Transcript Changes in the Mathematics Curriculum

Everything You Wanted to Know
About Algebra Two/
Trigonometry
Bruce C. Waldner
Contact Information
[email protected]
Coordinator of Mathematics, K – 12
Syosset Central School District
Syosset High School
70 SouthWoods Road
Syosset, New York 11754
Changes in the Mathematics
Curriculum
The new
New York State
Mathematics Learning Standards
Is it really what it sounds like?
Three proposed Regents
Examinations
–Integrated Algebra
–Integrated Geometry
–Integrated Algebra 2 and
Trigonometry
NYS Regents program
over the years
1977 1999
Sequential
Math I
1999 –
2008?
Tenth Year
Mathematics
(Geometry)
Sequential
Math II
Math A (1.5 Geometry
years)
Eleventh Year
Mathematics
(Algebra and
Trigonometry)
Sequential
Math III
Math B (1.5 Integrated
Algebra and
years)
Before
1977
Ninth year
Mathematics
(Elementary
Algebra)
2008? +
Integrated
Algebra
Trigonometry
The new proposed NYS Regents
program in Mathematics
Reverts to a more traditional sequence of high school
mathematics courses
Includes the real-world connections and the constructed
response format of questions found in Math A and Math
B
Three Regents examinations
Graphing calculators needed
Includes probability, and statistics as in the Sequential
Math program and Math A and Math B as well as some
of the logic
More in-sinc with other parts of the country
Based on NCTM Standards
When will students take the Mathematics
Regents Examination(s)?
The current Regents
program
– Math A – June of 9th
grade (grade 8 for
accelerated students)
– Math B – June of 11th
grade (grade 10 for
accelerated students)
The new Regents
program
– Integrated Algebra –
June of 9th grade (or
grade 8)
– Geometry – June of
10th grade (or grade 9)
– Integrated Algebra and
Trigonometry – June
of 11th grade (or grade
10)
Normal Approximation
In a binomial distribution of n trials, the
mean = np and the standard deviation =
or. Let r represent the number of
successes in n trials. Since the data in a
binomial distribution is discrete rather than
continuous, then to estimate the
probability of at least r successes in n
trials, it is necessary to subtract 0.5
from r .
New topics
The two major new topics are:
– Normal Approximation to a Binomial
Distribution
– Sequences and Series
Check out the handout taken from the NYSED
Crosswalk for Algebra Two/Trigonometry
Normal Approximation for a


Binomial
Probability


Math Facts

P( x  r)  P  r  0.5  x  r  05
P  x  r   P  x  r  0.5
P  x  r   P  x  r  0.5
P  x  r   P  x  r  0.5
P  x  r   P  x  r  0.5
P( x  r)  P  r  0.5  x  r  05
P  x  r   P  x  r  0.5
P  x  r   P  x  r  0.5
P  x  r   P  x  r  0.5
P  x  r   P  x  r  0.5
Example 1
A manufacturer of light bulbs knows that
the probability that a light bulb produced
by his company being defective is 0.01.
Out of 30 light bulbs sold to one of his
customers, use a normal distribution to
approximate the probability that no more
than 3 are defective?
P  30 C0 (0.01)0 (0.99)30  30 C1 (0.01)1 (0.99)29  30 C2 (0.01)2 (0.99)28  30 C3 (0.01)3 (0.99)27
manual solution
P  30 C0 (0.01) (0.99)  30 C1 (0.01) (0.99)
0
30
1
29
 30 C2 (0.01) (0.99)  30 C3 (0.01) (0.99)
2
28
3
27
 0.7397  0.2242  0.0328  0.0031  0.9998
Solution to Example 1
In this binomial distribution the mean = and the
standard deviation = . . The graphing calculator
can be used to determine this result using a low
value of 0.5 lower than the least possible
number 0 or –0.5 and 3.5 as the highest
number, mean = 0.3 and standard deviation of
0.545, press
2nd VARS 2 –0.5 , 2.5 , 0.3 , 0.545 )
ENTER
.
Calculator screen
Example 2
Anytime Gary plays James in a game of
chess, he has a 70% probability of winning
the game. If they play 10 chess games,
use a normal distribution to approximate
the probability that Gary wins at least 8
games.
Pnpq
P  r  8  0.5
 r  8 10(0.7)(0.3)
  P  r  7.5
 1.45
Solution to Example 2
In this binomial distribution the mean =
10(.7) = 7 and the standard deviation = . .
npq  10(0.7)(0.3)  1.45
P  r  8  P  r  8  0.5  P  r  7.5
Using the calculator the answer is
revealed as: