y  2( x  2
x
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
int[log2 ( x 1)]
S
2
2
4
2
4
6
8
2
4
6
8
10
12
14
16
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
)
Algebra 1 - POW
Project Granny
While driving down a foggy highway in her brand new S.U.V., Grandma Mary was worried about
how far she could see ahead. On the radio, the newscaster stated, “Visibility is down to 350
feet.” Suddenly Grandma could see the flashing lights of a stalled vehicle; she slammed on the
brakes and her S.U.V. screeched towards the helpless car. Before she knew it, Grandma’s front
end was smashed up against the smaller vehicle. Fortunately, no one was in the car, and
Grandma came away with only scrapes and bruises. However, when the State Troopers came to
the scene, a husky officer came over to Grandma Mary and told her, “ I am going to have to give
you a speeding ticket, by the looks of things, you were going beyond the speed limit of 65 miles
per hour.” Grandma responded with, “You are out of your mind Sonny, I always drive safely.
Anyways, you weren’t even here.” With a confident look, the officer stated, “I didn’t need to be
here, I am good at math, I measured the distance of your skid to figure it out. Here is you ticket.”
“You will be hearing from my lawyer, and my math teacher,” Grandma shouted as the officer got
in his car.
Is Grandma correct? Or is the officer correct? Use the table below to answer that question.
Thoroughly explain and validate your answer by using all the necessary and appropriate math.
Algebra 2
POW – The Birthday Cake
Determining the maximum /minimum number of pieces in
which it is possible to divide a circle (birthday cake) for a given
number of cuts is called the circle cutting or pancake cutting
problem. Use the table below to help organize your work to
come up with your answers.
1 Slice
2 Slices
3 Slices
4 Slices
5 Slices
Diagram(s)
Diagram(s)
Diagram(s)
Diagram(s)
Diagram(s)
Minimum
Regions: ___
Minimum
Regions: ___
Minimum
Regions: ___
Minimum
Regions: ___
Minimum
Regions: ___
Maximum
Regions:___
Maximum
Regions:___
Maximum
Regions:___
Maximum
Regions:___
Maximum
Regions:___
Algebra 2
Slices
POW – The Birthday Cake
Min
Max
1
2
3
4
5
n
Extra Serving:
The problem of dividing a circle by lines can
also be generalized to dividing a plane by
circles. As can be seen above, the maximal
numbers of regions obtained from n = 1, 2, 3,
circles are given by 2, 4, 8. What is the
maximum number of regions a plane can be
divided by 4 circles. Show the drawing and
explain the numerical pattern.
Project: Follow Me
Consecutive Numbers
Which natural numbers can be expressed as the sum of two or more consecutive natural numbers?
Use your calculator and your equation solving skills to find the solutions.
n
Sum
n
1
21
2
22
3
1+2
23
4
24
5
25
6
26
7
27
8
28
9
29
10
30
11
31
12
32
13
33
14
34
15
35
16
36
17
37
18
38
19
39
20
40
Sum
10+11, 6+7+8,1+2+3+4+5+6
Project: Follow Me
Consecutive Numbers – Page 2
Describe in a complete sentences three patterns that you found after finishing the
table.
1.
2.
3.
Which numbers cannot be written as a consecutive sum? What is special about these
numbers?
Write 95 as the sum of 5 consecutive natural numbers. Write 64 as the sum of 4
consecutive numbers.
In algebra, the sum of any two consecutive numbers is x + (x+1)= 2x +1. Complete
the table below to express the sum of different lengths of consecutive numbers.
Sum of Consecutive
Numbers
Expression
Result
2 Numbers
x + (x+1)
2x+1
3 Numbers
x + (x+1) + (x+2)
4 Numbers
5 Numbers
6 Numbers
10 Numbers
(Try to use a pattern
to find the result)
Follow Me- Homework Consecutive Integers Word Problems
Solve each problem below by a guess and check method and then by writing and solving an equation.
Show your work in the table
Word
Problem
Equation
Simplified Equation
Solution
Find two
consecutive
integers whose
sum is 45.
x + (x+1) = 45
2x+1 = 45
The numbers
are 22 and 23
Find two
consecutive
integers whose
sum is 99.
Find three
consecutive
integers whose
sum is 99.
Find three
consecutive
integers whose
sum is 207.
Find two
consecutive odd
integers whose
sum is 92.
Find two
consecutive even
integers whose
sum is 54.
Find three
consecutive odd
integers whose
sum is 369.
x + (x+2) = 92
GEOMETRY
POW #1 – The Checkerboard
How many squares are there on an 8x8 checkerboard? And the answer is
not 64.
Oh yeah, the answers is not 65 either.
Mathematical Survivor
Project: Last One Standing
The cast of “Mathematical Survivor” is a collection of n not necessarily distinct real numbers {x1,x2,x3,…,xn},
where n>1. From this collection, we select any two numbers, say xa and xb, delete these from the collection, and
insert the number xaxb+xa+xb into the collection. The process to find the mathematical survivor includes
continuing the selection of two random numbers from the new collection and performing the deletion and
insertion process. Proceed until the collection has a single number left. This number is the survivor.
Part 1
Find the survivor for the set of numbers {2, 4, 6, 8}. You can randomly choose the two numbers to start
with. Once you find the survivor, repeat the process two more times to find the surviving number. Make
sure to alter your choice of numbers to delete.
How many different ways can a survivor be produced when starting with 4 numbers in your
collection.You know there has to be at least 3 different ways since you completed part 1.
EXTRA:
Part 2
Using you inductive reasoning skills, make a conclusion about the survivor from the set of numbers {2, 4,
6, 8}. Choose your own set of 4 numbers and find the survivor. Find the survivor two more times for
your set. What conclusions can you make now?
Part 3
The next obvious question is whether or not a mathematical survivor of a collection of numbers is
predictable at the outset and is it totally independent of the selection process made throughout the process.
The answer to the question is YES. The theorem below explains the results.
If S = {x1, x2,…, xn} is a collection of n not necessarily distinct real numbers, where n>2,then the
mathematical survivor of S is guaranteed to be
(x1+1)(x2+1)…(xn+1)-1
Use the theorem to verify that you found the correct survivor for the sets in Part1 and Part 2.
Part 4
Use the theorem above to find the survivors for the following sets.
{2, 2}
{2, 2, 2}
{2, 2, 2, 2}
{2, 2, 2, 2, 2}
{5,5}
{5,5,5}
{5,5,5,5}
{5,5,5,5,5}
Use the results from above to find the survivor for {c,c,…,c} (n copies), where c is some number .
EXTRA, EXTRA
1 1 1
1
Find the mathematical survivor for the following set: {1, , , ,..., }
2 3 4
n
Marty Romero, Wallis Annenberg High School, Adapted from Math Horizons Magazine, February 2007
What Goes Around Comes Around
Project: Hailstone Numbers
A particularly famous problem in number theory, the hailstone problem, has
fascinated mathematicians for several decades. It has been studied primarily
because it is so simple to state yet apparently intractably hard to solve. This
problem is also known as the 3n+1 problem, the Collatz algorithm, and the
Syracuse problem.
If the number is even, divide by 2, if it is odd, multiply by 3 and add 1.
Number
1
2
3
4
5
6
Steps to 1
0
1
7
2
5
8
11
12
13
14
15
16
Number
Steps to 1
9
7
8
9
3
17
18
10
6
19
20
4
Answer the following questions
1. What is the pattern for the number of steps for 2, 4, 8, and 16? Predict how
many steps the number 32 will have? How many steps for 128?
2. What is the pattern for any of the numbers that are doubles of each other? For
example, 5 and 10, 7 and 14?
3. Predict how many steps are needed for the numbers 40, 80 and 100. How many
steps does it take 76 to get to 1?
4. Fill in the missing numbers from the number chain. There are two answers.
_____, 15, 46, 23, …
_____, 15, 46, 23, …
5. Of the first 1,000 integers more than 350 have their maximum at 9,232. Find
one of the integers that has a maximum of 9232.
What Goes Around Comes Around
Project: Hailstone Numbers
Hailstone Numbers By Ivars Peterson Muse, February 2003, p. 17.
Nothing could be grayer, more predictable, or less surprising than the endless
sequence of whole numbers. Right? That's why people count to calm down and
count to put themselves to sleep. Whole numbers define booooooooring. Not so
fast. Many mathematicians like playing with numbers, and sometimes they
discover weird patterns that are hard to explain. Here's a mysterious one you can
try on your calculator. Pick any whole number. If it's odd, multiply the number by
3, then add 1. If it's even, divide it by 2. Now, apply the same rules to the answer
that you just obtained. Do this over and over again, applying the rules to each new
answer. For example, suppose you start with 5. The number 5 is odd, so you
multiply it by 3 to get 15, and add 1 to get 16. Because 16 is even, you divide it by
2 to get 8. Then you get 4, then 2, then 1, and so on. The final three numbers
keep repeating. Try it with another number. If you start with 11, you would get 34,
17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, and so on. You eventually end up at
the same set of repeating numbers: 4, 2, 1. Amazing! The numbers generated by
these rules are sometimes called "hailstone numbers" because their values go up
and down wildly—as if, like growing hailstones, they were being tossed around in
stormy air—before crashing to the ground as the repeating string 4, 2,
1.Mathematicians have tried every whole number up to at least a billion times a
billion, and it works every time. Sometimes it takes only a few steps to reach 4, 2,
1; sometimes it takes a huge number of steps to get there. But you get there
every time. Does that mean it would work for any whole number you can think of—
no matter how big? No one knows for sure. Just because it works for every number
we've tried doesn't guarantee that it would work for all numbers. In fact,
mathematicians have spent weeks and weeks trying to prove that there are no
exceptions, but they haven't succeeded yet. Why this number pattern keeps
popping up remains a mystery.
“Looking Out for No. 1”
Project: Benford’s Law
Benford's Law
35
30
25
Pe r ce n t
In the late 19th century, Simon Newcombe, an astronomer
and mathematician, noticed that the pages of heavily used
books of logarithms, were more worn at the beginning than
the end. This suggested that scientists tended to look up
smaller numbers more often than larger ones. In 1938 Dr.
Frank Benford, physicist for General Electric, noticed the
same phenomenon that Newcombe observed earlier. Dr.
Benford went on to conclude that it was unlikely that
physicists and engineers had some preference for
logarithms starting with one. He embarked on a numerical
investigation that analyzed over 20,000 numbers that he
got from collections as obscure as the drainage areas of
rivers, stock market figures, baseball statistics, and atomic
weights. He discovered that 30% of the observed numbers
began with the digit 1.
20
15
10
5
0
0
2
4
6
8
10
D igit
Benford’s Law goes on to state that that the
1
probablity of a given first digit D is:
log10 (1 
)
D
Experiment
1. Your first job is to complete a table of values for Benford’s formula. Once your table is complete, make a scatter
plot of the data. It should look similar to the one above.
2.
Using the randInt() command on your calculator, multiply two randomly large numbers together and
record the first digit of the result. Use the following command,
randInt(1000,9999)*randInt(1000,9999), to obtain your results. Make at least one hundred
calculations.
3.
Once you have completed your tabulations, calculate the percentages for each of the digits. Make a scatter
plot for your collected data. Draw the function for Benford’s Law with your data. How close does it come to
satisfying formula?
4.
It is your task now to find some data to analyze with respect to Benford’s Law. Use the internet to help give
you ideas as to what sets of data to use. No student is allowed to use the same set of data. Once you have
chosen your set, make a complete analysis of the frequency and percentage of the first digit of the numbers.
Test to see if you data is valid for Benford’s Law.
5.
Last but not least, write a one page research summary for Benford’s Law. Make sure to include how the law
gets applied in the real world. Also, give an example of a set of data that does not pertain to Benford’s Law.
Explain why this set does not work.
1
2
3
4
5
6
7
8
9
References:
http://students.bath.ac.uk/ma2decr/Applications.html
http://www.abc.net.au/science/k2/moments/s116315.htm
http://www.math.yorku.ca/Who/Faculty/Brettler/bc_98/benford.html
Marty Romero, Los Angeles Wilson High School
Wilson High School
Activity Card
Wilson High School wants to boost interest in sports and
school activities. It has decided to sell an activity card that
will allow the holder to enter all sporting events free as well
as get discounts on other school activities. The entire
student body was surveyed and asked the question, “What
is the most you would pay for an activity card?” The results
of the survey are given below. Use the data to determine the
optimal ticket price.
Maximum Price
Total Number Willing to
Pay for Activity Card
50
75
85
105
115
135
150
170
765
620
565
460
405
285
210
115
Policy Brief #14 - Dropouts
Project: We Will Make It
Addressing California’s high school dropout crisis requires understanding the academic lives of students. Although
the causes of dropping out are many and complex, students’ school experiences certainly play a critical role.
Because the trajectories leading students either to high school graduation or to dropping out begin years before
these events, identifying relevant school-related factors requires a comprehensive analysis of longitudinal district-,
school-, and student-level data. In this project you will get a chance to use mathematics to analyze the things that
can predict if a student is not going to make it through high school. Hopefully, with your analysis, you will be able
to think deeply about what it will take for all of you to make it.
Percent Graduating
GRADUATION RATES BY COURSES FAILED
Preschool
1. Read Policy Brief #14 from the
California Dropout Research
Project - Make a list of the things
you now know after reading the
brief and make a list of things you
now wonder about.
2. After hearing each group's
presentations, including your own,
write a thoughtful response to one
of the things someone is wondering
about? Respond to the best of your
ability, there are no right or wrong
answers.
Courses Failed
3. Share your response from above with your group - then describe an "aha" moment you had
while listening to others present.
4. What do you think are some things that prevent students from finishing high school? What
do you think are some things that help students graduate high school?
Elementary School
5. Explain what it means for something to be 50/50. What does it mean in the context of this policy brief?
6. Based on the research described in the policy brief, approximately how many the original students in
the study graduated on time? Show the math you used to calculate your answer.
7. Based on the fail-rate statistic stated in the policy brief, how many students in your school are
expected to fail Algebra 1? You will need to ask someone other than your teacher (ME) how many
students are taking Algebra 1 in the school. Show your work.
8. Based on the policy report, the chances of an English Language Learner (ELL) in our school of
graduating is one and three. What does that mean, and how many of our 9th grade ELL's will graduate?
Middle School
9. The graph below represents the percentage of students who graduate when considering the number of
courses these students fail in middle school and high school. Make some conclusions about what the
graph tells us.
10. Now that you are in high school, you can predict the chances you will graduate high school by
recounting how many classes you failed in middle school. How many classes did you fail? Use the graph
to help you determine your chances of graduating. Do you agree or disagree with this result? Why?
11. Now use the graph to estimate the actual values by "eyeing" the data - make a good guess at each of
the values and record them in a table that looks like the provided. Check with a peer to verify that you
are getting similar values- Make sure to make your table on a separate sheet.
Project: We Will Make It
Policy Brief #14 - Dropouts
12. Once you have the data in the table, hand plot the
points on a correctly labeled coordinate plane.
13. Using any method described in class, find a line of
best fit for the high school data. Depending on which
points you choose to use, you might have a different
result form others in the class. Check with others and
record a different equation than yours.
14. If your best friend who is in 12th grade has failed 4
classes, what do the equations predict as their chances
of graduating? Show your work.
Courses Failed
Middle School
Graduation
Rate
High School
Graduation
Rate
15. How many classes would a student have to fail for them to have a 0% chance of graduating? Use
your equations to calculate these values.
16. In a real-world context, explain what the value of the slope means - explain how this is related to
the policy brief. What does the value of the y-intercept mean?
High School
Write a summary explaining what you learned in this project and how it will or will not change the
way you plan out your academic future. Also, include a discussion about other things (factors) that
happen in a student’s school or personal life that can predict whether or not a student will graduate
high school. There is no wrong or right answer, I just want you to think critically and discuss with
others these issues.
College (Extra Credit)
The middle school graph represents another more advanced function that you will study in Algebra 2,
but we can introduce it to you now. Instead of finding a line of best fit, you would have to find the
exponential function of best fit because the graph of the middle school data is curved.. The equation
that represents the middle school data is y=69(0.82)x. Complete the table of values by using your
equation, then plot the values on the graph to see how they match your estimates. Lastly, research
exponential functions and explain the meaning of the numbers in the equation y=69(0.82)x .
y  69(0.82) x
x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
y
What do each of the variables represent?
x:__________________________________________________
y:__________________________________________________
Could You Live Forever?
Project: Life Expectancy
When it comes to long life, Jeanne Calment is the world’s record holder. She was born before
Edison invented the light bulb and lived to the ripe age old age of 122. When asked the secret of
her longevity, Calment guessed that God must have forgotten about her. In this project, we will
investigate the life expectancy of humans and maybe answer the question, could we actually live
forever?
PART I
1. The table from the right comes from The Muse
magazine, February 2004. Using your
calculator or on graph paper, carefully graph
each of the sets on the same axes.
2. After some analysis, it is obvious that the data
is linear in nature. Using your method of
choice, find a line of best fit for the data. What
is the physical interpretation of your slope and
y-intercept? Explain why these values make
sense.
Male
Age
Female
Days of Life
Age
Remaining
Days of Life
Remaining
9
23814
9
26006
10
23449
10
25677
11
23084
11
25312
12
22719
12
24947
13
22353
13
24581
14
21988
14
24216
3. Using your equations from above, how
15
21659
15
23851
many days remaining does a 50 year old
16
21294
16
23486
male and female have to live? How many
years is that?
4. Using the equations once again, find out at what age does a male and female have zero
days of life remaining. What is the interpretation of your answer? Explain why there is a
difference between men and women?
PART II
Year
1950 1960 1970 1980 1985 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Life
Expectancy
68.2
69.7
70.8
73.7
74.7
75.4
75.5
75.8
75.5
75.7
75.8
76.1
76.5
76.7
76.7
77
77.2
5. The data above on life expectancies for all Americans comes from the Center for Disease and
Control. Make a careful graph of the data, you may want to use ’50’ for 1950 and so on. Aside
from the value in 1970, you should see that most of our points line on a line. Any possible
explanation for this one point?
6. Using your preferred method, find a line of best fit for the data. Then using your equation,
what is the projected life expectancy in the year 2050 and 2100?
7. Although the projections of life expectancy is not a sure science, two scientist Steve Austad
and Jay Olshansky placed a bet on whether anyone alive in the year 2000 will be still around
in the year 2150. In other words, will someone alive today live to be 150? Use your
equation to help determine whether or not it seems possible for someone to live to 150 by
the year 2150. Explain your reasoning.
EXTRA CREDIT
Both guys drew up a contract and each put $150 in a bank account. The winner’s heirs will
get the cash. With interest over 150 years, how much money could that be?
Does Race Matter?
Projected Life Expectancy
http://abcnews.go.com/WN/us-hispanics-longer-life-expectancy-white-black-americans/story?id=11883156#.Tw6IAlZki7s
Table 10. Projected Life Expectancy at Birth by Sex, Race, and Hispanic Origin for the United States1: 2010 to 2050
Sex, Race, and Hispanic Origin 2
BOTH SEXES
.White
.Black
.Asian
.Hispanic
2010
2020
78.3
78.9
73.8
78.8
81.1
2030
79.5
80.0
76.1
80.0
81.8
2040
80.7
81.1
78.1
81.1
82.6
2050
81.9
82.2
80.0
82.2
83.3
83.1
83.3
81.8
83.3
84.1
Table 10. Projected Life Expectancy at Birth by Sex, Race, and Hispanic Origin for the United States: 2010 to 2050 (NP2008-T10)
Source: Population Division, U.S. Census Bureau
Release Date: August 14, 2008
What do you know? / What do you Wonder?
1. Make a list of the things you now know from analyzing the table of values and make a list of things
you now wonder about.
2. After hearing each group's presentations, including your own, write a thoughtful response to one of
the things someone is wondering about? Respond to the best of your ability, there are no right or
wrong answers.
Data Analysis
3. Using a clean sheet of graph paper, make a scatter plot of the data for the white, black, asian, and
hispanic groups. The year (2010=10) should be the dependent variable and the projected life
expectancy should be the independent variable. Does the graph confirm what you know?
4. Using the graphical representation along with the members of the group to decide, which function
best represents the data? Find equations that best represents that data.
5. What are the equations?
Extrapolation
6. Just by looking at the equations you found in part 5, what were the life expectancies for each of the
races in the year 2000? Which group has the highest life expectancy in the year 2000? Does this
surprise you? Why or why not?
7. Use your equations to predict when the life expectancy for each of the races will be 100 years.
which group will live to 100 first? Is it the same answer as part 6? What values in your equations
help you understand what your answer in part 7 is not that same as part 6? Explain your answer?
8. Use your algebra skills to find the year that whites and hispanics have equivalent life expectancies.
Do the same whites and blacks, hispanics and asians, and hispanics and blacks.
Analysis
9. In the article Why do Hispanics outlive Whites and Black Americans, the reporters are surprised by
these findings. Why do you think they were surprised? Why do you think Hispanics outlive the
other groups?
10. Read the article to see if some of your answers in part 9. are similar to the scientists trying to
explain the results. What do you think about their findings?
Mathematical Modeling
Project: The Need for Speed
Fuel economy at steady speeds with selected vehicles were studied in 1973, 1984, and 1997. The most recent study
indicates greater fuel efficiency at higher speeds than earlier studies; for example, some vehicles achieve better
mileage at 65 than at 45-mph, although not their best economy, such as the 1994 Oldsmobile Cutlass, which has its
best economy at 55 mph (29.1 mpg), and gets 2 mpg better economy at 65 than at 45 (25 vs 23 mpg). All cars
demonstrated decreasing fuel economy beyond 65 mph (105 km/h), with wind resistance the dominant factor, and
may save up to 25% by slowing from 70 mph to 55 mph.
Log on to the website http://www.bgsoflex.com/mpg.html to complete the
table of values for three of the cars. Make sure to input the correct drag
coefficient, vehicle weight, and frontal area before computing fuel
efficiency. You will leave all other categories at their default values.
Category
Civic
Altima
Explorer
Escalade
Hummer
Weight
2751
3192
4546
5838
6400
Frontal
Area
21.04
25.5
42
45.5
49
Drag
Coefficient
.34
.39
.60
.90
.90
Car 1:______________
Car 2:______________
Car 3:______________
Speed
Speed
Speed
MPH
15
25
MPG
MPH
15
25
MPG
MPH
15
25
35
45
35
45
35
45
55
65
55
65
55
65
MPG
PART I (Making the Graph)
1. Using the calculated data sets, make accurate hand plots on graph paper with speed on the x-axis and MPG on
the y-axis. Scale your axes so that your x-max goes up to 150 and y-max goes to 50. Use different
colors/styles to distinguish each of the plots.
2. Now use your handheld calculator to create a scatter plot. Scale your windows to match your hand plots. Do the
plots resemble a function you recognize? Discuss with your peers which function can be used to model the
plots. Use a guess and check method to find a quadratic equation that fits one of your cars.
3. Use the quadratic regression function on your handheld to model each of the three plots. It is okay to round the
coefficients to three decimal places. Plot the regression equations to check how well they fit. We will be using
the equations to do some algebra and make predictions.
PART II (Crunching the Numbers)
1. Using the methods learned in class, algebraically find the vertex for each of the regression equations. In the
context of the problem situation, what does the vertex mean for each car? How do these values compare to the
statistics stated in the opening paragraph?
2. Based on the look of the graph, do you think there is a time when fuel economy is ever zero? Use your graph
to estimate the speeds that produce a fuel economy of zero.
3. After you make your estimates from the graph, use the quadratic formula to accurately calculate the speed that
produces a fuel economy of zero. Round your answers to three decimal places.
PART III (Making Predictions)
1. For the rest of the project, you will use the graph and equation for only one of the cars from part I and II. After
choosing the car, use the equation to complete the table below for the predicted values. Add these values to
your graph.
Data from online calculator
Speed
MPH
15
25
MPG
Predicted values from equation
Speed
MPH
75
85
MPG
Data from online calculator
Speed
MPH
75
85
35
45
95
105
95
105
55
65
115
125
115
125
MPG
2. Check your predicted values from your equation to the actual calculated values from the online calculator. Use
the table above to help you organize your work. How well do they match up? Explain why you think they are
not the same. Add these new values to the graph, the shape should no longer be a parabola.
3. Since the actual data no longer fits our original equation, some of our work might be invalidated. Using your
knowledge of polynomials and the shape of their graphs, find the appropriate regression equation that fits the
new data. Work with a partner to help determine the equation that fits the best. You may need to change some
of the numbers by hand to get a good fit.
4. With the new equation, now determine when fuel economy will be zero. How different is this answer compared
to the one found in part II? Also, check to see if the speed that produces the best fuel economy is the same.
Finally…
The last line in the opening paragraph states that reducing speeds may save up to 25% by slowing from 70 mph to
55 mph. With the new equation, do the math to see what percentage is saved by reducing speeds from 70 mph to
55 mph for your chosen car. Write a paragraph summarizing and informing a non-math person the key findings of
the project.
Occupy Exponential Functions
Project: Minimum Wages
Discouraged, but not Yet Demonstrating
Students at Cal State Dominguez Hills bemoan their short-term job prospects. But nationwide protests that include
criticism of education cuts have failed to drive many of them to action.
October 28, 2011 | Hector Tobar
That was the headline in the Los Angeles Times in October of 2011 during the apex of Occupy Movements
flourishing across the country and even across the world. In this project you will examine the contents of the article
and mathematically investigate some statements made by those who were interviewed. You will start by reading the
article and then use the table of minimum wages to start your investigation.
Entry-Level Position
California Minimum Wage
1. Read the article from the Los Angeles Times - Make
Effective Date Minimum Wage Amount of Increase Percent of Increase
a list of the things you now know after reading the
1-Jan-08
$8.00
$0.50
article and make a list of things you now wonder about.
2. After hearing each group's presentations, including
1-Jan-07
$7.50
$0.75
your own, choose the top two things you are now
1-Jan-02
$6.75
$0.50
wondering about and explain why you choose them.
1-Jan-01
$6.25
$0.50
3. Use at least two resources to define plutocracy and
1-Mar-98
$5.75
$0.60
middle class worker? Make sure to cite your sources.
1-Sep-97
$5.15
$0.15
4. What do you think the author meant when he said,
1-Mar-97
$5.00
$0.25
“The institutions of American meritocracy are teetering.
But these students still think they have a fighting
1-Oct-96
$4.75
$0.50
chance.” Ask someone in your family what they think
1-Jul-88
$4.25
$0.90
this means and then ask a teacher at school what they
1-Jan-81
$3.35
$0.25
think it means. Make sure to document their answers.
Middle Management
"Some of those positions in there are paying barely
above minimum wage for students with degrees," she
said, after speaking with various corporate and
government recruiters. "You wonder: Did I go to college
and work all this time just to make that?“
5. Lets examine the history of minimum wages in
California. Complete the table of values by determining
the percent increase for each of the boosts in minimum
wages.
6. Assuming that you are able to work 40 hours a week
for weeks a year, how much would your yearly be if you
only earn a minimum wage?
7. When you are attending college, you might not be
able to work 40 hours a week, so go to the following
website to find the average cost of attendance at any
Cal State University:
http://www.calstate.edu/sas/costofattendance
1-Jan-80
1-Jan-79
1-Apr-78
18-Oct-76
4-Mar-74
1-Feb-68
30-Aug-64
30-Aug-63
15-Nov-57
1-Aug-52
1-Jun-47
8-Feb-43
1920
1919
1918
1916
$3.10
$2.90
$2.65
$2.50
$2.00
$1.65
$1.30
$1.25
$1.00
$0.75
$0.65
$0.45
$0.33
$0.28
$0.21
$0.16
$0.20
$0.25
$0.15
$0.50
$0.35
$0.35
$0.05
$0.25
$0.25
$0.10
$0.20
$0.12
$0.05
$0.07
$0.05
Keep in mind that I know you might go to a community college, a UC school, or a private college, so the costs will
be different for those institutions. Community college will be less expensive than Cal State, UC more expensive than
Cal State, and a Private schools are usually more expensive than all of the schools. When the time comes, you will
also apply for financial ad to lower those costs. We can talk about that later. For now, choose the Cal State that is
nearest to you or one that you want to of living attend, and calculate how many hours you would need to work to
cover the costs of living at home, living on-campus, and living off-campus.
Upper Management
8. Take the data from the table and make a graph with year on the x-axis and minimum wage on the y-axis. To make
things easier for you, let 1916=0, and adjust all the other years accordingly.
9. Using what you know about exponential functions, use a well thought out strategy to determine the equation that
best fits the data. Remember, the general for of an exponential function is y=abx where a is the initial value and b is
the multiplier that is related to the y-values.
Occupy Exponential Functions
Project: Minimum Wages
Upper Management cont.
10. Once you have a fit that makes you happy, use the equation to predict what the minimum wage will be when you
graduate college. What will the minimum wage be in the year 2050 and 2100? Do you think these are answers are
reasonable?
11. The average hourly salary of a teacher is about $50 an hour, when will the minimum wage be equal to that amount?
CEO
Do some research to investigate the hourly rate for the profession or career you are interested in. Use the average
yearly salary of that profession and assume you work 40 hours a week for 50 weeks. Will getting a college degree help
you accomplish those financial goals? Why or why not?
The following list contains the description of seven historical events. Without talking to anyone write
down your estimate for how many years ago from today that event occurred. Make a guess if you do
not know the answer. How will you decide who is the most knowledgeable historian?
Historical Event
The Treaty of Guadalupe Hidalgo - the peace treaty, largely dictated by
the United States that ended the Mexican-American War. Under the
terms of the treaty Mexico ceded to the United States all of present-day
California, Nevada and Utah as well as most of Arizona, New Mexico and
Colorado. Mexico relinquished all claims to Texas and recognized the Rio
Grande as the southern boundary of the United States.
The passage of the Nineteenth Amendment to the United States
Constitution, which provided: "The right of citizens of the United States to
vote shall not be denied or abridged by the United States or by any State
on account of sex."
The Civil Rights Act was a landmark piece of legislation in the United
States that outlawed major forms of discrimination against African
Americans and women, including racial segregation. It ended unequal
application of voter registration requirements and racial segregation in
schools, at the workplace and by facilities that served the general public
("public accommodations").
The inauguration of Barack Hussein Obama as the 44th President of
the United States. The inauguration, which set a record attendance for any
event held in Washington, D.C., marked the commencement of the fouryear term of Barack Obama as President and Joe Biden as Vice
President.
The Senate voted to confirm Judge Sonia Sotomayor to the U.S.
Supreme Court, making her the first Hispanic Supreme Court justice and
just the third woman to sit on the court.
World Trade Center (Twin Towers)- terrorists hijacked American Airlines
Flight 11 and crashed it into the northern façade of the north tower at
8:46 a.m., the aircraft striking between the 93rd and 99th floors.
Seventeen minutes later, at 9:03 a.m., a second team of terrorists crashed
the similarly hijacked United Airlines Flight 175 into the south tower,
striking it between the 77th and 85th floors.
World War II Japanese Internment Camps – President Roosevelt
signed Executive Order 9066. Under the terms of the Order, some
120,000 people of Japanese descent living in the US were removed from
their homes and placed in internment camps. The US justified their action
by claiming that there was a danger of those of Japanese descent spying
for the Japanese. However more than two thirds of those interned were
American citizens and half of them were children.
Estimated
Years Ago
Actual Years
Ago