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.