Real World Connections for Grade 12 PreCalculus..IS IT POSSIBLE?

My Grade 12 PreCalculus students have been working on  the "problem" below for the past few weeks:

We have a problem:  There is a common mind set out there that the math concepts  that we learn in grade 12 Pre- Calculus math are irrelevant and too theoretical for students to make any connections with the real world.  

Their Challenge was introduced as stated below: 

By using your knowledge, creativity and innovative thinking it will be your job to prove that this is not a correct statement.  Your task will be to choose one or more of the topics studied this year in our 40SP course and then to prepare a presentation of that topic showing clearly its real world application.  We have discussed and blogged about various applications of the concepts we have learned, but now it will be your job to dig deeper to truly help others see the connection.   You may use some of the ideas discussed in class, or find a new real world application of your own choosing.    Are you up for the challenge?

Description of the Process:

 Identify, Research, Describe, Explain, Demonstrate, Organize, Summarize, and  Create a final presentation of a mathematical concept of your choosing.  You can create your presentation in a format of your choice, and the final results will be posted on our blog or website.   Remember the goal is to help others understand how your chosen math concept is a true application in the Real World.   Pay close attention to your audience.   Think about creativity and innovation, engage the audience, and make them want to learn about what you have to say.  Your math teachers have always told you “math is everywhere”, so now it is your challenge to prove that and share with others. 

 In the next few days students will be posting their "presentations" on this blogspot, so please stay tuned.  

My students welcome your comments and feedback.

Can you identify this mathematician?

Who is he and what is his story?

Probability Lessons

Probability Lesson 1

Probability Lesson 2

Probability Lesson 3

Conditional Probability Warm Up questions

40 PreCal Welcomes Glogster...

http://jucordova.edu.glogster.com/grade-12-precalculus/

Probability

Probability Ex. 39, 40, 41

Probability is the measure of how an event is. In other words,

P (A) = n(A)        ®      Probability = Number of Favorable outcomes

                 n                                                   Total Possible Outcomes

Probability of event A is the number of ways event A can happen, divided by the total possible outcomes.

Sample Space is the complete set of all possible outcomes.

Ex.  Rolling a die, the sample space would be 1,2,3,4,5,6

Sample Spaces can be represented using tree diagrams or charts.

Addition Law (Or)           

When 2 events, A and B are mutually exclusive. The probability that A or B will take place is the sum of both events.

P (A or B) = P (A) + P (B)

Ex. A single 6-sided die is rolled. What is the probability of rolling a 2 or a 5?

P (2)	=	1
		6

P(5)	=	1
		6

P(2 or 5)

=

P (2)

+

P (5)

=	1	+	1
	6		6

=	2
	6

1

3 Mutually Exclusive- if the occurrence of one will mean that the other will not occur (Cannot have 2 events taking place at the same time). Mutually exclusive events add up to one (complement).  Ex. Venn Diagram, the circles do not overlap Non-Mutually Exclusive- if they have one or more outcomes in common Independent events - If the result of the first draw/event does not affect the outcome of the second draw/events. Ex. Event A – Drawing a card from a deck. Then returning the card in the deck. Event B – Drawing from the very same cards. Dependent Events-  when you don’t replace the first item before drawing the second item. Ex. What is the probability of getting a face card and then an Ace without replacing the face card? P (Face) = 12/52 P (Ace after Face) = 4/51 (12/52)(4/51) = 4/221 Multiplication Law (And) When 2 events, A and B are dependent and influence one another.  P (A&B) = P (A)P (B|A) You would read P (B|A) as “the probability of B given A has already occurred”, also known as, conditional probability. Ex. A jar contains black and white marbles. Two marbles are chosen without replacement. The probability of selecting a black marble and then a white marble is 0.34, and the probability of selecting a black marble on the first draw is 0.47. What is the probability of selecting a white marble on the second draw, given that the first marble drawn was black? P (White|Black)  =      P(Black and White)               =  0.34    P(black)                                  0.47                                                = 72% Thanks Blaine!

Probability and Let's Make a Deal....

The Let's Make a Deal Dilemma

Investigate the Let's Make a Deal Paradox. This paradox is related to a popular television show in the 1970's. In the show, a contestant was given a choice of three doors of which one contained a prize. The other two doors contained gag gifts like a chicken or a donkey. After the contestant chose an initial door, the host of the show then revealed an empty door among the two unchosen doors, and asks the contestant if he or she would like to switch to the other unchosen door. The question is should the contestant switch. Do the odds of winning increase by switching to the remaining door?

Fountain Parabolas

Just came across a wonderful blogspot:  http://mathtourist.blogspot.com


This is Ivars Peterson's blogspot and he posts about anything in the world that catches his eye and is related to math and computer science.   Check out his blogspot for more real world mathematical connections.  Enjoy!

Thank you Mr.Peterson for your sharp eye and for providing the relevant, real life visual connections to mathematics.

Fountain Parabolas

Shooting graceful arcs of water into the air, fountains can offer lessons in geometric spectacle. The fountain at the National Gallery of Art Sculpture Garden in Washington, D.C., is a notable example.

Grade 12 Jimmies: You are Invited.....

ST.JAMES COLLEGIATE  MATHEMATICS EXAM CRAM   STUDY SESSION WHO:  Grade 12 PreCalculus Students  WHEN:  Thursday June 9th, 2011 from 3:30 - 7:30 & Monday June 13th, 2011 from 3:30 – 7:30 WHERE:  Room 204 PLEASE CONFIRM YOUR ATTENDANCE WITH MRS. CORDOVA BY:  TUESDAY JUNE 7TH. JOIN US!  SNACKS will be provided!  Yum Yum! Mark your Calendars EXAM Date:  June 16th from 8:30-12:00

Hello,

So today I will blog about circles and ellipses.

First Circles ,I hope we all know what circles are, but if not circles can be defined as a set of points that are a given distance from a given point. The general equation of a circle is (x-h)^2+(y-k)^2=r^2. H and K is the center of the circle, remember that the H and K value are the opposite sign so if a given circle was located at (-3,4) it would read (x+3) and (y-4). The radius or R, is the distance from the center to any point on the circle. It is important to remember that when given an equation the R value must be square-rooted because it had been squared when R was put in to the equation. For example, if a given equation was (x+1)^2+(y-2)=16, then the radius would be 4 because the square root of 16 is 4.

Next is ellipses, ellipses are similar to circles except that not all points on the ellipses are equal distance from the center (there is no radius). The equation is (x-h)^2/a^2 + (y-k)^2/b^2. Again H and K are the center of the ellipse. 'A' represents the horizontal distance from the center, and B represents the vertical distance from the center. Remember again that H and K are the opposite signs of what is in the equation. An easy way to remember if the ellipses is horizontal or vertical is if; A greater than B than it is horizontal, and B is greater than A then it is vertical. You may notice that if the value of A and B are the same, then the equation turns into the circle equation. That being said if A and B are the same it forms a circle. This

is the case because a circle is actually a special case of an ellipses.

Ellipses are actually all over the place! Planets orbit in an elliptical way, the electrons also move elliptically around the nucleus. Have you ever heard of whispering galleries? This is when you whisper in one focal point in a building and at another focal point across the room you can hear the person as though they are standing right beside you, this occurs because the building is an ellipse.

Thank you for your time,

KG

More on Hyperbolas...

Lesson 2 B Conics

Lesson 3 Conics

For students looking for the Permutations & Combinations Quiz corrections from this morning, they will be posted in Edmodo. 

Conics Lesson Updates

Conics Lesson 1

Conics Lesson 2

Thanks to www.math40s.com for this useful resource.

What does a Sonic Boom have to do with Hyperbolas?

A sonic boom shock wave has the shape of a cone, and it intersects the ground in part of a hyperbola. It hits every point on this curve at the same time, so that people in different places along the curve on the ground hear it at the same time. Because the airplane is moving forward, the hyperbolic curve moves forward and eventually the boom can be heard by everyone in its path.