There is a BIG difference between learning and just being there. Learning is an interactive sport; not a spectator sport. There has to be a conversation between us, back and forth, as we work through the material. Learning doesn't happen when I talk and you listen; learning happens when you have a conversation -- with me and with each other.
I am going to offer you up to 5 bonus points on your test with completion of a simple assignment. I would like you to post your reflections on the material covered so far. Just comment on this post. To get that bonus on your test, the kind of post I'd like you to make should have one or more of these characteristics:
I am going to offer you up to 5 bonus points on your test with completion of a simple assignment. I would like you to post your reflections on the material covered so far. Just comment on this post. To get that bonus on your test, the kind of post I'd like you to make should have one or more of these characteristics:
- A reflection on a particular class (like the first paragraph above-how did that class enhance your learning?).
- A reflective comment on your progress in the course.
- A comment on something that you've learned that you thought was "cool".
- A comment about something that you found very hard to understand but now you get it! Describe what sparked that "moment of clarity" and what it felt like.
- Have you come across something we discussed in class out there in the "real world" or another class? Describe the connection you made.
I liked the class where we we studied how to solve a absolute value equation. I found it every helpful and easy to understand. Through this course I have progressed but more slowly than some of the other units because I get confused more. Solving compound inequalities is harder for me than other math problems so it took me longer to figure it out. I thought it was cool that you get a positive value when you solve for the absolute value even if the number was negative. I found the word problems in solving inequalities hard. My moment of clarity came when I realized that I just had to translate the word problem into math terms and then I could solve it. I think that inequalities relate to the real world in lots of ways. An example would be if Ava got 3 more pieces of candy than I did. x< 3 would be me and x>3 would be Ava.
ReplyDeleteI liked the class where we went over the word problems. It helped me understand it a lot better. I feel like I am making a lot of progress in the course. I am not having trouble with anything yet. I thought it was cool when we did the absolute value problems, it made it a lot more fun when Jojo related it to football. My moment of clarity today was when Jojo related the absolute value problems to real life, I didn't get them before but after he explained it I understood. I have found that absolute value problems relate to real life. The touchdown problem was extremely helpful.
ReplyDeleteI like the class were we learned about 3.3 solving absolute values and inequalities. I already knew how to solve absolute value but i didn't know that /-a/= -(-a) which is if you think about it very much true. I also learned that when you have an equation inside the absolute value sign you should solve for a negative and you should solve for a positive. With this understanding of inequality i have realized that there is much more to absolute value.
ReplyDeleteI really liked the class we had today, (on 3.3,) last year I struggled a lot with absolute values, just the whole concept of two equations and how you graph them. Well, after the class we had today with the really long example, going step by step and even after only doing half the homework I feel like I understand 16 times better. It was really nice to really understand it because it will definitely come up again in future math classes. I want to make sure that I understand 3.1 and 3.2 as much as I know understand 3.3, because in that case, I would be in great shape for the test as well as building upon these ideas in future sections.
ReplyDeleteBrigid
I liked the class when we went over the word problems that were in section 3.1 because at first they all seemed really confusing and hard to set up, but once we did a problem aloud and went through each step it really enhanced my learning because now the problems don't feel as challenging. I think that my math has been improving a lot this year because now instead of just learning everything really fast, we take things slower which really helps me understand a lot of the material fully. I thought it was cool today when we learned that absolute value inequalities can have two possible answers. My moment of clarity was when we did some of the word problems together and went through each step because at first it was really hard for me to know how to step up each problem, but after going over it I understand a ton better now. In section 3.1 there are problems having to do which averaging test scores, which relates to the real world. I never knew how to average them before, so now I know which is really helpful.
ReplyDeleteToday in class, when we where discussing how if the value of a was negative then: |a|=-a. last year I never understood why this was true if I would always get a positive answer. The example: a=-7; |-7|=-(-7) that we did in class really help me clarify why the answer would come out as a positive number in a way that made complete sense to me instead of being told that it "just works out". Today I also learn how to solve an absolute value problem for if x was positive or negative. which was also very neat because I always assumed that there was only one out come. Again it really helped to see why each problem worked out the way that it does, instead of just memorizing an equation and learning where to plug in certain numbers.
ReplyDeleteYesterday in class I needed help on an inequality that involved a fraction. I was really confused how to solve the equation, until JoJo and Jonathan helped me. First you have to clear the fraction by multiplying the denominator by itself and then from there you solve and divide each side of the problem by he variable given. And now you will have your answer. By, doing that problem in class, i have a better understanding in solving the problems.
ReplyDeleteToday's class was really helpful because we went over absolute value. Someone said that a way to think about absolute value is thinking about the distance from zero the number is. Or drawing a number line. Then I can see the distance visually and on paper so I won't mess up.
ReplyDeletefor example -3 is 3 away from zero
<--|---|---|---|->
-3 -2 -1 0
The other day, when we talked about inequality signs, I went to spanish and we were learning how to say if someone had more or less of something. And I was all like "we just talked about that in math!" :)
I really enjoyed class today, it felt like a break from just compound inequalities as we moved into absolute value problems. I really understood what we went over today because we had seen absolute values before in the year. I feel like I have been continuosly improving throughout the year. I am really proud to be doing better! I thought it was really cool when JoJo talked about solutions to absolute values problems as, a and -(a). It was confusing at first but it made sense when he specified. At first, I didn't understand how there could be two answers to one problem, but then I understood that there is the negative form and the positive form that you need to solve for. Intersections definately apply to everyday life! They are everywhere on the way to school!
ReplyDeleteI really liked the way Jojo elaborated in class today. I personally thought that finding the two possible solutions to an absolute value equation was quite pointless and a waste of time. But he gave a good example on a current event. He explained that in order to find the number of Football scores(touchdowns) Alabama would make knowing that they would make +1 or -1 more than their average.The equation was this:
ReplyDelete|x + 4|= 1
And figuring out both negative and possitive answers would tell me that they were going to make either 3 or 5 touchdowns! :) It was confusing at first, but I finally got it and now I don't think it is much of a waste of time as I used to think.
I really liked the class where we went over the word problems from that nights homework. I felt like I learnt a lot from this class. In chapter 3, I feel pretty good only because this is a review for me. I actually love solving for inequalities! One think I think is cool is in section 3.3, |x| can be two things, a negative or a positive. I thought this was pretty cool! One thing I did NOT get was how to solve an inequality like this:
ReplyDelete4< 2x +4 > 8
I did not get that you had to add 5 to BOTH sides AND divide 2x by BOTH sides of the equation. When I finally figured this out I felt great! One example I though of in the "real world" was shopping!
I liked todays class because it helped me understand some things I did not know before. Before, I never thought about an absolute value problem when i saw one. I automatically knew that if it was a negative number that it had to be positive. I never thought that there could be negative absolute values. I also never thought that an absolute number is the distance from zero. Like with negative absolute values, i never thought about it, it just clicked automatically for me. So, I am glad we had todays class.
ReplyDeleteWhat i learned that i thought was cool was how to solve an absolute value equation. I didn't think the actual process of learning this was cool but what you can use it for is awesome. I used what i learned to calculate the scores for the Alabama vs. LSU game (NOT UNTIL NEXT WEEK ON NOVEMBER 6). The equation i used was | x+ average of touchdowns a game| = 1. The minimum for the score of Alabama was 22.566 points and there maximum score was 34.56 points. LSU's scores on the other hand we much lower there minimum is 16.748 and there maximum is 23.748. But it is still possible if Alabama scores 1 touchdown under there average and LSU scores 1 touchdown over there average that LSU can beat Alabama, but this is EXTREMELY unlikely because LSU has one of the lowest scoring offenses in the SEC and the offense has no real big play maker that can gash you on a single play. Were on the other hand Alabama has 3 NFL caliber players on offensive who every time they touch the ball the can score. So that is why i think solving absolute value equation are cool and why Alabama is going to beat LSU
ReplyDeleteMy understanding of absolute values has... increased; this due to my new realization of how each absolute is written. My initial confusion about
ReplyDelete"X(negative number -- |x|=-x"
was replaced by a feeling of greater understanding after you (JoJo) worked the problem. Thanks!
Also, though this is not about absolute values, i now understand the function of some programs written that i had not grasped the concept before. (In python shell). This probably means nothing to anyone except me, but thanks. I'll try to say what i mean.
>>> any(i>5 for i in xrange(10))
True
>>> all(i>5 for i in xrange(10))
False
So, that is a program written to save time in a loop for a greater program, like... source code if one were to write something like a music shuffle program. Or a website. Or something else. It doesnt matter- the point is, this program now actually means something to me; i understand how it works, all due to JoJo's uncanny ability to explain math terms in a simple and understanding way.
So, i thank you.
PS:
Dont think about this previous code, son.
>>> bar = range(5)
>>> map(lambda f: True if f>3 else False, bar)
[False, False, False, False, True]
probably this function would end up helping more, but, for sake of what you have helped me with, this is not really important.
What we did in class that I found useful is going over how to solve inequalities with absolute values. What I learned is that in order to solve the problem you need to set up two equations. One asuming the value inside the absolute value is positive an one asuming it is negative.
ReplyDeleteExample: |X+2|>3
X+2>3 or -(X+2)>3
X>1 X+2<-3
X<-5
I thought the absolute value could never be negative no matter what.
I found todays class helpful when we went over inequalities with absolute values. Also using football and more real life sitiutations and problems helped me understand how to set up the two equations and solve the problem. This was kind of a moment of clarity when Jojo used these comparisons. I thought this was cool.
ReplyDeleteI enjoyed class yesterday and today, on absolute values, because I thought that I could really understand the material. I feel as though that going over this made me feel sure that I could understand math if I looked at it the right way. Last year in eight grade we went over problems similar to this and I never really understood how a negative number could just change to a positive, just because of the distance between zero. Yesterday in class we went over how and why a negative absolute value would change to a positive, going over this really cleared up all the previous confusions I had about absolute values and now I feel like I can go about doing these problems without having any problems. I feel like since switching from A2 math I have progressed forward in understanding the things we had gone over in the beginning of that class, and I have been relieved from a lot of stress I had that math was bringing me.
ReplyDeleteI am new to the class, but so far I really like it! I liked today a lot because we devote 15 to 20 minutes of our class period going over questions we have about the homework the night before. I also think it is cool with the absolute value equations, that we can compare them to real life situations. Someone in class yesterday was talking about football statistics and was using absolute value equations to solve the problems. This shows how people may not think some parts of math will help them when they are older, but they really do. I also forgot from last year that each absolute value equation or inequality has two answers, so it was nice to revisit this during the class period the other day.
ReplyDelete