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Friday, April 29, 2005

Bouncing Around

The bouncing ball question from tonight's homework might be a little difficult to visualize. Watch this animation which shows the height of the ball bouncing and simultaneously draws the graph of it's height over time -- it'll help. We'll be talking about it in class on Monday.

Whew! Today was a tough class for me. Actually, the last few have been that way. I feel like I'm up there bouncing around the class, asking questions, trying to get everyone involved, and more often than not, it seems like the room is empty. You're all there in body but there seems to be a lack of spirit. What's up folks? Should I shower more often? ;-) Feel free to comment anonymously to this post if you like. It just seems to me that we've got a bit of a "disconnect" going on and I'd like to get past that.

BTW, can you tell if that ball is bouncing up? or down? Does it make any difference if you tilt your head 90 degrees to the left? ;-)

Wednesday, April 27, 2005

Fun With Sequences

Can you tell arithmetic and geomteric sequences apart? Find out here.

Play with the Sequencer tonight! Starting number is the first term in the sequence. For an arithmentic sequence make the Multiplier one and change the Add-on; for a geometric sequence make the Add-on zero and try different values of the Multiplier. Once you've made your choices click on the [Calculate Sequence!] button. It might also be fun to see what happens when both are not zero. Try it! See what happens ....

Now you're ready for your blogging promts -- 3 tonight!

Blogging Prompt 1 of 3
What effect does a negative starting number have on the sequence? What effect does a large negative starting number have on the sequence? What effect does a positive starting number have on the sequence? What effect does a large positive starting number have on the sequence?

Blogging Prompt 2 of 3
What effect does a decimal multiplier have on the sequence? What effect does a negative multiplier have on the sequence? What effect does a large multiplier have on the sequence?

Blogging Prompt 3 of 3
What effect does a negative add-on have on the sequence? What effect does a large negative add-on have on the sequence? What effect does a positive add-on have on the sequence? What effect does a large positive add-on have on the sequence?

Sunday, April 24, 2005

Mr K, I have a question....(^_^)

I'm just wondering about logarithm problems like 2^x = 3^(2x+5), (long answer 1.a on the pre-test) and the answer is x = (5ln3)/(ln2 - 2ln3). My question is, when should I use the "ln" instead of "log"? I mean, if I solved that problem using common log and got x = (5log3)/(log2- 2log3), am I wrong? I have no problem on dealing with exponents and logarithms (i hope so, for my sake), just the use of "ln" and "log" confuses me. Im thinking to ask this question tomorrow, but maybe you don't have time tomorrow to answer questions.

Friday, April 22, 2005

Review and Learn With the Wiki

Lots of homework this weekend! Today was our last day to review before the test on Monday. Don't forget to earn your blog mark before then.

If you didn't make your way through all the questions on our Companion Review Site today you can still access it here or from the [Links] menu over there --> on the right.

Over the weekend you can also try these online reviews to help get ready for Monday:

Also, as we discussed in class, take advantage of the tremendous learning and studying opportunities available to you over at our wiki. Start small, just write the first step. The next person can annotate what you did. Another person can do the next step; and so on. Work together on this folks!

Make sure you can draw transformations of the graphs of both the exponential and logarithmic functions without using your calculator. Using your calculator too much can make your vision blur. ;-)

Have a great weekend! And don't forget .... NUMB3RS is on tonight ....

Wednesday, April 20, 2005

Modeling Annotated Wikis

Here are some more examples of how to solve exponential modeling problems. The problems are followed by detailed, annotated solutions. There are also a couple of exercises for you to try and, of course, the answers are provided.

Even if you don't need the practice spend some time looking over the material there. Look at how it's laid out on the page. Is it clear; easy to read and understand? If you were going to rewrite it how would you do it? Would you incorporate any pictures or diagrams? Would you have some kind of table of contents linked to the various parts of the page? Maybe you would split it up into several different pages?

Then head over to the Logarithms and Exponents page of our wiki. There are 3 (or 4; depends how you count) problems for you all to solve, as a class, collaboratively. Explain the steps you take to solve these problems. Some guidlines:

  • Show all calculations done. They should be annotated, so that another student who missed class the day the material was taught will be able to replicate your work.
  • Explain what the numbers mean? Interpret the results in light of the problem given.

Over the next week or two I will also add similar problems to the other sections of our wiki. Drop by often, work together, and have fun!

The dinosaur problem is there .... waiting to be solved ..... ;-)

Monday, April 18, 2005

Spiral Prompt

Blogging Prompt
Isn't this a beautiful picture? It's a picture of a giant sea shell in the Phuket Seashell Museum in Thailand. Have you ever seen this type of spiral shape before? It pops up in many places in nature. It's called a "Logarithmic Spiral." A successful response to this Blogging Prompt (you will earn your blogging mark) will answer ALL of these questions:

  1. What is a logarithmic spiral? Write it in your own words, don't copy and paste. ;-)
  2. What does it have to do with logarithms? i.e. Why is it called a Logarithmic Spiral? (Hint: Find out how it is different from an "Archimedian Spiral." Knowing what exponential functions have to do with it will help too.)
  3. Find a picture, not of a seashell, that illustrates a logarithmic spiral in nature. Post it with your reply.

Have fun with this one!

Thursday, April 14, 2005

Solving Purple Logs

We're learning how to solve logarithmic equations. You can find an excellent two page tutorial here. Just click on [Next] when you get to the bottom of the page. The site is called Purplemath. It's really well done. It may even be worth spending some time there exploring. If nothing else, this may be a good time in the semester to take their Study Skills Self-Survey: "Do I Have What It Takes?" This may also be a good time to recall The Curve of Forgetting.

BTW, can you see the math in this picture? .... Not yet? .... Well, wait until we study Pascal's Triangle. You'll never look at a flower the same way again! ;-)

Tuesday, April 12, 2005

Laws of Logarithms

Here is a review of the material we discussed in class today: the three basic laws of logarithms. One of the better features of this site is that the explanation is followed by annotated examples. After that, you'll find some exercises for you to practice with; this part is excellently done! Here's why. The detailed solutions are also provided, but they're covered up. By moving your mouse over the pink boxes, each step of the solution is revealed. Don't just wave your mouse over the answers. Try working the question using paper and pencil. If you get stuck you can reveal just one line. You can even try revealing just one side of the equation in the next step of the solution. Use this site wisely to get a hint when you need it. By the time you're done you'll know your stuff really well.

Friday, April 08, 2005

Random Order "To Do List"

Enjoy your long weekend folks! Also try to get these things done as well, in random order:

  • Here is your first logs assignment, as promised. ;-)
  • For the few that were mentioned in class, start your quiz before 11:30 tonight.
  • Share your WikiThoughts
  • I'd love to get more Quizzing Feedback
  • Don't forget to watch NUMB3RS tonight.
  • Commit random acts of kindness. ;-)

Mr. K.

Thursday, April 07, 2005

Exponential Assistence and Quizzing Thoughts

Here is a great place to get help with your homework if you had any trouble understanding what was happening in class today. Similar questions, complete step-by-step solutions, and a brief online quiz.

Speaking of online quizzes, don't forget that our first online quiz expires at midnight tonight. Get started no later than 11:30 pm.

So far the feedback from those of you that have completed the quiz is very positive. The message I've received is that you want to do more quizzes like this. Alright then, we will. I've been doing some more thinking about this as well. I've decided that each of you will make up one multiple choice question for each unit that we'll be studying. When they are handed in I will enter them into the online database. When exam time rolls around the entire set of questions will be released for you all to review. This means we'll have about 25 questions per unit of study which we can use to prepare for the exam. I will develop a set of guidelines for this assignment which I will share in class, post here or both. This would also be a good place for you to share your questions, comments, complaints, compliments, concerns, confusions, anxieties and other general inquiries about this project. Your thoughts ....

Wednesday, April 06, 2005

Exponential Functions and WikiThoughts

This site has several interactive activities to help understand what we were talking about in class today: exponential functions and their transformations. Read the whole page before starting the java applet.

After you click the start button, you'll find it helpful (and instructive) to flip back and forth between the original page and the applet window. There are 4 "games" for you to play. ;-)

  1. The Definition of the Exponential Function
  2. Increase and Decrease of the Exponential Functions
  3. Range and Horizontal Asymptote of the Exponential Functions
  4. Shifting, Scaling and Reflection of the Exponential Functions

Follow the directions given for each one .... after that your homework will be a breeze!

For those of you who like variety, this is another applet you can play with to look at how you can change the parameters a and b in the general equation of an exponential function: f(x) = a(bx).

Lastly, as we discussed in class today, this would be a good place to share your thoughts about the wiki:

  • What does someone have to contribute to earn a bonus mark?
  • We had a suggestion of one contribution, one edit. Does a spelling correktion count?
  • Maybe we should just forget about marks altogether. Those of you that want to take advantage of this opportunity go ahead! You'll only benefit from it. Non-contributors may benefit also, but they wont get nearly as much out of it.

Your WikiThoughts.....

Monday, April 04, 2005

Online Quiz Goes Live Tomorrow

In today's class we were working with trig functions, their inverses and exact values. In order to test your understanding of that material you'll be writing a quiz.

The quiz will be written online here. It goes live at 4:00 pm tomorrow and will no longer be available as of midnight on Thursday. When you get to the site follow these instructions:

  1. Click on the big yellow "Sign Up" arrow.
  2. Use only your first name and last initial as indicated.
  3. Pick a username that will allow me to easily identify you, i.e. first name and last initial.
  4. Make up any password you like.
  5. Click on [Register] then [Search] by teacher's name (kuropatwa) and you'll find me.
  6. Click on the box next to Pre-Cal 40S and then [Register].
  7. Follow the instructions on the screen.

Actually, if you read each page carefully, you'll see that the sign up process is very straight forward and self explanatory. If you hit any snags email me and we'll sort it out together.

This quiz is timed. You'll only have 25 minutes to complete it once you've begun. It consists of 10 multiple choice questions. DON'T PANIC. Take your time. I know you'll all do well. ;-)

Good Luck!

Of Wikis and Inverse Trig Functions

Check out the post just before this one for more info on our wiki. Today we decided that contributions to the wiki would be voluntary and count as bonus marks, 1 or 2 per unit test. We still need to decide exactly what someone has to do to actually earn that mark. Rachel suggested that each person make at least one contribution and one edit. Think about it and bring your ideas with you to class tomorrow. We'll talk more about it then.

Here is an excellent animation showing the relationship between each of the basic trig functions and their inverses. Spend some time there trying to understand what's being illustrated. Clicking on the little red square and dragging it left and right will help. Also, make a point of looking at all six of the examples available. Don't forget to hit [Load Example] after selecting each one.