tag:blogger.com,1999:blog-101320152024-03-25T01:09:54.923-05:00Pre-Cal 40SAn interactive log for students and parents in my Pre-Cal 40S class. This ongoing dialogue is as rich as YOU make it. Visit often and post your comments freely.Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.comBlogger59125tag:blogger.com,1999:blog-10132015.post-1125778355411447972005-09-04T17:27:00.000-05:002006-04-07T15:54:12.826-05:00The Adventure Continues ...Our adventures in blogging continue....
<p>
Watch for 3 new blogs going live September 7, 2005 ...
<p>
<blockquote>
<ul>
<li><a href="http://pc20s.blogspot.com">Pre-Cal 20S</a> (Grade 10)</li>
<li><a href="http://pc30s.blogspot.com">Pre-Cal 30S</a> (Grade 11)</li>
<li><a href="http://apcalc.blogspot.com">AP Calculus AB</a> (Grade 12)</li>
</ul>
</blockquote>
<p>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com7tag:blogger.com,1999:blog-10132015.post-1120183021876608452005-06-30T20:46:00.000-05:002005-06-30T20:59:27.363-05:00So LongI'm so glad we've had this time together,
<br><br>
Just to have a laugh or learn some math,
<br><br>
Seems we've just got started and before you know it,
<br><br>
Comes the time we have to say, "So Long!"
<br><br>
So long everybody! Watch this space in the fall for pointers to new blogs for each of my classes. Some of the students from this class will be mentoring the students in the new classes. If anyone else (former students or other mathophile readers of this blog) is interested in being a mentor <a href="mailto:dkuropatwa@wsd1.org">email me</a> and let me know.
<br><br>
Farewell, Auf Wiedersehen, Adieu, and all those good bye things. ;-)Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1118864003293232842005-06-16T12:17:00.000-05:002005-06-16T16:38:01.353-05:00Class Survey ResultsThe exam is over and we did a little survey in class. The results are below; 20 students participated. We also discussed the future use of blogs and wikis in this course. The consensus seems to be that the next class should have their own blog but there should be a link back to this one for the new students to see what the old ones did. We also talked about having students from this class volunteer to be mentors for students in next year's classes. I've got a few volunteers signed up already. If you'd like to mentor one or more of my classes (grade 10, 11 or 12) next year please <a href="mailto:dkuropatwa@wsd1.org?subject=Pre-Cal 40S Survey&body=Hi there, I'd like to comment on the survey. Here are my thoughts:">email me</a> or leave a comment below this post.
<p>
Without any further ado, here are the results of our class's survey. Please share your thoughts by commenting (anonymously if you wish) below .....
<p>
<b>How prepared were you to write this exam? (Average score out of 100)</b><br>
66.75%
<p>
<b>How much effort did you put into preparing for this exam? (Average score out of 100)</b><br>
67.75%
<p>
<b>How good a job did your teacher do preparing you for this exam? (Average score out of 100)</b><br>
89.55%
<p>
<b>Did you have enough preparation using your calculator?</b><br>
Yes 85% No 15%
<p>
<b>Did you have enough preparation without using your calculator?</b><br>
Yes 65% No 30% Middle 5%
<p>
<b>Was I too hard or too easy on you??</b><br>
Easy 5% Hard 0% Middle 95%
<p>
<b>What was the best learning experience you had in this class?</b><br>
<center>
<table width=90% border=4 bordercolor=green>
<tr><td width=50%>group work (14)</td><td>review sites</td></tr>
<tr><td>math dictionary (8)</td><td>quizzes</td></tr>
<tr><td>online quizzes (3)</td><td>humour</td></tr>
<tr><td>lectures (3)</td><td>clearly detailed lessons</td></tr>
<tr><td><a href="http://adifference.blogspot.com/2005/05/calculus-reflections-go-for-gold.html">Go For Gold</a> assignment</td><td>showing how math affects our daily lives and history</td></tr>
<tr><td>pre-tests</td><td>using stories to help us understand</td></tr>
<tr><td>this blog (6)</td><td></td></tr>
</table>
</center>
<br><p>
<b>What was the worst learning experience you had in this class?</b><br>
<center>
<table width=90% border=4 bordercolor=green>
<tr><td width=50%>quizzes</td><td>too long getting back tests</td></tr>
<tr><td>online quiz (3)</td><td>none (6)</td></tr>
<tr><td>class time too short</td><td>sun shining on the white board</td></tr>
<tr><td>learning too fast</td><td>group work</td></tr>
<tr><td>this blog (5)</td><td>web assignments</td></tr>
<tr><td>not always going over homework</td><td>tests</td></tr>
<tr><td>homework (2)</td><td>exercises that have answers but not solutions</td></tr>
</table>
</center>
<br><p>
<b>What suggestions can you share for next year?</b><br>
<center>
<table width=90% border=4 bordercolor=green>
<tr><td>no quiz for marks on blog</td><td>project work (3)</td><td>give make-up tests</td></tr>
<tr><td>fewer jokes and stories</td><td>more online quizzes</td><td>make blogging optional</td></tr>
<tr><td>more group work (4)</td><td>tell more jokes</td><td>give take home tests</td></tr>
<tr><td>an extra class every 2<sup>nd</sup> day</td><td>homework should count for marks</td><td>don't use the same exercise books</td></tr>
<tr><td>keep blogging (7)</td><td>students should do more work at the board</td><td>more class participation</td></tr>
<tr><td>more time on binomial theorem</td><td>give tests back ASAP</td><td>keep using the same teaching strategies</td></tr>
<tr><td>go over selected homework exercises in class</td><td>have a mentor for this class</td><td></td></tr>
</table>
</center>
<br><p>
It's interesting to compare the items that were considered both the worst and best learning experiences. Also, take a look at the list of worst learning experiences compared to suggestions for next year. Help me do a better job next year by commenting on what you see here ....Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1118383151053721352005-06-10T16:17:00.000-05:002005-06-10T16:22:14.196-05:00Gearing Up For The Exam!!<img src="http://photos12.flickr.com/18538501_becc71108b_m_d.jpg" align="right" hspace="8">
A whole lot of reviewing going on!!
<p>
<a href="http://quizstar.4teachers.org/indexs.jsp" target="_blank">Here</a> is where you can login to the online quiz site to try your hand at the review quiz we made as a class.
<p>
There's lots more you can do to get ready for Tuesday!
<p>
<a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=13&lesson=4" target="_blank">Take this quiz</a> on Probabilities of Compound Events.
<p>
<a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=13&lesson=5" target="_blank">Take this quiz</a> on Conditional Probability.
<p>
<a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=13&lesson=6" target="_blank">Take this quiz</a> on The Binomial Theorem and Probability.
<p><br>
<img src="http://photos13.flickr.com/17600067_12595a0fb9_m_d.jpg" align="left" hspace="8">
<p><br><br>
<a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=13" target="_blank">Take this test</a> on Combinatorics and Probability.
<p><br><br>
<a href="http://www.funtrivia.com/playquiz.cfm?qid=172889" target="_blank">Take Harry Potter's quiz</a> on Combinatorics. Try not to run into any walls. ;-)
<p><br><br>
<p><br><br>
<a href="http://chuwm2.tripod.com/test/ch7.htm" target="_blank">Try this</a> Probability quiz.
<p>
<img src="http://photos11.flickr.com/13158805_10a055f9de_m_d.jpg" align="right" hspace="8">
And finally, <a href="http://bama.ua.edu/~fcmath/" target="_blank">take your own customized quiz</a> on a variety of topics we've studied. You can create customized review quizzes by choosing up to 15 questions from: Algebra, Trigonometry, Exponents and Logarithms, Geometry, Problem Solving and Graphs (Transformations). Create as many quizzes as you like and practice, Practice, PRACTICE!!! When you start each quiz a timer counts down from 50 minutes -- that's how you prepare for a timed test -- you take LOTS of timed tests! You can probably skip the Geometry questions and not all of the Problem Solving and Algebra applies to our course, but the kind of thinking you need to do for these questions WILL DEFINITELY help you gear up for the exam!
<p>
Remember, luck has nothing to do with it! It's all about doing your best! How well you do is a direct function of the effort you put into preparing!!!Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1117602208120235442005-05-31T23:55:00.000-05:002005-06-01T00:04:10.956-05:00Some Counting ReviewHere are some additional exercises on combinatorics. The interactive "tests" here will also give you explanations of why the correct answer is correct. Enjoy!
<p>
<ul>
<li><a href="http://regentsprep.org/Regents/math/counting/PracCnt.htm" target="_blank">The FUNdamental Principle of Counting</a></li>
<li><a href="http://regentsprep.org/Regents/math/factnot/PracFact.htm" target="_blank">Factorial Notation</a></li>
<li><a href="http://regentsprep.org/Regents/math/permut/PracPerm.htm" target="_blank">Permutations</a></li>
<li><a href="http://regentsprep.org/Regents/math/combin/excomb.htm" target="_blank">Combinations</a></li>
</ul>
<p>
If you click on the [Back To {topic}] button at the bottom of each quiz you'll be able to find pages that give helpful lessons on each topic.Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1117514038236403302005-05-30T23:19:00.000-05:002005-05-30T23:33:58.246-05:00More FunWell, you folks liked the last test so much, try this one on for size (6 questions):
<p>
<blockquote>
1. What do you put in a toaster? ... Think carefully and scroll down.
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<b>AND THE ANSWER IS:</b> The answer is bread. If you said "toast," then give up now and go do something else. Try not to hurt yourself. If you said, "bread," go to question 2.
<p>
2. Say "silk" five times. Now spell "silk." What do cows drink? ... Think carefully and scroll down.
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<b>AND THE ANSWER IS:</b> Cows drink water. If you said "milk" please do not attempt the next question. Your brain is obviously overstressed and may even overheat. It may be that you need to content yourself with reading something more appropriate such as "Children's World." If you said, "water" then proceed to question three.
<p>
3. If a red house is made from red bricks and a blue house is made from blue bricks and a pink house is made from pink bricks and a black house is made from black bricks, what is a greenhouse made from? ... Think carefully and scroll down.
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<b>AND THE ANSWER IS:</b> Greenhouses are made of glass. If you said "green bricks," what the heck are you still doing here reading these questions????? ... if you said "glass," then go on to question four.
<p>
4. It's twenty years ago, a plane is flying at 20,000 feet over Germany. If you will recall, Germany at the time was politically divided into West Germany and East Germany. Anyway, during the flight, TWO of the engines fail. The pilot, realizing that the last remaining engine is also failing, decides on a crash landing procedure. Unfortunately the engine fails before he has time and the plane crashes smack in the middle of "no man's land" between East Germany and West Germany. Where would you bury the survivors - East Germany or West Germany or in "no man's land"? ... Think carefully and scroll down.
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<b>AND THE ANSWER IS:</b> You don't, of course, bury survivors. If you said anything else, you must never try to rescue anyone from a plane crash. Your efforts would not be appreciated. ...... If you said, "Don't bury the survivors" then proceed to the next question.
<p>
5. If the hour hand on a clock moves 1/60th of a degree every minute then how many degrees will the hour hand move in one hour? ... Think carefully and scroll down.
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<b>AND THE ANSWER IS:</b> One degree. If you said "360 degrees" or anything other than "one degree," you are to be congratulated on getting this far, but you are obviously out of your league. Turn your pencil in and exit the room. Everyone else proceed to the final question.
<p>
6. Without using a calculator - You are driving a bus from Downtown Brooklyn (let's say starting at Court Street) to Brighton Beach in guess where (Brooklyn). At Atlantic Avenue, 17 people get on the bus. At Prospect Park, six people get off the bus and nine people get on. At Eastern Parkway, two people get off and four get on. At Newkirk Avenue, 11 people get off and 16 people get on. At Kings Highway, three people get off and five people get on. And then in Sheepshead Bay, six people get off and three get on. And now you arrive at Brighton Beach ... Scroll down for the question.
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
What was the name of the bus driver? ... Think carefully and scroll down.
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<p><br><br>
<b>AND THE ANSWER IS:</b> Just look back at the question, look at the first line; it was YOU ... "You are driving a bus from..."
<p>
Humbling isn't it? And just think, you are among the most intelligent in the population. ;-)
<p>
</blockquote>
<p>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com2tag:blogger.com,1999:blog-10132015.post-1117377211405330312005-05-29T09:25:00.000-05:002005-05-29T09:33:31.420-05:00Just For FunI found this "test" over at <a href="http://careo.elearning.ubc.ca/weblogs/vschools/archives/2005_05.html#012159">Teaching and Developing Online</a>. Try it out .... just for fun. ;-)
<p>
<blockquote>
Below are four (4) questions and a bonus question. You have to answer them instantly. You can't take your time, answer all of them immediately.
<p>
OK?
<p>
Let's find out just how clever you really are. No looking at the answers in advance.
<p>
Ready? GO!!! (scroll down)
<p>
<b>First Question:</b>
<p>
You are participating in a race. You overtake the second person.
<p>
What position are you in?
<p><br><br>
Answer:If you answered that you are first, then you are absolutely
wrong!
<br>
If you overtake the second person and you take his place, you are
second!
<p>
Try not to screw up in the next question.
<br>
To answer the second question, don't take as much time as you took for the first question.
<p>
<b>Second Question:</b>
<p>
If you overtake the last person, then you are...?
<p><br><br>
Answer:If you answered that you are second to last, then you are wrong
again. Tell me, how can you overtake the LAST Person?
<p>
You're not very good at this! Are you?
<p>
<b>Third Question:</b>
<p>
Very tricky math! Note: This must be done in your head only.
<p>
Do <b>NOT</b> use paper and pencil or a calculator. Try it.
<p>
Take 1000 and add 40 to it. Now add another 1000. Now add 30.
Add another 1000. Now add 20. Now add another 1000 Now add 10.
<p>
What is the total?
<p>
Scroll down for answer.
<p><br><br>
Did you get 5000?
<br>
The correct answer is actually 4100.
<br>
Don't believe it? Check with your calculator!
<p>
Today is definitely not your day.
<p>
Maybe you will get the last question right?
<p>
<b>Fourth Question:</b>
<p>
Mary's father has five daughters: 1. Nana, 2. Nene, 3. Nini, 4. Nono.
What is the name of the fifth daughter?
<p>
Answer:Nunu?
<p>
NO! Of course not.
<p>
Her name is Mary!
<p>
Read the question again.
<p>
Okay, now the bonus round:
<p>
There is a mute person who wants to buy a toothbrush. By imitating the action of brushing one's teeth he successfully expresses himself to the shopkeeper and the purchase is done.
<br>
Now if there is a blind man who wishes to buy a pair of sunglasses, how should he express himself?
<p><br><br>
He just has to open his mouth and ask, so simple.
<p><br><br>
So simple it is...
<p>
</blockquote>
<p>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com1tag:blogger.com,1999:blog-10132015.post-1116992662066513772005-05-24T22:35:00.000-05:002007-07-27T14:04:00.885-05:00Fundamental Principle of Counting<img src="http://photos7.flickr.com/6390169_0d1b37e6f0_m_d.jpg" align="right" hspace="8">
<a href="http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut55_count.htm" target="_blank">This</a> is a good review of the the material we covered in class today. It has step-by-step explanations and solved examples. There are even a few sample questions for you to try!
<p>
<a href="http://www.saskschools.ca/curr_content/math30/MATHA30/UnitA/LessonA1/LessonA1.htm" target="_blank">Here</a> is another good review site from Saskatchewan. You can choose to <a href="http://www.saskschools.ca/curr_content/math30/MATHA30/UnitA/LessonA1/LessonA1FormL/LessonA1.htm">review the lesson</a>, get <a href="http://www.saskschools.ca/curr_content/math30/MathHelpA30/dwcounting1a.htm">extra help and examples</a> or try some <a href="http://www.saskschools.ca/curr_content/math30/SITES/counting/FundCounting/FundCounting1.htm">practice questions & quizzes</a>. Ignore the <b><i>Assignment</i></b> link; it's broken.Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com2tag:blogger.com,1999:blog-10132015.post-1116366437362983762005-05-18T15:24:00.000-05:002005-05-18T15:27:01.700-05:00Let's Make It 100% This Time!Test day tomorrow. Get your <a href="http://pc40s.blogspot.com/2005/02/blogging-on-blogging.html">Blogging mark</a> here!
<p>
If you haven't finished the Conics Review on our <a href="http://www.wsd1.org/dmci/kuropatwa/pc40s/" target="_blank">Companion Review site</a> you should <a href="http://www.wsd1.org/dmci/kuropatwa/pc40s/Conics/q01.htm" target="_blank">do it now</a>.
<p>
I've collected a number of great links to help you learn and study. When you click on each link below you will be able to select:
<p>
<ul>
<li>A review lesson on the topic.</li>
<li>A selection of problems to review that have been solved step-by-step.</li>
<li>An online quiz with immediate feedback.</li>
<li>An "assignment" with some more solved practice problems</li>
</ul>
<p>
So here are the things you need to know about for the test with links to the resources described above:
<p>
<ul>
<li><a href="http://www.saskschools.ca/curr_content/mathc30/Unit5a/outline1.htm">Circles</a></li>
<li><a href="http://www.saskschools.ca/curr_content/mathc30/Unit5a/outline2.htm">Parabolas</a></li>
<li><a href="http://www.saskschools.ca/curr_content/mathc30/Unit5a/outline3.htm">Ellipses</a></li>
<li><a href="http://www.saskschools.ca/curr_content/mathc30/Unit5a/outline4.htm">Hyperbolas</a></li>
<li><a href="http://www.saskschools.ca/curr_content/mathc30/Unit5a/outline5.htm">Identifying Conics</a></li>
</ul>
<p>
If you like, you can also try this <a href="http://www.funtrivia.com/playquiz/quiz18411715155e0.html" target="_blank">humourous conics quiz</a>. Try it out; you'll learn something!
<p>
By the way, what do you think our chances are of hitting 100% blogging participation this time around? ;-) Let's go for it and translate that effort into 100% scores on this test!Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1116279547643101212005-05-16T16:35:00.000-05:002005-05-16T16:39:07.650-05:00Hyperbola Help<a href="http://www.analyzemath.com/EquationHyperbola/EquationHyperbola.html">Get help</a> with your hyperbola homework if you need it. The site I've linked to has some exercises you can do tied to a java applet. It will show you what changing the values of "a" and "b" in the standard form of the hyperbola's equation will do to the graph. Play with it for a while .... it'll help you get a feel for the geometry behind the algebra. ;-)Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1115928151812529822005-05-12T14:29:00.000-05:002005-05-12T15:02:31.936-05:00The Muddiest PointMost of you seem to have a good grasp of the ellipse! Fantastic! If you need any help with your ellipse homework you can find it <a href="http://www.webmath.com/ellipses.html" target="_blank">here</a>.
<p>
<img src="http://photos6.flickr.com/6815978_76a2d8e3c2_m_d.jpg" align=right hspace=8>
By far the muddiest point in our class seems to be the parabola. <a href="http://www.keymath.com/DAA/dynamic/constructing_parabola.html" target="_blank">Here</a> you can play with the parabola as it's defined from the locus definition (which is what we're studying). Play with the java applets, there are two of them, to get a sense of the role "p" plays in the geometry of the parabola.
<p>
<b><u>IMPORTANT:</u></b> "p" is half the distance between the focus and the directrix when they are perfectly aligned vertically. By dragging the point "B" along the directrix you will sketch out a parabola. Look for when the point "P" is on top of the point "A".
<p>
The second applet will show you what happens when you move the focus around. We will discuss these things in class tomorrow, so even if this doesn't entirely make sense to you right now play with the applets so that you will understand what we're talking about in class. ;-)
<p>
There were a couple of other questions that came up in our <b><i>Muddiest Point</i></b> exercise:
<p>
<ul>
<li>about circles</li>
<li>arithmetic series</li>
<li>changing from general to standard form and back again</li>
</ul>
<p>
We'll be talking lots more about that last point. Please speak to me one-on-one about the first two -- there were only about 3 of you that were feeling muddy about them. ;-)Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1115672476303393052005-05-09T16:01:00.000-05:002005-05-09T16:22:15.983-05:00Parabolic Dishes and The Ellipse Game<img src="http://www.hscbemidji.org/images/dish.jpg" width="208" height="178" align="right" hspace="8">
Today we discussed parabolas as <a href="http://www.math.odu.edu/cbii/calcanim/consec.avi">conic sections</a> in depth. In particular I emphasized how important it is to keep in mind the geometry of the parabola as you work with its equation.
<p>
<a href="http://www.ies.co.jp/math/java/conics/focus/focus.html" target="_blank">Watch this!</a> Tomorrow I'm going to ask you why parabolas are important in connection with satelite dishes, television and radio signals. ;-)
<p>
Tomorrow we will also review circles and begin our discussion of ellipses. <a href="http://johnbanks.maths.latrobe.edu.au/Games/Ellipse/index.html" target="_blank">Find out more</a> about what an ellipse is and then you'll be ready to play <b>The Ellipse Game</b>:
<p>
<blockquote>
Your mission, should you choose to accept it, is to find a focus. You will be given an ellipse of random dimensions and you will have to try to click on one of the foci. Should you fail in this mission at first, you will be given some clues. We will deny any responsibility for holes or other damage caused should you decide stick pins into a drawing board or any other item of household equipment.
</blockquote>
<p>
Ready? <a href="http://johnbanks.maths.latrobe.edu.au/Games/Ellipse/javaellipse.html" target="_blank">Let's play!</a>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1115178829528609412005-05-03T23:17:00.000-05:002005-05-03T23:18:10.610-05:00Geometric ReviewAs promised, here is a list of reviews for you ....
<p>
<ul>
<li><a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=12&lesson=2" target="_blank">Geometric Sequences and Series</a> - 5 Questions</li>
<li><a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=12&lesson=3" target="_blank">Infinite Sequences and Series</a> - 5 Questions</li>
<li><a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=12&lesson=4" target="_blank">Convergent and Divergent Series</a> - 5 Questions</li>
<li><a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=12&lesson=5" target="_blank">Sigma Notation and the n<sup>th</sup> Term</a> - 5 Questions</li>
</ul>
<p>
You can also find a fairly detailed review <a href="http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut54d_geom.htm" target="_blank">here</a> with step-by-step solved examples and 8 practice questions with answers.
<p>
Don't forget to bring your ruler with you to class tomorrow. You'll need it to play .... ;-)Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1115083733635649832005-05-02T20:03:00.000-05:002005-05-02T20:31:18.840-05:00Geometric PromptingThe unit test is on Wednesday and the deadline is getting close to get your blogging done. In an effort to make your lives easier ;-) by giving you things to blog about consider this problem:
<p>
<blockquote>
A student strained her knee in an intramural volleyball game, and her doctor prescribed an anti-inflammatory drug to reduce the swelling. She is to take two 220-milligram tablets every 8 hours for 10 days. Her kidneys eliminate 60% of this drug from her body every 8 hours.
</blockquote>
<br>
<font size=+1><b><u>Blogging Prompt</u></b></font><br>
<ol>
<li>How much of the drug will remain in her body after 10 days, just after she takes her last dose of medicine? If she continued to take the drug for a year, how much of it would be in her system just after she took her last dose?</li>
<li>If the initial dose is halved, what will happen to the stabilization level of the medicine in the body?</li>
<li> If the recurring dose is halved, what will happen to the stabilization level of the medicine?</li>
<li> If the elimination rate is halved, what will happen to the stabilization level of the medicine?</li>
</ol>
<p>
A successful response to this blogging prompt will <b>answer #1 above and at least one of #2 - #4</b>. It will <b>also show all work</b> done to get the answers. If you want to check your work you can use <a href="http://standards.nctm.org/document/eexamples/chap7/7.2/standalone1.htm" target="_blank">this interactive applet</a>. Instructions on how to use the interactive applet are <a href="http://standards.nctm.org/document/eexamples/chap7/7.2/using.htm" target="_blank">here</a>.
<p>
<b><i>Have Fun and Happy Blogging!!</i></b>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1114804380921842212005-04-29T15:14:00.000-05:002005-04-30T16:40:37.770-05:00Bouncing Around<img src="http://photos7.flickr.com/9526671_a78ad92024_m_d.jpg" align=right hspace=8>
The bouncing ball question from tonight's homework might be a little difficult to visualize. Watch <a href="http://www.ima.umn.edu/~arnold/calculus/bounce/bounce1/bounce-g.html" target="_blank">this animation</a> 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.
<p>
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.
<p>
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? ;-)Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1114634941752695662005-04-27T15:50:00.000-05:002005-04-27T15:49:01.756-05:00Fun With SequencesCan you tell arithmetic and geomteric sequences apart? Find out <a href="http://www.univie.ac.at/future.media/moe/tests/grenz/arigeo.html" target="_blank">here</a>.
<p>
Play with the <a href="http://occawlonline.pearsoned.com/bookbind/pubbooks/billstein_awl/medialib/shodor_site/activities/sequencer/index.html" target="_blank">Sequencer</a> tonight! <b>Starting number</b> is the first term in the sequence. For an arithmentic sequence make the <b>Multiplier</b> one and change the <b>Add-on</b>; for a geometric sequence make the <b>Add-on</b> zero and try different values of the <b>Multiplier</b>. Once you've made your choices click on the <b>[Calculate Sequence!]</b> button. It might also be fun to see what happens when both are <b>not zero</b>. Try it! See what happens ....
<p>
Now you're ready for your blogging promts -- 3 tonight!
<p>
<b><u>Blogging Prompt 1 of 3</u></b><br>
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?
<p>
<b><u>Blogging Prompt 2 of 3</u></b><br>
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?
<p>
<b><u>Blogging Prompt 3 of 3</u></b><br>
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?Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1114371690803537782005-04-24T14:31:00.000-05:002005-04-24T14:41:30.803-05:00Mr K, I have a question....(^_^)I'm just wondering about logarithm problems like 2^x = 3^(2x+5), <em>(long</em> <em>answer 1.a on the pre-test)</em> and the answer is x = (5ln3)/(ln2 - 2ln3). My question is, <strong>when should I use the "ln" instead of "log</strong>"? I mean, if I <strong>solved</strong> that problem using <strong>common log</strong> and got x = (5log3)/(log2- 2log3), am I <strong>wrong?</strong> 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.Anonymousnoreply@blogger.com1tag:blogger.com,1999:blog-10132015.post-1114115448459838162005-04-22T15:15:00.000-05:002005-04-22T15:21:22.043-05:00Review and Learn With the WikiLots of homework this weekend! Today was our last day to review before the test on Monday. Don't forget to <a href="http://pc40s.blogspot.com/2005/02/blogging-on-blogging.html">earn your blog mark</a> before then.
<p>
If you didn't make your way through all the questions on our <b>Companion Review Site</b> today you can still access it <a href="http://www.wsd1.org/dmci/kuropatwa/pc40s/">here</a> or from the [Links] menu over there --> on the right.
<p>
Over the weekend you can also try these online reviews to help get ready for Monday:
<p>
<ul>
<li><a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=11&lesson=1">Working With Exponents</a> - 5 Questions.</li>
<li><a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=11&lesson=2">Exponential Functions</a> - 5 Questions.</li>
<li><a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=11&lesson=3">The Number <i>e</i></a> - 5 Questions.</li>
<li><a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=11&lesson=4">Logarithmic Functions</a> - 5 Questions.</li>
<li><a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=11&lesson=5">Common Logarithms</a> - 5 Questions.</li>
<li><a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=11&lesson=6">Natural Logarithms</a> - 5 Questions.</li>
<li><a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=11&lesson=7">Modeling Real-World Data</a> - 5 Questions.</li>
<li><a href="http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=0-02-834135-X&chapter=11">Mixed Practice</a> - 14 Questions.</li>
</ul>
<p>
<img src="http://photos1.flickr.com/372855_4fa16c2379_m_d.jpg" align="right" hspace="8">
Also, as we discussed in class, take advantage of the tremendous learning and studying opportunities available to you over at <a href="http://pc40s.jot.com">our wiki</a>. 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!
<p>
Make sure you can draw transformations of the graphs of both the exponential and logarithmic functions <b>without</b> using your calculator. Using your calculator too much can make your vision blur. ;-)
<p>
Have a great weekend! And don't forget .... NUMB3RS is <a href="http://www.tvtome.com/tvtome/servlet/GuidePageServlet/showid-25043/epid-398600/">on tonight</a> ....Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1114030996088617482005-04-20T16:03:00.000-05:002005-04-20T16:10:36.490-05:00Modeling Annotated Wikis<a href="http://www.uncwil.edu/courses/mat111hb/EandL/elmodels/elmodels.html#sec1">Here</a> 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.
<p>
Even if you don't need the practice spend some time looking over the material <a href="http://www.uncwil.edu/courses/mat111hb/EandL/elmodels/elmodels.html#sec1">there</a>. 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?
<p>
<img src="http://photos4.flickr.com/9056494_e6847cbddc_m_d.jpg" align=right hspace=8>
Then head over to the <a href="http://pc40s.jot.com/ExponentsAndLogarithms">Logarithms and Exponents</a> 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:
<p>
<ul>
<li>Show all calculations done. They should be <a href="http://www.freesearch.co.uk/dictionary/annotated">annotated</a>, so that another student who missed class the day the material was taught will be able to replicate your work.</li>
<li>Explain what the numbers mean? Interpret the results in light of the problem given.</li>
</ul>
<p>
Over the next week or two I will also add similar problems to the other sections of <a href="http://pc40s.jot.com">our wiki</a>. Drop by often, work together, and have fun!
<p>
The dinosaur problem is <a href="http://pc40s.jot.com/ExponentsAndLogarithms">there</a> .... waiting to be solved ..... ;-)Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com2tag:blogger.com,1999:blog-10132015.post-1113806487574131912005-04-18T01:41:00.000-05:002005-04-18T01:42:42.063-05:00Spiral Prompt<img src="http://photos2.flickr.com/1842717_1b342b6bf7_m_d.jpg" align=right hspace=8>
<b><u><font size=+1>Blogging Prompt</font></u></b><br>
Isn't this a beautiful picture? It's a picture of a giant sea shell in the <a href="http://www.bangkoksite.com/Phuket/SeashellMuseum.htm" target="_blank">Phuket Seashell Museum</a> in <a href="http://www.worldatlas.com/webimage/countrys/asia/th.htm" target="_blank">Thailand</a>. 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 <b>Blogging Prompt</b> (you will earn your blogging mark) will answer ALL of these questions:
<p>
<ol>
<li>What is a logarithmic spiral? Write it in your own words, don't copy and paste. ;-)</li>
<li>What does it have to do with logarithms? i.e. Why is it called a <b>Logarithmic</b> Spiral? (<b>Hint:</b> <i>Find out how it is different from an</i> "Archimedian Spiral." <i>Knowing what exponential functions have to do with it will help too</i>.)</li>
<li><a href="http://flickr.com/" target="_blank">Find a picture</a>, not of a seashell, that illustrates a logarithmic spiral in nature. <a href="http://help.blogger.com/bin/answer.py?answer=916" target="_blank">Post it</a> with your reply.</li>
</ol>
<p>
Have fun with this one!Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com3tag:blogger.com,1999:blog-10132015.post-1113540945323170842005-04-14T23:17:00.000-05:002005-04-14T23:55:45.323-05:00Solving Purple Logs<img src="http://photos8.flickr.com/9405998_07d81082f6_m_d.jpg" align=right hspace=8>
We're learning how to solve logarithmic equations. You can find an excellent two page tutorial <a href="http://www.purplemath.com/modules/solvelog.htm" target="_blank">here</a>. Just click on [<a href="http://www.purplemath.com/modules/solvelog2.htm" target="_blank">Next</a>] when you get to the bottom of the page. The site is called <a href="http://www.purplemath.com/" target="_blank">Purplemath</a>. 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 <font color=purple>Study Skills Self-Survey: <a href="http://www.purplemath.com/stdysrvy.htm" target="_blank">"Do I Have What It Takes?"</a></font> This may also be a good time to recall <a href="http://www.adm.uwaterloo.ca/infocs/study_skills/curve.html" target="_blank">The Curve of Forgetting</a>.
<p>
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! ;-)Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1113335528946541992005-04-12T14:44:00.000-05:002005-04-12T14:56:21.686-05:00Laws of Logarithms<a href="http://www.themathpage.com/aPreCalc/logarithms.htm#laws">Here</a> 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. <b>Don't</b> 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 <b>hint</b> when you need it. By the time you're done you'll know your stuff really well.Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1112994162365025002005-04-08T16:03:00.000-05:002005-04-08T16:04:11.770-05:00Random Order "To Do List"Enjoy your long weekend folks! Also try to get these things done as well, in random order:
<img src="http://www.wsd1.org/dmci/kuropatwa/images/numb3rs.jpg" align=right hspace=8>
<p>
<ul>
<li><a href="http://www.wsd1.org/dmci/kuropatwa/pc4pdf/logex1.pdf">Here</a> is your first logs assignment, as promised. ;-)</li>
<li>For the few that were mentioned in class, start your <a href="http://quizstar.4teachers.org/indexs.jsp">quiz</a> before 11:30 tonight.</li>
<li>Share your <a href="http://pc40s.blogspot.com/2005/04/exponential-functions-and-wikithoughts.html">WikiThoughts</a></li>
<li>I'd love to get more <a href="http://pc40s.blogspot.com/2005/04/exponential-assistence-and-quizzing.html">Quizzing Feedback</a></li>
<li>Don't forget to watch <a href="http://www.cbs.com/primetime/numb3rs/">NUMB3RS</a> tonight.</li>
<li>Commit random acts of kindness. ;-)</li>
</ul>
<p>
Cheers,<br>
Mr. K.Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1112910028056553592005-04-07T16:38:00.000-05:002005-04-07T16:40:28.056-05:00Exponential Assistence and Quizzing Thoughts<a href="http://www.saskschools.ca/curr_content/mathb30/exps_logs/les3/intro3.html" target="_blank">Here</a> 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.
<p>
Speaking of online quizzes, don't forget that our first <a href="http://quizstar.4teachers.org/indexs.jsp">online quiz</a> expires at midnight tonight. Get started no later than 11:30 pm.
<p>
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 ....Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0tag:blogger.com,1999:blog-10132015.post-1112817036446697832005-04-06T14:50:00.000-05:002005-04-06T14:50:36.450-05:00Exponential Functions and WikiThoughts<a href="http://www.analyzemath.com/expfunction/expfunction.html" target="_blank">This site</a> 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.
<p>
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. ;-)
<p>
<ol>
<li>The Definition of the Exponential Function</li>
<li>Increase and Decrease of the Exponential Functions</li>
<li>Range and Horizontal Asymptote of the Exponential Functions</li>
<li>Shifting, Scaling and Reflection of the Exponential Functions</li>
</ol>
<p>
Follow the directions given for each one .... after that your homework will be a breeze!
<p>
For those of you who like variety, <a href="http://members.shaw.ca/ron.blond/TLE/ExpFcn.APPLET/" target="_blank">this</a> is another applet you can play with to look at how you can change the parameters <b>a</b> and <b>b</b> in the general equation of an exponential function: f(<i>x</i>) = <b>a</b>(<b>b</b><sup><i>x</i></sup>).
<p>
Lastly, as we discussed in class today, this would be a good place to share your thoughts about the wiki:
<p>
<ul>
<li>What does someone have to contribute to earn a bonus mark?</li>
<li>We had a suggestion of one contribution, one edit. Does a spelling correktion count?</li>
<li>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.</li>
</ul>
<p>
Your WikiThoughts.....
<p>Darren Kuropatwahttp://www.blogger.com/profile/08462283847470560887noreply@blogger.com0