I am leaving this week a bit frustrated. I find probabilities to be rather confusing. It leads me to ask one question. Do elementary students really do these problems? I am thinking it must be geared more towards middle school. Then again maybe I am just trying to make myself feel better for not getting it.
Now, don't get my wrong. I get the importance of probabilities. I think they are an everyday tool, I just think in my head there must be an easier way. I think this is part of my problem though. There isn't a formula you "always" use. It is based on the question. Does it or doesn't it? Regardless, I need more practice and probably should have put in some extra time to try to gain a better understanding of it. And for the students that get this: KUDOS to you!
Since I do like formulas, I am going to focus on one. The definition of odds.
Odds in favor: A = P(A)
1- P(A)
Odds against: A = 1- P(A)
P(A)
These formulas are easy to use and if only they applied to most probability questions, we would be in business.
I found this video on youtube that is called the Monty Hall Problem and discusses the probability of opening a door to win a car and what your strategy should be. It gives the mathematical reasoning behind the choice. It's interesting.
Monday, June 27, 2011
Wednesday, June 22, 2011
1510 Week 3
I am consumed with estimations! I feel like I really gained a lot from this last chapter. I always had a good idea of how to estimate something, but it was neat to see so many different ways to figure out a problem. I was always taught the traditional algorithm way of adding numbers and subtracting, like 8 + 10. Put it in the flowing format and solve right to left.
10
+ 8
18
But breaking up the numbers like the break apart method where you take a problem like 4 x 28 and break it up into the place values, so take 4 x 20 = 80 and 4 x 8 = 32 then add 80 + 32 = 112.
I think this technique is great for not only solving problems in your head, but also for getting a clear understanding of place values and the role they have in math. Here is a video I found on youtube that gives a few examples of multiplying in your head.
10
+ 8
18
But breaking up the numbers like the break apart method where you take a problem like 4 x 28 and break it up into the place values, so take 4 x 20 = 80 and 4 x 8 = 32 then add 80 + 32 = 112.
I think this technique is great for not only solving problems in your head, but also for getting a clear understanding of place values and the role they have in math. Here is a video I found on youtube that gives a few examples of multiplying in your head.
Doing math problems in my head has never been a strong suit for me. I can do simple math of course, but when it comes to figuring out larger numbers, I am a pencil and paper person or calculator). In the classrooms I observed last year, I spent a lot of time in an advanced math class of fourth graders. I was taken back on how quickly they could compute the problems, many times in their heads.
Chapter 3 explained to me how that was done. It seems silly to me that I wasn't taught this way because it not only makes it easier to figure out, but it really explains the "meat and potatoes" behind place values (which is so important). An example of a mental computation is the " Choosing Compatable Numbers Technique". It never dawned on me as a student to try and make the problem simpler and that is what this technique does. Here is an example:
(5x6) (30x2) so 5x30 is easy to figure out 150, and 150 x2 is 300, take 300x6 and you get 1800.
Another technique that is easy to use is the "Equal Additions Technique". In this technique you change the numbers to make them easier to solve. Here is an example:
82-47=? To solve this, you would figure out what changes you can make o the numbers to make the subtraction easier. Well, subtracting by 10 is easy, so if I add 3 to each number (82 becomes 85 and 47 becomes 50) you can make the subtraction much easier. So the new problem becomes 85-50=35, so 82-47=35.
Using these techniques can help a student that struggles with math a bit easier and, like I said earlier, it helps to give an understanding to how these numbers work.
Chapter 3 explained to me how that was done. It seems silly to me that I wasn't taught this way because it not only makes it easier to figure out, but it really explains the "meat and potatoes" behind place values (which is so important). An example of a mental computation is the " Choosing Compatable Numbers Technique". It never dawned on me as a student to try and make the problem simpler and that is what this technique does. Here is an example:
(5x6) (30x2) so 5x30 is easy to figure out 150, and 150 x2 is 300, take 300x6 and you get 1800.
Another technique that is easy to use is the "Equal Additions Technique". In this technique you change the numbers to make them easier to solve. Here is an example:
82-47=? To solve this, you would figure out what changes you can make o the numbers to make the subtraction easier. Well, subtracting by 10 is easy, so if I add 3 to each number (82 becomes 85 and 47 becomes 50) you can make the subtraction much easier. So the new problem becomes 85-50=35, so 82-47=35.
Using these techniques can help a student that struggles with math a bit easier and, like I said earlier, it helps to give an understanding to how these numbers work.
Monday, June 20, 2011
1512 Week 2 post
Chapter 8 was a brain frying chapter. No, I mean that in a good way. I actually really took a lot away from this chapter. This chapter was on "Analyzing Data". It was a lot of, take this info and tell me a, b and c.
The first part of the chapter went over the basics of graphs, like a dot plot, stem and leaf plot, histographs and the classic bar graph. One thing that I found interesting was the difference between a histograph and a bar graph. They look the same, L shaped with vertical columns. The histograph's are side by side and the bar graphs are spaced apart. Our textbook calls it "nonadjacent intervals". Does a graph have a positive, negative or zero correlation? That was pretty easy to recognize. This was not the part that made my brain hurt.....that was the next section.
Like I explained in the beginning. The challenge of figuring it all out was a good thing. I have discovered that I am not an "abstract" math learner. I prefer to be told this is how you solve a problem, now follow along and do it. This may bring a further challenge to me as a teacher though because I need to be open to different ways of figuring things out. My husband for example, does a lot of math in his head. When I am working on problems, he peeks over and just blurts out the answer. I have to kindly remind him, "Hey dude, back off. I can't learn that way!" But maybe I should be asking him to show me how he does that. Maybe it would "click" with me and allow me to broaden my scope of teaching. Even if it doesn't "click" with me, it may be helpful and "click" with one of my students down the road.
I do like formulas that you can just plug in your numbers. I, however, do not enjoy memorizing them. Something else I have to work on. I feel like I have a good understanding of "mean" - the average "median"- the middle and "range" - the distance between the smallest and largest numbers. Ah the variance. It is tedious work. But having the green box pop up "FANTASTIC!" is so rewarding. I made it and I look forward to the next.....
PS Here is a link to enchanted learning with a sample of a worksheet that can be used to teach graphing to students using dinosaurs.Enchanted Learning
The first part of the chapter went over the basics of graphs, like a dot plot, stem and leaf plot, histographs and the classic bar graph. One thing that I found interesting was the difference between a histograph and a bar graph. They look the same, L shaped with vertical columns. The histograph's are side by side and the bar graphs are spaced apart. Our textbook calls it "nonadjacent intervals". Does a graph have a positive, negative or zero correlation? That was pretty easy to recognize. This was not the part that made my brain hurt.....that was the next section.
Like I explained in the beginning. The challenge of figuring it all out was a good thing. I have discovered that I am not an "abstract" math learner. I prefer to be told this is how you solve a problem, now follow along and do it. This may bring a further challenge to me as a teacher though because I need to be open to different ways of figuring things out. My husband for example, does a lot of math in his head. When I am working on problems, he peeks over and just blurts out the answer. I have to kindly remind him, "Hey dude, back off. I can't learn that way!" But maybe I should be asking him to show me how he does that. Maybe it would "click" with me and allow me to broaden my scope of teaching. Even if it doesn't "click" with me, it may be helpful and "click" with one of my students down the road.
I do like formulas that you can just plug in your numbers. I, however, do not enjoy memorizing them. Something else I have to work on. I feel like I have a good understanding of "mean" - the average "median"- the middle and "range" - the distance between the smallest and largest numbers. Ah the variance. It is tedious work. But having the green box pop up "FANTASTIC!" is so rewarding. I made it and I look forward to the next.....
PS Here is a link to enchanted learning with a sample of a worksheet that can be used to teach graphing to students using dinosaurs.Enchanted Learning
1510 Week 2 post
What a chapter, chapter 2 was. One word, YUCK! I spent much of this chapter wondering a few things. What is this "math" all about? Is it really for elementary kids? Why learn this?
Ok, let me back up a bit. I realize my introduction may seem a bit negative. I think this intro is similar to many students when it comes to math. Math can be a confusing bustle of numbers, surrounded by formulas, rules and exceptions. It can be hard to keep it all straight. More importantly, if you can't find a link to life with math, then it seems like a drag. So, let's briefly recap what I learned.
As I started with Chapter 2, I developed an understanding for sets. Ok, a set is just a grouping of something. I got that. One to one correspondence? Do they align up to another set equally? Sure, no problem. Subsets - come on. Is this group in that group. Zing. A proper subset, sure it's a subset of a given set, but one element is missing from the first set that is listed in the second set. That's a breeze. Unions, intercepts, uh, I can do symbols. A U and a upside down U, not so tough.
Next, we got properties. Closure, Identity, Commutative and Associative. I don't recall this from school, but hey, I open to new things. Now, I am a bit of a definition freak. I like them. Give me a word and tell me what it means. Closure property - "For whole numbers a and b, a+b is a unique whole number." (Mathematics for Elementary Students, 2008) Ok, um let's move on to Cartesian product with A cross B. Ohhhh, like 6 x 6 = 36. Not so bad. Let's skip forward to Hindu and Egyptian numerical systems. Oh and let's not forget Mayan and Babylonian. Ok, as weird as this was, I actually felt like I got these down.
These examples are just a snapshot of what I have learned. As I pull in the beginning of this post and ask my questions, WHAT? WHY? HOW? I think it is really important for students to understand these questions. As I went through the information, I found that when the book gave examples in "real life" I had a much better understanding of what the definition of a word was and how it does relate to everyday. It made it easier to learn and well, worth learning.
Here is a link to a website called Yummy Math. It is designed by some math teachers to help make math relevant to everyday life. Yummy Math
Ok, let me back up a bit. I realize my introduction may seem a bit negative. I think this intro is similar to many students when it comes to math. Math can be a confusing bustle of numbers, surrounded by formulas, rules and exceptions. It can be hard to keep it all straight. More importantly, if you can't find a link to life with math, then it seems like a drag. So, let's briefly recap what I learned.
As I started with Chapter 2, I developed an understanding for sets. Ok, a set is just a grouping of something. I got that. One to one correspondence? Do they align up to another set equally? Sure, no problem. Subsets - come on. Is this group in that group. Zing. A proper subset, sure it's a subset of a given set, but one element is missing from the first set that is listed in the second set. That's a breeze. Unions, intercepts, uh, I can do symbols. A U and a upside down U, not so tough.
Next, we got properties. Closure, Identity, Commutative and Associative. I don't recall this from school, but hey, I open to new things. Now, I am a bit of a definition freak. I like them. Give me a word and tell me what it means. Closure property - "For whole numbers a and b, a+b is a unique whole number." (Mathematics for Elementary Students, 2008) Ok, um let's move on to Cartesian product with A cross B. Ohhhh, like 6 x 6 = 36. Not so bad. Let's skip forward to Hindu and Egyptian numerical systems. Oh and let's not forget Mayan and Babylonian. Ok, as weird as this was, I actually felt like I got these down.
These examples are just a snapshot of what I have learned. As I pull in the beginning of this post and ask my questions, WHAT? WHY? HOW? I think it is really important for students to understand these questions. As I went through the information, I found that when the book gave examples in "real life" I had a much better understanding of what the definition of a word was and how it does relate to everyday. It made it easier to learn and well, worth learning.
Here is a link to a website called Yummy Math. It is designed by some math teachers to help make math relevant to everyday life. Yummy Math
Thursday, June 16, 2011
First timer
So this is my first blog. At first I was a little doubtful on creating a blog. I am not very computer literate and furthermore I don't really like math. But then I started to really think about what I could post on this blog and I am kind of excited. It is a great place for me to post what I have learned so I can share tricks and also have a quick reference to look back on.
That's it...I am believer!
That's it...I am believer!
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