Debbie Poss's Blog

Accelerated Math III - Polar Graphing - March 29, 2012

We are still on schedule for polar graphs.  That means that Monday we discovered in class how to name and plot points and how to change point forms from polar to rectangular and vice versa.  Download Polar Coordinate System Introduction  Tuesday, we looked at graphs of polar equations and how to change equations from polar to rectangular and vice versa.  Wednesday, students investigated some classic polar curves - the limacon (and the cardioid), the lemniskate, circles and roses.  Today we learned how to write certain conic sections in polar form.  Tomorrow students have a quiz on all the polar information they have learned so far and the assignment after the quiz is a "Polar Graphing" Download Polar Geometry investigation that focusses on how changing the values of theta affects polar curves.  This and their parametric egg Download Parametric Project  are the only assignments for the break - and the egg isn't due until Thursday, April 12, 2012.  (The polar designs look so pretty on the eggs!)  Enjoy the break!

Accelerated Math II - Probability and Conics - March 29, 2012

As we had tentatively planned, we reviewed Monday and the Conics test was taken in 2 parts (on Tuesday and Wednesday) to insure that students would have time to complete the test.

Today, students worked in groups to determine the probability that a certain general form equation would produce a particular conic.Download Probability and Conics Lab  Successful completion of this task resulted in a classwork grade, so please show me these tasks if you were absent today.  Tomorrow, I will be checking homework assignment that follows it. Download Probability Homework

Tomorrow, we will be doing a "Large Ellipse Task" that students should be able to complete in class.  Therefore the only homework over the spring break will be to complete their "face project" for conics that is due Tuesday, April 10, 2012.

 

 

Accelerated Math III - Parametrics are just so cool! - March 20, 2012

Yesterday we got back the parametric quizzes and looked at rotating parametric figures.  Today we explored writing equations of graphs and each class took a different direction, but both ended up learning similar concepts - that by isolating the x and y movements of a shape (graph) we can write parametric equations of it. (2nd period started with the infinity symbol and went to shapes with 3 and more loops, while 3rd period rotated that symbol to draw a flower.)

Tomorrow we review for a test on parametric functions and the test is scheduled for Thursday, March 23.

Accelerated Math II - Still working on Conics - March 20, 2012

Happy First Day of Spring!  We have still been (more or less) on schedule until today.  We had a quiz on conics today - including hyperbolas and identifying all sorts of conics and rewriting them in standard form.  But our plans for the next week are as follows:

Tuesday, March 20 - Take quiz in class.  For homework, on page 196, problems 1-12 - just solve these equations for y.  (We need to look at ways to graph these conics on our "function machines", so that means we need to do some algebra!)

Wednesday, March 21 - Look at 3-D coordinates.  We have a nice task that works through the concept of graphing in 3-D - including locating points, finding distances, midpoints, equations of planes and equations of spheres.  Homework for Wednesday night will be to continue working through this task or to work problems on page 207: 21 - 22 and on page 208: 1 - 20.  If I remember, I'll tell students about their conic face project.

Thursday, March 22 - Continue to look at 3-D coordinates and/or more applications of conic sections.  Many applications come by looking at cross sections of 3-D figures, so following the 3-D work, we will look at more instances of conics in the real world.

Friday, March 23 - Fun ellipse activity!  We will, in class, construct a large ellipse and use it to reinforce some of the neat aspects of an ellipse.

Monday, March 26 - Review.  We have an older chapter test with answers that will be perfect to remind students of all the conic work they have done during this unit. 

Tuesday, March 27 - Test on conic sections.  Included will be not only the major conics (circles, ellipses, parabolas and hyperbolas) and all their features (vertices, foci, asymptotes, directrices, etc.), but also distances and midpoints in 2-D and 3-D, equations of lines, and equations of planes and spheres.

 

Accelerated Math II - Hyperbolas - Pi Day!

Today we compared and contrasted the hyperbola and the ellipse.  The assignment for the evening is the attached worksheet.Download Hyperbola  If this won't open for you, drop by tomorrow morning and pick up a copy!

Accelerated Math III - Quiz Tomorrow - Seriously! - March 14, 2012

Yesyerday's blog is now fixed (I hope) and several tudents realized that I had only written the equations for #9 on the application worksheet.  Here is the "Rest of the Problem".

9.  Let x_ball­  = 40tcos 30º and y_ball = 6 + 40tsin 30º - 16t² and let x_rec = 28t and y_rec = 5

     A)  Setting the y’s equal to each other yields 16t² – 40sin 30º + 1 = 0, and occurs when t=1.19782 or t=.052178.  Substituting these values in for x, we get the ball at 41.4937 ft when the receiver is at 33.539 ft, which means he couldn’t catch it.     

           However, if we look at the distance between the ball and the receiver, we get: D = 
and the minimum point of that graph is (1.13662, 8.1457), which means at t = 1.137sec., the ball is 8.15’ away.  I still don’t think he caught it.

       B)  This can be modeled by letting the receiver run for 2 additional seconds, so D =  
 but this means the receiver ran too far and the minimum distance now s 46.04’.

       C)   It takes the ball 1.1978 sec. to go 41.4937’, so find how long it takes the receiver to go that far:  41.4937’/28 = 1.4829 sec, so the quarterback should wait .284 sec for the receiver to run down the field.

Study for your quiz and remember that tonight's assignment is the set of 6 problems entitled  "Worksheet".  They take a while...

Accelerated Math II - Quiz - March 13, 2012

Today students took a quiz on lines, circles, parabolas and ellipses.  The assignment for tonight is to read over pages 190-191 about hyperbolas and to attempt problems 1-14 on page 193.  Tomorrow we will compare and contrast the hyperbola and the ellipse and look at translating the hyperbola. 

Accelerated Math III - Quiz Review - March 13, 2012

Third period has a quiz tomorrow, but second period decided to put theirs off until Thursday.  At any rate, the quiz will include:

1.  Be able to graph parametric equations, finding the correct values for t, and stating the domain and range of parametric functions.  (Ex.   Given x = 3/(t-2) and y = sin (t), the t values must go from 0 to 2pi to locate all possible values of y, but should contain all reals except 2 to get all the values for x.  The x-values of this function would be all reals except 0 and the y-values will be [-1, 1].)

2.  Be able to locate points on parametric equations given t-values, x-values or y-values.  (Ex. Given the above parametric equations, find the point when t = 3 (3, .1411), the y-intercept (There isn't one) and one of the x-intercepts ( -3/2, 0).)

3.  Be able to eliminate the parameter.  (Ex. Given the above equations, we could solve the x equation for t, getting t = 3/x +2 or (2x+3)/x.  Then sub that into the y equation, leaving:  y = sin ((2x + 3)/x). )

4.  Write parametric equations of lines, circles, parabolas, ellipses and hyperbolas (especially using trig functions for circles, ellipses and hyperbolas).

5.  Set up and solve applications involving circular motion and objects affected by gravity.

Speaking of applications, here is problem #10 from the worksheet today.

A) x_Chrissy = 40(5280/3600)tcos 29^o  and y_Chrissy = 2.5 + 40(5280/3600)tsin 29^o - 16t² .  Meanwhile, x_Katie = 60 - 35(5280/3600)tcos 38^o  and y_Katie = 3 + 35(5280/3600)tsin 38^o - 16t²

B) Find the vertex of each y equation and we find that Chrissy's ball achieved a height f 15.14' at .889 seconds and that Katie's ball reached 18.61' at .9876 seconds. 

C)  At t = .6529, the balls are 2.566' from each other.  (Graph the distance between them in function mode.)

D)  It would be difficult for either girl to return the other's ball, but it might be possible.  Although after 1.169 sec. (when Chrissy's ball is 60' away), it is 13.88' off the ground, when t = 1.6 seconds, the ball is only 7' off the ground, so if Katie can run 22 feet back in 1.6 seconds, she can return Chrissy's ball.  Similarly, after 1.483 seconds (when Katie's ball is where Chrissy is), the ball is 14.68' off the ground, when t = 1.9, the ball is only 5.28' and only 16.86 feet back, so if Chrissy can run 17' in 1.9 seconds she can return Katie's ball.

 

Accelerated Math II - Conics so far... - March 11, 2012

Today we reviewed the "Conics so far" problems and students should continue to work on this tonight.  We have a quiz on lines, circles, parabolas and ellipses tomorrow.  Some answers to that worksheet are below:

1.  sqrt(89)    2. y = 3x -10    3.  5x + 4y -4 = 0    4.  y = 3/5x -3/5    5.  2x + 3y - 20 = 0  

 

Accelerated Math III - Applications and Figures - March 11, 2012

Just to reimind students , our assignments for parametrics have been:

Tuesday, March 6:           Intro to Parametric Worksheet

Wednesday, March 7:      More Parametrics Worksheet

Thursday, March 8:         Read pages 37-38 and work 9-19 odd

                                      Read pages 176–179 and work Q1 – Q10 and 1-6

Friday, March 9:              Application of Parametrics Worksheet

 Today I checked the More Paramtrics Worksheet and the pages from the book.  Although most students are keeping up with this unit, I discovered that several were not.  This is a new unit and there are some nice questions on the assignments for you to ponder - just like questions that will appear on the test for this unit.  Please be advised of this information!  Although today we didn't get a chance to look at this assignment, students need to attempt the following assignment.:

Monday, March 12            Pg. 180:  7-22

Tuesday, we plan to catch up with past 2 assignments and  a quiz is planned for Wednesday.  Friday we will be watching the movie clip from "Speed" in which the bus attempts to jump across a missing bridge to determine if this is actually possible.  If you have any problems with allowing students to watch this clip, please let me know.

Further assignments planned are:

Wednesday, March 14:     Quiz on parametric equations

Thursday, March 15:        Physics Problems

Friday, March 16:             Speed problems and NASA Problem     

 

Monday, March 19:           Another green review

Tuesday, March 20:         Test on parametric equations