the time since the ball left the bat, and y is the height of the ball above the ground, I could already see a graph forming in my mind. I could see an imaginary line measuring time going from the bat to the outfield, I could see another imaginary line from the group up towards the ball, measuring its height.
On the next page , they explain that after hitting a lot of fly balls, they came up with the equation f(x) = -x^2 + 7x. I don't understand how the data was transferred into this function. I re-read the passage a few times and I still feel like there was a step skipped.
The professor then said that f (x) = 10. I'm confused why this is, but I guess you just have to trust him.
After plugging that in we got that x^2 - 7x +10 = 0.
After finding this equation, we could use it to make a graph. I could see the lines of the graph, with the x and y axis. After having an image in my head, I thought that if we plug in numbers for x, we will get the y coordinates, and then we can graph the equation. Looking at the graph I was confused to what the curve meant, at what point could Pal catch it? What did all these numbers mean?
I re-read the entire problem. I realized that when f (x) = 10, that was where Pal could catch it, so we were trying to figure out the time. After plugging in numbers, we found that there were 2 different points on the graph that solved the equation. I couldn't figure out which was the right one, even after re-reading the problem and looking at the graph. I double checked my numbers and they still worked.
I think that was enough math for one night, so I'm going to put it aside and hopefully return refreshed another time.
When the king described the function for the ball, that x is the time since the ball left the bat, and y is the height of the ball above the ground, I could already see a graph forming in my mind. I could see an imaginary line measuring time going from the bat to the outfield, I could see another imaginary line from the group up towards the ball, measuring its height.
On the next page , they explain that after hitting a lot of fly balls, they came up with the equation f(x) = -x^2 + 7x. I don't understand how the data was transferred into this function. I re-read the passage a few times and I still feel like there was a step skipped.
The professor then said that f (x) = 10. I'm confused why this is, but I guess you just have to trust him.
After plugging that in we got that x^2 - 7x +10 = 0.
After finding this equation, we could use it to make a graph. I could see the lines of the graph, with the x and y axis. After having an image in my head, I thought that if we plug in numbers for x, we will get the y coordinates, and then we can graph the equation. Looking at the graph I was confused to what the curve meant, at what point could Pal catch it? What did all these numbers mean?
I re-read the entire problem. I realized that when f (x) = 10, that was where Pal could catch it, so we were trying to figure out the time. After plugging in numbers, we found that there were 2 different points on the graph that solved the equation. I couldn't figure out which was the right one, even after re-reading the problem and looking at the graph. I double checked my numbers and they still worked.
I think that was enough math for one night, so I'm going to put it aside and hopefully return refreshed another time.
Tuesday, September 29, 2009
The Things They Carried by Tim O'Brien (Part 3)
On page 612, there is a line "It wasn't cruelty, just stage presence. They were actors and the war came at them in 3-D. When someone died, it wasn't quite dying, because in a curious way it seemed scripted..." This made me remember when I saw Apocalypse Now, this movie provided my mind with a specific image of how I picture the Vietnam war. Every time I read anything related to the Vietnam war, this film allows me to envision how the characters would look. Their uniforms, their weapons, the things they carried are all things that I can see through this film. This is a clip of one of the iconic scenes in the film:
On page 614, there is a description of Jimmy burning Martha's letters and photos. Here I make a connection to in the past when I have felt the need to destroy physical objects that represent a certain aspect of a failed relationship. Throwing away the objects, deleting the images, nothing erased them memories that I had. I predict this will happen to Jimmy, even though the physical reminders of Martha are gone, she will always be in his mind. The narrator later says, "You couldn't burn the blame." I can see the image of the flames burning the photos and letters but Jimmy still felt the guilt about Ted Lavender's death.
The last mention of "weight" occurs on page 615, "their days would seem longer and their loads heavier." I could see the platoon of men struggling with the weight of their heavy equipment with the added emotional weight of Ted Lavender's death. The weight of responsibility dragged them down and made their loads seem heavier.
I can see the men marching on, with grim faces and dragging their heavy loads, but they keep marching...
On page 614, there is a description of Jimmy burning Martha's letters and photos. Here I make a connection to in the past when I have felt the need to destroy physical objects that represent a certain aspect of a failed relationship. Throwing away the objects, deleting the images, nothing erased them memories that I had. I predict this will happen to Jimmy, even though the physical reminders of Martha are gone, she will always be in his mind. The narrator later says, "You couldn't burn the blame." I can see the image of the flames burning the photos and letters but Jimmy still felt the guilt about Ted Lavender's death.
The last mention of "weight" occurs on page 615, "their days would seem longer and their loads heavier." I could see the platoon of men struggling with the weight of their heavy equipment with the added emotional weight of Ted Lavender's death. The weight of responsibility dragged them down and made their loads seem heavier.
I can see the men marching on, with grim faces and dragging their heavy loads, but they keep marching...
Tuesday, September 22, 2009
The Things They Carried by Tim O'Brien (Part 2)
Before I did the next part of the reading, I thought to myself...what do I see when I think about the Vietnam War.
This is the first image that comes to mind. This is a famous photograph taken after a napalm attack. This image of cruelty and violence is what I see.
The next thing I think of is a personal connection, my dad was drafted but intentionally failed the mental health standards so didn't have to fight. However, many of his friends were drafted and died while fighting. So I think of protests and resistance against the war.
They carried weapons, I visual machine guns and lots of ammo. I recall the weight of lifting a rifle at a shooting range, I could barely lift it with both hands. I imagine how physically straining carrying 3 weapons would be.
On 607, I feel the weightlessness of the small pebble Martha gave Jim. I imagine a balance scale that has the weight Jim carries on one side and the weight that Martha carries on the other. Jim carries the weight of his life, his men's lives, and a responsibility to his country. Martha carries a love of poetry, and college life. 
"Imagination was a killer." (p 608) This line leads me to predict that Jim's imagination was going to get him in a serious situation.
When Jim has to stand watch on a tunnel mission, his mind wanders and he day dreams of Martha. "he was not there." (p 608) His mind is far away, thinking of Martha and where he should be, with her. He cannot handle all the weight he has been given to carry. "He was just a kid at war, in love." ( p 609) I thought of the contrast of love and war and how love was the message of peace which is the opposite of war. I thought this is a powerful line that really explains the emotional condition of Jim.
Friday, September 11, 2009
The Things They Carried by Tim O'Brien (Part 1)
For my content area reading, I selected "The Things They Carried" by Tim O'Brien. Although many of my friends read this short story in high school, I wasn't exposed to it until college. It is one of my favorite short stories. The work is fiction but because of his real life experience in Vietnam, it has chilling realism. You can read a short biography about Tim O'brien here: Tim O'Brien's Wiki. This is the story of a platoon of American men and what they carried with them during the Vietnam War.
The first paragraph of this story draws the reader into Lieutenant Jim Cross' character and his imagination. The description of these scenes are highly visual, which lead me to picture Martha. I could see Martha sitting in her college classrooms, her reading and writing the letters to Jim. I pictured her slowly and carefully licking the envelope's seal.
The next paragraph introduced the reader to more characters and what they carried. This made me think of what I would carry with me, what I would deem a "necessity" and how it would vary with the characters in the story. I also related characters to people I know, Henry Dobbins reminded me of my friend Gerard because is a big guy who loves dessert. Dave Jensen reminded me of my boyfriend, since he values cleanliness. Ted Lavender reminded me of my friend Joe I. since they are both paranoid and rely on drugs to medicate their emotions. Norman Bowker reminded me of myself, because I would want a diary with me. Those were only some of the connections I made with the characters.
When the narrator discusses the weight of items, I added it up and tried to picture/feel what carrying that amount of weight, all the time, would be like. It would be exhausting. I also pictured Ted Lavender being wrapped in a poncho and carried away by the men.
The next section brings the reader back to Martha. The text is so descriptive it automatically formats images in my mind. I could see the photographs, I could feel the wear of them, the color starting to fade, lines forming where it gets folded. I saw Martha leaning against a brick wall. I could see Martha in the middle of an intense volleyball game. The mention of Bonnie and Clyde reminded me of the death scene, full of gunshots and violence and wondered how it relates to the whole story.
In the next section, the narrator points out the Jim carried "The responsibility for the lives of his men." At this point, I predicted that this meant their would be a failure on his part. That it was too much for him to carry.
When it is revealed that Fat, the medic carried M&M's, I pictured a wounded solider being fed colorful candy to alleviate his pain. I also predicted there would be wounds were so painful that nothing could fix them, whether it was mental or physical.
Kiowa description of Ted's death on page 606 was extremely visual, especially when it was directly contrasted to what it looks like in the "movies." I pictured a human body falling, like a rock or sandbag falling from a high elevation. The repetition of the story made me predict that Ted's death will effect the whole platoon.
The first paragraph of this story draws the reader into Lieutenant Jim Cross' character and his imagination. The description of these scenes are highly visual, which lead me to picture Martha. I could see Martha sitting in her college classrooms, her reading and writing the letters to Jim. I pictured her slowly and carefully licking the envelope's seal.
The next paragraph introduced the reader to more characters and what they carried. This made me think of what I would carry with me, what I would deem a "necessity" and how it would vary with the characters in the story. I also related characters to people I know, Henry Dobbins reminded me of my friend Gerard because is a big guy who loves dessert. Dave Jensen reminded me of my boyfriend, since he values cleanliness. Ted Lavender reminded me of my friend Joe I. since they are both paranoid and rely on drugs to medicate their emotions. Norman Bowker reminded me of myself, because I would want a diary with me. Those were only some of the connections I made with the characters.
When the narrator discusses the weight of items, I added it up and tried to picture/feel what carrying that amount of weight, all the time, would be like. It would be exhausting. I also pictured Ted Lavender being wrapped in a poncho and carried away by the men.
The next section brings the reader back to Martha. The text is so descriptive it automatically formats images in my mind. I could see the photographs, I could feel the wear of them, the color starting to fade, lines forming where it gets folded. I saw Martha leaning against a brick wall. I could see Martha in the middle of an intense volleyball game. The mention of Bonnie and Clyde reminded me of the death scene, full of gunshots and violence and wondered how it relates to the whole story.
In the next section, the narrator points out the Jim carried "The responsibility for the lives of his men." At this point, I predicted that this meant their would be a failure on his part. That it was too much for him to carry.
When it is revealed that Fat, the medic carried M&M's, I pictured a wounded solider being fed colorful candy to alleviate his pain. I also predicted there would be wounds were so painful that nothing could fix them, whether it was mental or physical.
Kiowa description of Ted's death on page 606 was extremely visual, especially when it was directly contrasted to what it looks like in the "movies." I pictured a human body falling, like a rock or sandbag falling from a high elevation. The repetition of the story made me predict that Ted's death will effect the whole platoon.
Tuesday, September 8, 2009
Literacy Autobiography
When I was a toddler, I wasn't allowed to watch much television. However, I was encouraged to watch Sesame Street. It became my favorite show (followed by Barney). I remember watching the colorful letters pop up on screen alongside a puppet and even accompanied by a song like"C is for Cookie..." This child's television show encouraged me to know my alphabet. I would walk around the house singing the songs and finding objects that started with different letters.
My parents soon realized that I had a good understanding of language, so they registered me for a placement test of a advanced program in elementary school. I don't remember the actual test, but I'll never forget the results. I failed. My pre-school friends all passed and were off to their fancy programs in their schools. My parents were devastated, I felt like I let them down. That's when they began the more formal at-home education.
Since I could read above my level my parents assumed my mathematical skills were below par. They also believed that males were better at mathematical skills and females were better at verbal skills. Everyday I was trained in math. By the time I was 7, I knew the 12 times tables. By the time I was in 4th grade and subject to state testing, my balance had completely shifted. My math scores were nearly perfect, however my verbal scores were just okay. I began to hate reading, since I thought I wasn't good at it. My dad had to bribe me to read books. Since I had became obsessed with popular music, we made a deal that for every book I read, he bought me one CD.
The bribery worked well for a few years, but I never really appreciated literature until I was in high school. My first English teacher was able to show me works that I was actually interested in, like ancient mythology. I also began turning to the Internet to further research and read articles about subjects I was interested in, like music and mythology.
I started reading books and magazines willingly. My dad signed me up for TIME and Rolling Stone magazines. I also began reading books like Go Ask Alice, that I could relate to. I also didn't feel any pressure attached to reading outside of school. I especially liked to read when I was traveling, it helped pass time even better than listening to my CD player. After a few college classes, I started to always carry a book with me.
My parents soon realized that I had a good understanding of language, so they registered me for a placement test of a advanced program in elementary school. I don't remember the actual test, but I'll never forget the results. I failed. My pre-school friends all passed and were off to their fancy programs in their schools. My parents were devastated, I felt like I let them down. That's when they began the more formal at-home education.
Since I could read above my level my parents assumed my mathematical skills were below par. They also believed that males were better at mathematical skills and females were better at verbal skills. Everyday I was trained in math. By the time I was 7, I knew the 12 times tables. By the time I was in 4th grade and subject to state testing, my balance had completely shifted. My math scores were nearly perfect, however my verbal scores were just okay. I began to hate reading, since I thought I wasn't good at it. My dad had to bribe me to read books. Since I had became obsessed with popular music, we made a deal that for every book I read, he bought me one CD.
The bribery worked well for a few years, but I never really appreciated literature until I was in high school. My first English teacher was able to show me works that I was actually interested in, like ancient mythology. I also began turning to the Internet to further research and read articles about subjects I was interested in, like music and mythology.
I started reading books and magazines willingly. My dad signed me up for TIME and Rolling Stone magazines. I also began reading books like Go Ask Alice, that I could relate to. I also didn't feel any pressure attached to reading outside of school. I especially liked to read when I was traveling, it helped pass time even better than listening to my CD player. After a few college classes, I started to always carry a book with me.
Subscribe to:
Posts (Atom)
