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An Old “Dog” Teaches New Tricks Presented by Cary and Jerry Chien

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					An Old “Dog” Teaches
New Tricks
Presented by
Cary and Jerry Chien



                British Columbia Association
                  of Mathematics Teachers
               2001 Fall Mathematics Conference
Our Bag of Tricks
 Tips for Teaching Transformations
 The Development of Logarithms
 Introducing the Concept of “e”
 Experiments with Logistic Curves
 Introducing Limits
 Probability Puzzlers
Teaching Transformations
  An explanation of f(2x)




  f ( x)  4  x   2
                         Zoom “Decimal”
 f ( x)  4  ( 2 x) 2   Double the domain
Teaching Transformations
  An explanation of f(x+1)




    f ( x)  4  x  2
                           Zoom “Decimal”
 f ( x)  4  ( x  1) 2   Add 1 to domain
Teaching Transformations
  An explanation of 2f(x)+1
                        Why are vertical
                        transformations
                        different from
                        horizontal ones?
                        They’re not!
    y  1 x   2
                            y 1
 y  2 4  ( x) 2  1
                                  f ( x)
                             2
Teaching Transformations
Here’s a bonus question:
  Imagine a function f(x)
 What is the order of steps

 in the transformation
 2f(-x+3)+1?
 a     b     c      d
 -x    -x    3     3
 3    3    -x     -x
 1    2y    1     2y
 2y    1    2y     1
Development of Logarithms
  Using Powerpoint presentations for
  more than just a high-tech
  chalkboard
  Mathematics has a rich history that
  students can appreciate
  Want to share presentations?
  Email me at jjchien@yahoo.com
Interesting Website Links
  Virtual TI – a TI-83 graphing calculator
  emulator www.zophar.net/ti.html
  Javaslide – a working slide rule
  www.taswegian.com/SRTP/javaslide/
  javaslide.html
  Jeopardy Powerpoint Template
  www.meadowthorpe.fcps.net/powerpoint_
  jeopardy_template.htm
Introducing “e”
  Once upon a time,
  there was a very
  nice bank (yes, it
  is a fairy tale).
  They decided one
  day to introduce a
  new interest rate
  of 100% per year.
Introducing “e” =2.718281828…
  $1 with interest rate (100%)
  compounded:
     Yearly (1+1)=$2
     Monthly (1+1/12)12 = 2.613
     Daily (1+1/365)365 = 2.715
     Every Second
     (1+1/31536000)31536000 = 2.717
     Continuously
     (1+1/109)10^9 = 2.718281827
Introducing “e”
  Little did they know, they’d calculated
  the mathematical constant e.
           e = 2.718281828459…
  For an investment of $100 over 10
  years, the bank has to pay 100 x e10
  ($2 202 600.47!!! Who want’s to be a
  millionaire?). The bank realized it was
  going to go bankrupt if this continued
  so they went back to an interest rate
  of 10%.
Introducing “e”
  If we perform the same calculations
  as we did before, we’ll end up with
  $1.11 after investing $1 for one year.
  (Which is the same as e0.1)
         e0.1 = 1.10517.
  According to the interest calculation,
  this should equal 1.1 Since the
  interest rate is low, there is very
  little difference between ex and the
  compound interest calculation
Introducing “e”
  e is used to calculate many functions in
  nature such as the growth of bacteria,
  population growth, and radioactive
  decay, which are growing or decaying
  continuously, rather than once a month
  or day like bank schedule
Experimental Logistic Curves
  There’s a secret that only I know.
  Using the randInt( function of the
  calculator, we can model the spread
  of this secret in our class
  Count off (remember your number!)
  For the TI-83, choose:
  MATH  PRB  randInt(1, n)
Experimental Logistic Curves
  Record the number of people who
  know the secret in each round
  Enter data into lists:
     Round # into L1
     # of people who know secret into L2
  Here is a sample set of data:
  L1 : 1, 2, 3, 4, 5, 6, 7, 8, 9.
  L2: 1, 2, 4, 7, 13, 20, 22, 23, 24
Experimental Logistic Curves
  Use logistic regression to find the
  equation:STAT  CALC  Logistic Y1
Experimental Logistic Curves
  Let’s see the first and second
  derivatives of our graph:
Introducing Limits
  Let’s find the limit of a function:
            x 1
            2
   f ( x) 
             x 1       By Graphing…
Introducing Limits
  Let’s find the limit of a function:
            x2 1
   f ( x)         x  1, x  1
            x 1
                            By Table…
Probability Puzzlers
 How many pathways are there
 from A to B if you are only able
 to travel right or down?
  A




                   B
Probability Puzzlers
 How many pathways are there
 from A to B if you are only able
 to travel right, diagonally down
 and right, or diagonally up and
 right?
         A

                                    B
Probability Puzzlers
  You meet a gentleman and his
  beautiful daughter. After some
  conversation, the gentleman
  tells you that he has two
  children. What the probability
  that this gentleman has a son
  and a daughter?
Probability Puzzlers
 You are in the final round of a
 game show where there is a million
 dollar prize behind one of three
 doors.
Probability Puzzlers
 You pick a door, but before the
 host opens it, he opens one of the
 two doors that you didn’t pick,
 showing you that it is empty.
Probability Puzzlers

  He offers you a change your
  choice. Should you trade? Why
  or why not?
The End
    Feel Free to Contact Us:
   Cary Chien carchien@hotmail.com
     Jerry Chien jjchien@yahoo.com

				
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