Lines

Here is a summary and review of what we've been learning over the last few days. There is a neat little java applet you can play with to see how changes in the slope and y-intercept effect the graph of a line.

Try the exercises here too if you wish. Towards the bottom of the page you'll find 3 animations of how changing slopes effect the graphs of lines with different y-intercepts. (Click on the animated gif links.)

How many lines do you see?

Update!
Since I noticed some of you are struggling with the homework I thought this online lab might help. The text in some places may be long, but stick it out and try it -- you'll learn a lot. And that's what we're all about, isn't it? ;-)

Slope AKA Rise Over Run AKA Rate of Change

We discovered the "slope" formula today. Remember the different ways to find and interpret the slope depending on if the function is described as a graph, table of values or an equation. You can find a review of the lesson here. Follow the [Now YOU try it!] links to practice what you learned.

You can also quiz yourself on what you learned here, and there. And this is a little review quiz on the midpoint formula.

Does that picture remind you of anything? ;-)

SCRIBE?

Well it seems that I am your scribe for today. I'll finish this and get it out of the way early so that most if not all of you can read it :D (other than the fact that I'm scared that I'll forget what we did during the class..)

During the start of our average class, we started off with the usual "Questions on board." Those questions included finding the perimeter of a rectangle given coordinates of each corner, finding the coordinates of one end point given the midpoint and the starting point of the line, and of course the new stuff which is about graphing lines and table of values.

NEW STUFF: example

y = 2x - 1

Words: Double the input and subtract one.

Table of Values:
X Y
-3 -7
-2 -5
-1 -3
0 -1
1 1
2 3
3 5

In this table of values you can see that the numbers go up by twos.

Graph: I don't know exactly how I can display a graph here so I'll just have to explain it to those who are reading this post. First of all, while creating your graph, make sure to add on your scale because without the scale, how can you interpret the data? Second, you have to place arrows on the end of each line showing that the lines do not stop and continue forever.. Finally, you MUST LABEL the HORIZONTAL LINE as the X-AXIS, and the VERTICAL LINE as the Y-AXIS! Make sure that you do not forget any of these while doing your homework or tests for if Mr. K sees that you have missed any of the important factors of a graph, the outcome is.. YOU LOSING MARKS and that's what we all don't want including Mr. K :).

HOMEWORK: Today's homework is indeed EXERCISE 6, not 7 or 8... "6"

Now the moment we've been all waiting for? Well at least I think we are all waiting for.. TOMORROW's SCRIBE! Well I really don't know who to pick on.. I was going to choose Jian but he was lucky during the weekend so I will pick instead..
I hope eeny meeny miny moe works T_SA.. I CHOOSE: uuhh.. Melissa_V which hope I spelled correctly. :D GOOD LUCK MELISSA AND GOOD LUCK TO YOU ALL ON HOMEWORK! If you have any further questions or comments, please leave a comment :D

Graphs - One Perspective

Today we learned how to graph a line by generating a table of values from an equation. Here is a review.

You can use this tool to generate a table of values and a graph from any linear function. Follow these steps:

1. Enter the expression in the box next to f(x) =. i.e. if the equation is y = 2x - 1, enter 2x - 1 in the box.



2. In the boxes under Values of x enter the x-values, say from -3 through 3. You can enter more if you like.



3. Click on the button marked [Evaluate] to find all the corresponding y-values (y-coordinates).



4. Enter the ordered pair [(x, y)] with the smallest x-coordinate -- i.e. (-3, y) -- in the box next to Left End-Point: do the same for the largest x-coordinate -- i.e. (3, y) -- in the box next to Right End-Point:



5. Click the button marked [Graph] to see the graph.



6. Click the button [Erase Everything] to begin again with a new equation.

We're going to spend the next several days talking about the equations of lines. Remember the 4 perspectives of the same object (my block of wood) we discussed in class today -- it's going to come up a lot. ;-)

We're Learning the Midpoint in Room 66!

Having trouble using the midpoint formula? Here is a little review of the lesson we had today.

Over there you can practice what you've learned. Use paper and pencil first, then click on the button marked answer -- not the other way around. ;-) You can find more help if you need it right here.

Cheers,
Mr. K.

Our Readership

I thought you might be interested to know about our readership. Our blog is being read by people all over the world. The graphic below shows where the last 87 visitors to our site have come from. Of course, this is constantly changing as more and more different people pop in to see what we're doing. While some of them visit only once a number of them do keep coming back. (Of the "unlisted" readers, one is from the US and the other is from Sweden.) People are interested in what you have to say and what you are learning.

Ladies and gentlemen, you have an audience. It's worth your while to make a good impression by making sure your spelling and grammar are correct when you post. ;-)

Pythagoras

We learned about the Distance Formula today. You can see that lesson again or just practice using the formula as much as you need to until you feel you understand it.

We ran out of time before I could tell you how Pythagoras died. I mentioned that there might be something "funny" about how (or why) it happened. Search for it and share your results here, in the comments to this post. If you don't find it maybe we'll have time in Monday's class to talk about it.

He doesn't look that bad to me.

Have Fun Searching!

What does samus think about today?

hmmmm, well today we had our very first pre Cal test. At the beginning of the day I was scared and I was thinking of skipping pre cal. But, I know that it would be worse if I skipped. I might as well get it over with and receive a very low mark then a zero!

To my surprise, I actually got what was on the test! Gosh, I was so relieved that I can do it! That's when my confidence came in. I'm confident, not cocky. Yeah, but I'm happy that its over with and now I just sit back and wait for the results. Hope I do get a good mark. Fingers crossed. Oh yeah, what's our next unit? One more question, what does everybody think of the test we had today? That's all.

-Toodles.
SAMUS

the test

who thinks the test was hard??? well its kinda easy except im just not use to the multiple choice though... i'm the long answer kind of guy

My Reflection Blog for the Test

One particular and hard class, I can remember is the class where Mr. K was teaching us how to do binomial and trimomial long division. The can't understand how to find the answer for the second term. It was horrible. I also remembered the moment I learned to do it. I asked Mr. K how to do it and he explained it to me slowly and I understood. It was a good feeling to understand.

I think my progress in the class in getting better. At the beginning of the year I didn't understand how to factor or multiply polynomials. I forgot what I learned in the 9th grade, but now I am doing better.

My post,
Thang N.

MY Blog

Today I am the scribe. LOL

Today in class, we when over the answers for Exercise 3, 8, 9 and 10. Mr. K explained why x² + 4 cannot be factored. We also had a pre-test. Remember everybody tommorrow is the TEST. Finally, tomorrows scribe is Jonh D.

Happy studying. :)

Blogging on blogging 8:) yo!

Pre-Cal math? When I first come in to this class I thought I can take care of anything that the teacher give me and I was half right and half wrong. I' am right about I can take care of anything the teacher gives me but I' am also wrong about I can take care of anything the teacher give me, what I' am trying to say is that pre-cal math AP is really hard to me and I don’t really understand much at first so I wasn't really able to do my homework at the beginning but with my good teacher "Mr. K" helping me all this way, I finally understand this "Pre-cal math" for example on how he teaches me and the fellow student about learning this cool math, here is a little reflection on how we do class everyday:

Everyday in first thing when the fellow student come in to class, Mr. K will have some math questions on the whiteboard for us to do, usually it is like a fell question that we know and a fell question that we don’t know, he will give us like 10 minutes of time to do the questions and then he will show us and explain to us on how to do the questions carefully and slowly to everyone in the class until we understand it…… ok so I lie, he do the questions carefully and making sure everyone understand it only but not slowly, he do it fast, the fastest teacher I know. After that we will correct our homework, and see if anyone have any questions about the home work and we will work it out and show the class, and after that we will give me home work.

Right now I love this class because this is really hard and I like hard works because this is the only way I can learn and I want to learn so I will have a good education in my future.

During all these class in math is all "cool" because that every time the teacher giving us hard work to do and that really need brain work finish it, the teacher will try to come up with a joke to tell the class so we are relax a bit.
I really like to the question (x+10)^2 because even if I like to learn but I still like to go with my life easy and this question is the easiest question I ever do in this class.

A couple day ago I came across a question on multiply question that I don’t understand how to do and the question is 4(2m+3n)(2m-3n), at first I try everything to get the answer but I just cant do it and because of this question I stay after school to ask the teachers help and explain it to me that this is really sample because it is just like 1+2+3 the answer is 6 and if I use 3+2+1 the answer will also be 6 or 3+1+2 it will still be 6 so this is the same with 4(2m+3n)(2m-3n), I can first use 4 x 2m, 4 x 3n then x 2m and x 3n. Or I can do (2m+3n)(2m-3n) and then x by 4 the answer will still be the same. So after I understand that I’ am really happy and I want to do more and more of the same problem and so I did because this I feel that every math problem I got it all in my hand and know it all.

What I have learn in this class is helpful to me on my science class because at the same time I am learning about measuring and I don’t really get it in this class but at the afternoon the math teacher talk about the same thing and then after he explain it to the class then I understand how to do measurement and go back to my science work.
After an hour of work I just find out I only need to do one or more characteristics and not all lol

Like what Mr. K said
Cheers
“Jan Hong”
Remember “There is many ways to skin a cat” but don’t really skin a cat because it isn’t cool.

A Whole Lot of Reviewing Going On!

Our test is tomorrow! Here are some online quizzes you can do to get ready:

• Multiplying Polynomials (5 questions)


• Special Products (5 questions)


• Factoring Using the Distributive Property (5 questions)


• Factoring Trinomials (5 questions)


• Factoring Differences of Squares (5 questions)


• Perfect Squares and Factoring (5 questions)


• Dividing Polynomials (5 questions)

Don't forget to get your post up before test day as described in my post Blogging on Blogging. Your "scribe" post doesn't count for this mark.

Also, if you haven't read this yet, make certain that you do before getting your post up. ;-)

B-L-O-G

This unit that we have been doing is really a lot of what we've been learning from s1. I like that it's not new and in some ways they can be simple and understanding. I really like that we learn as a group and help eachother out if needed. I also like it when we go over things that we don't understand. Mr. Kuropatwa stops the class if one person doesn't get it or it's not sinking in. And I like that.

What I really enjoy is Mr. K's jokes! haha, no really i find them funny... in a way? No, but the factoring and stuff really is sinking in. I like the idea of making a math dictionary up. When Tests and Quizes come up, then we'll all have something to look back on and understand.

The concerns I have so far are that the dividing with intergers throw me off from the answer. And I really hate, I mean really hate is dividing with fractions. Jeez, i hate them so much! But yes, i know, fractions are our friend. If i keep working on many questions that deal with the difficulties I have, it will not be a concern no more.

A test on Thursday, darn. Well, I really hope that this test isn't timed and that it won't be as hard as the quiz. hah I wish. Well, to wrap this up I will say, I really enjoy this class a lot. It makes me laugh with the daily jokes that he has. The class is going in a good pace and math is fun.

-see you all in class =)
SAMUS!

Blog? bloooooooogg.. iiiiing..

Wow! Everyone is blogging! Soon it will be flooded :D.. well.. straight to my blog.
I like the way we start to do questions on the board because when we do, we - a.) don't have to solve the questions using the concept of time rather to solve them with focus and concetration making sure that you understand the lesson, and b.) work as a whole group usually at the same pace because there aren't very many questions as well. Well.. I could also say that I don't like the way that works because it leaves us with more homework rather than to do it in class.. :D Well.. It's probably not because it takes long, it's cuz time flies by? yepp... -.-
Hmm what else to say... Oh Math Dictionary! well.. I like the way Mr. K explains it and all but I just don't like the fact of me not writing as fast as he explains. This leads to.. me not taking in the facts he is trying to explain :P..
I think i could say that i'm doing okay in this class.. there isn't anything that i don't understand so that must be good progresss?
Well errmm what I think Mr. K should do is.. get more jokes so he can tell us MORE! (you here that mr. K? i hope so :P)

I'm Blogging

Well today's class was pretty good because I was able to get some of my problems cleared up. It also helped to get all taht information into our Math Dictionaries so I can look over it. I hope that this calss helped me with factoring and when it's the appropriate time to use the different formula things. It makes me a little more confident for the test on Thursday. That's me blogging.=)

Your Factoring Problems Are Solved!

This applet will factor pretty much any expression you enter. If you like you can have it generate a random expression and it will factor it. Here's what I'd like you to do to help get ready for your test:

  (1) Click the [Random] button.

  (2) Try to factor the given expression yourself using pencil and paper.

  (3) Click the [Factor] button and check your work. If you got it wrong, try to figure out your mistake before you try again. Refer to your math dictionary if you're having trouble.

  (4) Repeat.

Factoring Movies!

I've found some more videos that cover the types of factoring we've been studying.

Update
You need to have the free RealAudio Player installed to watch these videos too. You can download it from here

Here are the review videos; each one is between 6 and 10 minutes long:

• The Greatest Common Factor and Factoring by Grouping


• Factoring Trinomials


• More Trinomials to Factor


• The Difference of Two Squares


• Factoring: A General Review

These last two are similar to the ones I posted yesterday.

• Special Factoring: Difference of Cubes
    (5 min. 28 sec.)


• Special Factoring: Sum of Cubes
    (6 min. 46 sec.)

If you have trouble understanding anything: "Pause ... Rewind ... Repeat ..." until it makes sense. ;-)

OMG

i cant believe i moved to consumers..i want back in:(..anyways...thanks to all my class mates that helped me when i didnt get it..and thanks to mr.k for talking with me..i realized i had just made the bigggest mistake:( byee guyys..i'll just see you around i guess

Video Help Is Here!

Class time seems to just fly by! Sometimes we get hung up on a difficult problem and time seems to  d r a g  and sometimes we cover so much material in such a short time that it just seems to fly by.

I know some of us are still struggling with factoring trinomials. Long division of polynomials isn't easy either if you haven't got the hang of it yet. Well, help is here. I've got some brief video taped lectures you can watch to help you with this material over the weekend if you need it. The movies are of an instructor from the University of Idaho.

In order to watch the video you need to download the free realaudio player from here. (It's a little more than 11 Mb so if you have a slow internet connection this isn't a very good option for you.) After that, just click on the link below for help with the topic of your choice!

• Factoring a Trinomial Part 1 (9 min. 27 sec.)


• Factoring a Trinomial Part 2 (10 min. 10 sec.)


• Long Division of Polynomials and Synthetic Division (10 min. 51 sec.)

Synthetic Division is an S3 Pre-Cal topic. You can watch and learn it if you like but are expected to use long division on all assessments in S2.

If you still have trouble help each other through the chat box or comments to this post.

Have a great weekend!

Long Division is Long!

Sometimes dividing polynomials can be very long! A whole page for one problem! Part of what makes it so hard is that a single division problem may require you to use all these skills:

• adding and subtracting integers


• adding and subtracting fractions


• adding and subtracting algebraic terms


• multiplying integers and algebraic terms


• dividing integers and algebraic terms

That's a lot to keep track of!

I have two bits of advice for you:

(1) Take it slowly; one step at a time. Focus on a single skill (listed above) at a time.

(2) Remember Sysiphus! Don't give up. Keep at it and you will succeed.

If you need a little review of what we did in class today you can find it here

Cheers,
Mr. K.

Chatting

I've noticed a lot of chatting going on in the comments of the posts. So I installed a little chat window, it's called a Shoutbox. Give yourself a screen name and anyone can talk anytime you're here!

You'll find the Pre-Cal 20S Chatbox window down there at the bottom of the right hand sidebar.

Cheers,
Mr. K.

HELP!!!

Does anyone know how to do Exercise 2.

comment:

todays class was alright. challenging in a way. but now that i get it im very happy. feels like i accomplished something. haha. well, i finally found out how to post up this. hah, yeah i know im slow. yeah, now i have to start my math homework and go over things from last year.

Dictionaries Of Mice and Men

I had planned to do some work in our math dictionaries today. Ah well, the best laid plans of mice and men .... ;-)

Some of the terms we'll enter tomorrow are:

• Term


• Monomial


• Binomial


• Trinomial


• Polynomial


• Dividend


• Divisor


• Quotient


• Remainder


• Factor

There are some very good math dictionaries that can be found online. I found one here and another there. Which one do you think has a better definition of the word "factor"? ;-)

The Scribe List

This is The Scribe List. Every possible scribe in our class is listed here. This list will be updated every day. If you see someone's name crossed off on this list then you CANNOT choose them as the scribe for the next class.

This post is can be quickly accesed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.

Cycle 3

Jan Hong rus-L John D. - #12 T-SA stePhANIE Jojo Ndrew SAMUS parvin

kimc Melissa V. janet Wendy_V Jor_Dan_0 marianne_c Diyaa Kristin_R tim-Math-y

A.Z Thang N. Ian nee-cole StevenF km natasha Brittany-R

hmmph.. i finally did it :P, now that im through with this, ill finish my my math homework T.T..

12o92k5

todays class was good because i got everything. anyways today in class we discussed long division of binomials and trinomials because barely anyone got it yesterday. we also corrected the worksheet but only a few numbers. todays classs was a great class. OH and we also learned how to factor binomials and trinomials. the end -charmyn



And tomorrows scribe is.... iTRICK.. whoever that is:)

Division and Factoring Help!

I feel a lot better about today's class than yesterday's. I think most of you left the room confused yesterday. Today I had the feeling that you felt a lot more comfortable with polynomial division and seemed to pick up factoring simple trinomials fairly well.

If you're still having trouble with polynomial divison you can get help here. Help with factoring simple trinomials (A.K.A. Quadratics) is a click away .... right here.

Students Made This!

Blogging is a very public activity. Anything that gets posted on the internet stays there. Forever. Deleting a post simply removes it from the blog it was posted to. Copies of the post may exist scattered all over the internet. I have come across posts from my students on blogs as far away as Sweden! That is why we are being so careful to respect your privacy and using first names only. We do not use pictures of ourselves. If you really want a graphic image associated with your posting use an avatar -- a picture of something that represents you but IS NOT of you.

Two teachers in the U.S.A. worked with their classes last year to come up with a list of guidelines for student bloggers.

One of them, Bud The Teacher, has these suggestions, among others:

1. Students using blogs are expected to treat blogspaces as classroom spaces. Speech that is inappropriate for class is not appropriate for our blog. While we encourage you to engage in debate and conversation with other bloggers, we also expect that you will conduct yourself in a manner reflective of a representative of this school.



2. Never EVER EVER give out or record personal information on our blog. Our blog exists as a public space on the Internet. Don’t share anything that you don’t want the world to know. For your safety, be careful what you say, too. Don’t give out your phone number or home address. This is particularly important to remember if you have a personal online journal or blog elsewhere.



3. Again, your blog is a public space. And if you put it on the Internet, odds are really good that it will stay on the Internet. Always. That means ten years from now when you are looking for a job, it might be possible for an employer to discover some really hateful and immature things you said when you were younger and more prone to foolish things. Be sure that anything you write you are proud of. It can come back to haunt you if you don’t.



4. Never link to something you haven’t read. While it isn’t your job to police the Internet, when you link to something, you should make sure it is something that you really want to be associated with. If a link contains material that might be creepy or make some people uncomfortable, you should probably try a different source.

Another teacher, Steve, developed a set of guidelines in consultation with his students. You can read them here.

Look over the guidelines and add the ones you like in the comments section below this post; either from one of Steve's students or one of your own. I think Bud's suggestions are excellent. We'll be using the one's I highlighted above as a basis for how we will use our blog.

Cheers,
Mr. K.

Blogging on Blogging

A good class today folks! I felt there was a lot of interaction between you as a class and myself. Lots of good questions and good thinking going on as I walked around the class. One observation: Some of you, when uncertain of how to do a particular problem, try your best, second guess yourself, and change what you had thought was the way to proceed at first. Your first instincts are usually good ones. Please try each question going on your instincts. When you get it wrong, leave your mistake on the page so I can see it. It's only by seeing your errors that I can help figure what you're doing wrong and why. Then we can correct it!

We were talking about exactly what sort of post you're supposed to make to get that mark 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).


• 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.


• Respond to a Blogging Prompt I posted. (see below)

Your posts do not have to be long. I'm far more interested in the quality of what you write rather than the quantity.

Blogging Prompt
To help us along our blogging journey I've decided that I will also occasionally post a Blogging Prompt. It will be easy to find because I'll always put it under a heading like the one above this paragraph. Feel free to create your own Blogging Prompt for the rest of us if you like. If it's a really good one (i.e. has rich possibilities for blogging) we'll count it as your post. ;-) Here's my first one:

We've learned how to multiply polynomials using the distributive law and using the area model for multiplication. Blog a brief paragraph identifying ways in which these two types of multiplication are similar. Blog a second paragraph outlining the ways in which they are different.

This sort of compare and contrast exercise can be made easier to do using Venn Diagrams. Draw two large overlapping circles. List the similarities in the overlapping section and the differences in the appropriate non-overlapping sections. If you like, you can use this web tool to do it online. If you do blog about this prompt and want to post your diagram we'll talk about how to post pictures sometime in class. ;-)

Happy Blogging!

You're Here! Let's begin ....

Hi There! You found our blog! This is the place to talk about what's happening in class; to ask a question you didn't get a chance to ask in class; to get copies of a handout you didn't get in class (here's the course outline); for parents to find out "How Was School Today;" to share your knowledge with other students;.... Most importantly it's a place to reflect on what we're learning.

Remember what I said about the Forgetting Curve? Well a big part of Learning and Remembering involves working with and discussing new ideas with other people -- THIS is the place to do just that. Use the comment feature below each post, or make your own post, or make your own blog and link it to this one, or....the sky's the limit...let your imagination soar and lets get down to some serious blogging!

Here's your first online assignment:

Do you see the Links list in the side bar over there on the right? Follow the Study Skills Resources link. Browse through the sites until you find one that you think has excellent suggestions on how to study math; then, on a piece of loose leaf paper (or this worksheet) to be handed in on Monday:

1. Write the address and name of the site you most liked.


2. Rate the site out of 100; i.e. give it a grade!


3. Write a brief description (no more than 4 or 5 sentences) of the site.


4. Include a comment on what it was about this site that made it stand out for you (no more than 1 or 2 sentences).

Repeat this exercise for the second link that deals with Test Taking, i.e. how to write a test.

If you take this assignment seriously now and invest some real time and energy into it, you'll probably do real well in my class this semester...who knows, it might even help you in your other classes too! ;-)

Have Fun!

PS Don't forget to email me ASAP and get signed up as a contributor to our blog!!