lecture preflight 01
1: The volume of a cylinder is pi x radius squared x height. I
would see how many jelly beans line up across the bottom to make the
radius and square that number and multiply it times pi. Next, I would
lay the jar on its side and see how many jelly beans make up the height.
Taking the number I got from the Pi x the radius squared, I would
multiply it by the height. Finally, I would take the square root of that
number and subtract that from the answer because I doubt the jelly beans
would be that neatly packed and that would account for some error.
2: I would need to remove four beans to guarantee that I would
get two of the same color. For example, I pull out the first bean and
get a red, the second bean and get a blue, I pull out the third bean and
get a yellow, but on the fourth draw I would have to get a repeat of one
of the other three bean colors. However, it may not take all four draws
to get a double of one color because I may draw a blue on the first draw
and another blue on my second draw. But, to guarantee it, I must allow
four draws.
3: In this scenario, I would have to pull out the total number
possible of yellow and blue jelly beans plus one to guarantee to have a
red. However, it is doubtful it would take that long to pull a red jelly
bean. But, once again, to guarantee I would pull a red, I would have to
pull all of the possible yellow and blues, plus one more to account for
the red bean to be pulled.
4: I did this problem in my high school physics class with the
city of Champaign. The first thing you would need to do is take the
population of America which according to the government the population
as of July 2006 is 298,444,215. Next you take the average sized family
in America which is about 4 people and divide the population by that
number which equals 74,611,053.75. Next you have to figure out the
average number of households that own a piano. That number turns out to
be 5. Then you divide the previous answer by 5 which equals
14,922,210.75 Next one must figure out how many pianos a piano play
tunes in a year. According to NASA, the number is 1,000. Therefore, you
divide the previous answer again by 1,000 and get 14,922.21075. Finally
I would round my answer to 14,922 piano tuners in the USA.
5: I enjoyed the square root estimation. I plan to use that in
the future!
6: Why is helium not flammable but hydrogen is?
lecture
preflight 01
1: One idea is to take the handful of jelly beans and put them
into the empty jar and see how far up the jar they go. If the small
handful, for example, reaches one inch of a five inch jar (assuming the
jar is equal from bottom to top) the number of jelly beans in the
handful times five would be a good estimate of the number of jelly beans
in the full jar. Another way that you could estimate the number of jelly
beans in the full jar is to weigh the filled jar as well as to find the
weight of the empty jar and of one jelly bean. If, say, the full jar
weighs 50 grams and the empty jar weighs 10 grams, you can know that the
weight of the jelly beans must be 40 grams. If each jelly bean is one
gram, you can estimate that there are about 40 jelly beans in the jar.
2: It depends on the number of each color jelly bean in the jar.
If there were 10 red jelly beans, 50 blue ones and 5 yellow, the
probability of having at least two blue ones on the desk in front of you
is a lot more likely than pulling out two yellows.
3: As before, it really depends on how many of each color is in
the jar.
4: 500,000... just a wild guess. However, I feel that to find an
approximate estimate of piano tuners in the US, you'd need to look in a
phone book for the number of piano tuners in a particular area. If the
population of a town is 100,000 and there are 2 piano tuners in the area
you can assume that of the United States population, .002% would be
piano tuners.
5: Science is uncertain. You don't always know the exact answer
and you don't always know how to go about finding solutions to problems
and questions. However, making predictions and testing hypotheses can
lead you closer to the truth.
6: How does Tylenol work? If I have a headache and take a Tylenol
it makes my head feel better. However, if my foot hurts and I take a
Tylenol, my foot feels better. How does the medicine know where to go?
lecture preflight 01
1: Well one way would be to take the empty jar and the jelly
beans and fill up the jar, then counr how many it took to fill it up.
For this way, you may need to buy alot more jelly beans to get an
accurate answer. Another way I might try is to put one layer of jelly
beans in the empty jar, so that the entire bottom is covered. Then see
how many layers it would take to get to the top of the jar. Then if you
multiply the original number of jelly beans it took to cover the bottom,
but the number of layers, you will get an answer.
2: You would have to pick at least four jelly beans out of the
jar in order to definitely get two of the same color. This is because if
you pull two out, you MIGHT get two reds, for instance, but you might
also get one red, one blue or one red and one yellow. This goes the smae
for if you choose three. Four is the only way to be sure.
3: I think you would have to pick out the sum of the blue and
yellow plus one, in order to get one red. For example, if there were 5
of each, you would need to pick out 11 beans in order to guarantee one
red.
4: I would assume that there are more piano tuners in larger
cities/more populated areas verses those that are more rurual or small.
I would go about making an educated guess by finding out how many piano
tuners there are in Chicago, and then the rest of IL. Then I would
multiply this by the numbers of states (50). Then maybe I'd add or
subject a few for bigger/smaller states. This would give me a figure.
I'm thinking around 5000 tuners.
5: One interesting thing I learned is how that tube/string thing
worked! Honestly I had no idea how it worked. At first I thought it was
a knot, but then I realized it was a loop. But not any kind of loop...a
horizontal loop.
6: I've been wondering about that one question from one of the
homeworks. It was the one about bowl A and bowl B and what happens when
an apple is put inside one. I keep changing my mind about the answer!!
Also, can you make one of those string/tube things with more than four
holes?
lecture preflight 01
1: one way is you can fill up the jar with water and weigh the
water, then weigh an individual bean and divid the total water weight by
the weight of a bean. You would have to account for gaps before making
your estimation
2: four. if you pull out three it is possible to have one of each
color, but on the fourth one, it has to match with at least one other.
3: all of them, technically there may be only one red bean in the
jar, and it could be the last one you pull out.
4: i dont even know what a piano tuner is.... but the US
population is 298,444,215 according to google. and in my experiance
about 1/5 of people i know own a piano, so would proably need a tuner
for it... so i guess i would estimate 59,688,843 tuners??
5: i learned what a caliper is.
6: why does cold air come out when you blow, but warm air comes
out when you just breath?
lecture preflight 01
1: step 1: go next door to the grocery store ( you said to use my
imagination, and in MY imagination, there IS a grocery store next door)
step 2: compare the size of the jelly beans to that of dried beans at
the store. Select and purchase the beans that are closest. (dried beans
are much cheaper than jelly beans, so this is a worthwhile investment if
it gets you closer to winning the large jar of jelly beans.) step 3:
bring the bag of dried beans back to the candy store, and fill the empty
jar. step 4: empty the jar of beans into a separate bag from the
leftover beans. step 5: bring this bag into the bathroom of the candy
store and count them. This will ensure that no one counts over your
shoulder and steals your answer. step 6: submit your answer and await
your prize!!!
2: Four because if you draw out a different color each time, that
can only last for the first 3 attempts, as there are only 3 different
colors. Therefore, the 4th try would have to be a duplicate of one of
the colors.
3: Because it does not specify HOW MANY there are of each color,
it is possible that there is only ONE red bean. As this is a
possibility, you could remove all the jelly beans and not get the red
one until the very last attempt.
4: 3000. I made this guess taking into consideration that the
United States has a population of roughly 300,000,000 people, and
assuming that piano tuners would account for a fraction of a percentage
of the population.
5: I learned what a calaper(spelling?) is.
6: What exactly does cough medacine do to help keep you from
coughing?
lecture preflight 01
1: I would weigh the full container of jelly beans. Then, I would
weigh the empty container and subtract this from the mass of the full
container. Finally, I would weigh one jelly bean. Then I would the
divide the difference of the masses of the jar and the mass of the jelly
bean, which would give me the amount of jelly beans in the jar.
2: Ideally, this would be six jelly beans. But, it depends on how
many of each color jelly bean are present in the jar. So, I would say
about 9 times.
3: Three...this gives you an opportunity to pull out all three
colors at least once.
4: 10,000? Maybe this has something to do with how many pianos
are in the US.
5: I really liked the experiment with the strings and the tube.
This really allowed me to see how it can often be much harder to figure
something out when you can't physically touch it.
6: What is the difference between mass and weight?
lecture
preflight 01
1: I would count the handful of jelly beans and put it into the
jar. I would measure with a ruler how many cm it filled the jar. I would
mark that measurement on the side of the jar. I would then advance the
measurement until I reached the top of the jar where I then could make
an approximation about how many jelly beans are in the jar.
2: The probablity of picking the same color of bean twice is the
total number of jelly beans!/3!3
3: You take the number of red jelly beans divided by the total
number of jelly beans.
4: 2000
5: That you can think of different ways to measure an item even
if you are not given the common measurement tool.
6: None right now.
lecture preflight 01
1: I would place a layer of jelly beans in the empty glass jar
and count how many fill the base when the jelly beans are only one deep.
I would count how many jelly beans that is. Then, I would turn the jar
on its side and place jelly beans in a row next to the jar, seeing how
many it takes to make a string from one end to the other, with some
turned each direction. Then I'd multiply the two numbers together (the
area and the height) and get an estimation.
2: 1/3 of the total plus one. You could potentially pull out the
same color over and over again until they were all gone, and then the
next would be the next color. This is, of course, assuming there is an
equal amount of each color. Otherwise, you'd have to pull all but one to
ensure that you have one of each; if there was only one blue and one
yellow, you'd pull all red until the last two beans, at which point
you'd grab the new color.
3: If there were and equal number of each color, you'd need to
pull 2/3 + 1 because you could pull 1/3 of the beans (all yellow) and
1/3 of the beans (all blue) and then guarantee a red one. Otherwise,
you'd have to pull every single one because if there were only one red
jelly bean, it could be the last you'd pull out.
4: Well, if we just look at Chicago, which has... a lot of people
in it, we could predict a number of piano tuners there. Then, multiply
that by 50 (the number of states). The Chicago estimate would be a safe
average because there are states without a big city, so all the small
ones would add up, and that would take into account the number of tuners
in Illinois not counted in the estimate. So, plus or minus a few, 50*
#Chicago-tuners ~~ US total.
5: I learned that Pooh Bear weighed 203 grams. And that I
recognize corn starch from its texture. And that you can't estimate a
measurement to more than half the smallest mark on your unit of
measurement.
6: Why does corn starch feel the way it does?
lecture
preflight 01
1: First, I would use a scale to find a very precise weight of
the jar with the jelly beans in it. Then I would measure the empty jar
using the same scale. I would then subtract the weight of the empty jar
from the weight of the full jar. This total is the weight of only the
jelly beans. Then I would find the weight of one jelly bean and see how
many times that fits into the weight of all the jelly beans in the jar.
2: In order to know how many times it would take you to pull two
of the same color bean, you would first have to know how many jelly
beans there are total and also how many of each color jelly bean there
are. Then, you divide the number of that color but the number of jelly
beans to find the probablility of pulling one bean of that color.
Multiply that number by two to find the probability of pulling two of
that color.
3: First you find out the exact number of beans in the jar, and
then exact number of red beans in the jar. Divide those numbers to find
the probability of pulling one red bean.
4: I think there are probably a lot more piano tuners in the
world than we know about. My guess would be about 10,000 because I'm
sure that there is probably one within every 50 mile radius.
5: I loved the project that we did with the tube and the strings.
I thought it was a really neat way for groups to come together and
problem solve. Our group had to go through a series of trial and error
to find the correct solution.
6: How do different types of mirrors work?
lecture
preflight 01
1: One way would be to put the handful of jelly beans into the
jar and estimate how many jelly beans would be in one layer. Then
measure the height of the jar with one jelly bean. Keeping in mind that
they will not form perfect layers, try to estimate how many would fit.
Also you could use math find the volume of the jar and the volume of the
jelly bean. Then use the results to determine how many jelly beans would
fit into the volume of the jar, again keeping in mind that there will be
space between the jelly beans.
2: It seems that the very least number would be 6 jelly beans but
this would only work if one third of the jelly beans were yellow,
another third, blue, and the last third red. The question doesn't
specify if this is the case, so for all we know there are only 10 red
ones on the top while the bottom 200 are blue and yellow.
3: Again if this question assumes that each color takes up one
third of the jar, you would need to take out 3 beans. However all of the
red beans could be at the bottom of the jar and then it would take many
beans to get to the red ones.
4: Well, there are about 300,000,000 people in the US and it's
important to note that piano tuning is a rare profession considering
that very few people play or own a piano. I would guess that there are
probably 3000 piano tuners in the US.
5: I learned the importance of experimentation in order to learn
something difficult.
6: Why can't pluto be a planet again?
lecture preflight 01
1: I would count the handfull of jelly beans and then put them in
the jar. I would use a ruler and measure how far the hand full of jellly
beans fills the glass, and then measure the class. Then, I would
multiply the number of jelly beans I had just counted times how many
more inches are needed to fill the glass, and then I would have my
guess.
2: You would have to pull out at least 4 jelly beans. In the
worst case senerio, you would pull out a red, blue, and yellow for the
first 3 tries, but on the fourth try, you are guarenteed to pull out a
red, blue, or yellow to match up with one of the origionals.
3: That depends. If there is exactly one third of each color,
then you would have to pull out at least one more than 2/3 of the jar,
because if for some reason you pull out all of the blue and and of the
yellows, which would be 2/3, then the next one you pull would have to be
red.
4: 50,000. I think there are probably about 4 piano tuners in the
average sized city in Illinois, and there are maybe about 250 cities in
Illinois, and so thats 1000 tuners in Illinois, times 50 others states
is about 50,000.
5: You can measure Winnie the Pooh with a thermometer
6: Is tanning really all that bad for you? (I read an article
that said tanning is really good for you because of the vitamin D and I
wondered if it was true)
lecture preflight 01
1: First, I would begin by take measurments of the jar to
determine the maximim volume in which it can hold. I would then put the
given handful of jellybeans in the jar and measure the percentage that
the handful has taken up of the jar. I would then use this number to
calcualte the number of jelly beans it takes to complete the percentage
of 100% full.
2: If I had to guess, it would take me 6 times before I am
guranteed to randomly have picked 2 jelly beans of the same color
without looking. If there are 3 different color of jellybeans, you have
to assume that there is an equal amount of all the colors. Using this
theory, picking out 3 beans would yield 3 different colors. And
therefore, to do this twice, I would need to reach in 6 times.
3: Well using the same theory as above, I would say that you need
to pull out 3 beans to gurantee that I have at least one red bean on the
desk in front of me.
4: There are 300 million people in the United States, dividing
this by 4(family of 4) there are 75 million famalies (yes I know not
everyone has a family). Out of these households, I would say half have a
piano, making it 37.5 million pianos. Assuming that there are half the
number of piano tuners as there are pianos, my wild guess would be 19
million piano tuners.
5: I learned that things are not always as hard as they seem.
Although it might appear difficult to make certain estimates, putting
your mind to the task at hand and using your brain and imagination can
yield succesful ways in making accurate estimations.
6: What is the chance that an asteroid or commet will ever hit
the Earth? And if there is a chance, how long into the future?
lecture preflight 01
1: I would put the handful of jelly beans into the empty,
identical jar. I would then figure out how much of the jar that handful
takes up in terms of height inside the jar. Using a ruler I would
measure that height. Then, I would measure the height of the jar. The
height of the jar divided by the height of the handful of jelly beans in
the jar would give me approximately how many handfuls it would take to
fill the jar. I would take the number of jelly beans in the handful and
multiply. This should give me an good estimate.
2: If there are three colors in the bag, a person has about a
33.3% chance of choosing a certain color out of the bag. So for every
three beans you pull out, statistically, you should have at least two
different colors out of those three. If you pull out another three
beans, the same should happen. Therefore, I think if you pull out six
beans you are guaranteed to have at least two of the same color.
3: Like I said above, you have about a 33.3% chance of pulling
out a certain color. I would say that it is likely, then, after three
beans, that you should have a red one, however, to be on the safe side
to GUARANTEE a red one I would again say out of six tries you should
pull out a red bean.
4: Clearly, to figure this out, one must ask many questions. The
first question would be, how many people live in the United States? The
population of the United States is approximately 300,000,000 people. Not
everyone will own a piano. How many of those people own pianos? Let's
just say one out of every 10 people own a piano. That means there are
30,000,000 pianos in the U.S. I have no idea how often a piano needs to
be tuned, and I have no idea how long it takes to tune a piano.
Therefore, I don't know how time consuming it is or how often it occurs.
If you assume a person can tune more than one piano a day and it does
not occur that often, I would take a random guess and say that there are
about 40,000 piano tuners in the United States.
5: From the first tube and string exercise, I learned that the
most simplistic models are usually the most effective and the most
accurate. I learned how to make that model by observing the properties,
not by seeing what is inside. I thought that was very interesting.
6: Why is the sky blue?
lecture preflight 01
1: You could take the jelly beans and the empty jar and put the
jelly beans that you have into the jar. Count how many jelly beans are
in the jar. Then you would need to estimate how many more handfuls of
jelly beans you need to put in the jar and then mulitply the number of
jelly beans you were given times the number of handfuls you believe it
would take to fill the jar. Another way to estimate would to look at the
jar that is already full of jelly beans. You could look at the very
bottom of the jar and see that there were maybe 23 jelly beans covering
the bottom. Then look at the jar and you would see that the jelly beans
almost sepearte into rows in the jar. Then you could multiple the number
of rows of jelly beans times how many jelly beans were in the bottom row
to get an estimate of how many total jelly beans were in the jar.
2: How many jelly beans you would need to pull out before you
would have two of each color infront of you would depend on the total
number of beans in the jar and if the three colors are distriubted
equally in the jar. We know it would need to be more then 6 beans
because chances are that in your first 6 pulls you would get exactly two
of each color.
3: If you wanted to have at least one red bean it is diffiuclt to
determing how many beans it would take to guarentee at least one red
bean. If you pulled out all the beans then you would be guarenteed at
least one red bean but luck and chance would affect the least amount of
beans that you would need to pull.
4: I would estimate that there is around 4500 piano tuners in the
United States. I think this because there might be on average around 100
piano tuners per states some states may have more or less depending on
size and if you mulitple 100*50= 5000. So I guess around 4500 because
not all states would need that many piano tuners.
5: That simple concepts can be applied to learning and modeling
more complex things. Like the thought process we went through to
understand how the tube and strings worked was the same concept that
scientists use to make and develop models on more complex things such as
the solar system.
6: How do animals who are able to change their color to
camoflauge themselves into their environment know how/when to change
color?
lecture preflight 01
1: One way could be to fill the bottom of the jar with jelly
beans and count them. Then you can count about how many rows the jar can
fit and times those two numbers together.
2: Since the question does not say if there is an even number of
red, blue and yellow jelly beans, it only says there are those three
different colors, then you need to pull out all but one to guarantee
yourself at least two different colors. There could be only one red, one
blue, and the rest yellow jelly beans for example so therefore you need
to pull out all but one to make sure you have at least two of the
colors.
3: Same as above, since you do not know if there are more than
one red jelly bean, you need to pull out every jelly bean to guarantee
yourself a red one is infront of you. Because there could only be one
red jelly bean in the jar so to make sure you get that one, all the
jelly beans need to be infront of you.
4: I am not sure if this is allowed or not but I looked up and
read that there are about 18 million pianos in the U.S. I estimate about
30% of those people have tuners and then there are probably others in
stores and with technicians so my answer is about 40% of 18 million
which is 7.2 million tuners in the U.S.
5: I learned how important it is to clarify what units you are
using to measure something. It can make a huge difference if you are
trying to measure the length with a thermometer or color with a ruler.
To measure length a ruler is probably best but it does depend on the
object of course, and to measure temperature a thermometer is probably
best, and to measure color the paint samples would work best.
6: A big science question I have is, first we as humans explored
and learned about space, and then we went small and learned about the
atom and dna; so my question is what is next? What is going to be the
next great research done? What topic are we to learn about next?
lecture preflight 01
1: get an approximation by using the few jelly beans and then use
the area of the empty container to obtain the approximation
2: probability of pulling out one color is 1/3 so you would have
to pull out atleast 4 to get different colors.
3: probability is 1/3. Pull out 3 and atleast one of them would
be 3
4: 50,000 seems like there would be a lot.
5: i really liked the lecture's coke demo
6: hows so elevators go really fast in skyscrapers?
lecture
preflight 01
1: Well, I would first count the number of sample jelly beans
that I was given. Then I would put those in the empty jar. Since we're
allowed to use any other tools/equipment, I would purchase a bag of
jelly beans that look identical to the one's in the big glass jar. Then
I would sit with the empty jar (which has a few jelly beans in it) and
add my new jelly beans to that jar until it is full. I would count each
jelly bean as I put them in the jar too. Then once it looks like it is
at the same level of fullness, I would use that number as my estimate!
Another way to estimate the number of jelly beans would be to count the
sample size and place those in the empty jar. Then grab a ruler and
measure the height in centimeters of the entire jar and the height of
the sample jelly beans. Next, I would divide the height of the jar by
the height of the sample jelly beans. Then I would take that number and
multiply it by the number of jelly beans that were in my sample size.
That answer would be my estimation!
2: You could pull out a red the first time, a blue the second
time, and a yellow on the third time. Therefore, in order to guarantee
having at least two of the same color on the desk, you would have to
draw out 4 jelly beans from the jar because whatever the 4th draw is, it
will match another color already picked.
3: Well, you could somehow manage to draw out all of the yellow
beans and then all of the blue beans. Therefore, you need to have drawn
2/3 of the jar (all of the yellows and blues if they are evenly
distributed) until a red will appear.
4: My guess would be 300 because there are 50 states so I'm
assuming that every state has at least one. Then, some states are bigger
than others, so they might have a piano tuner in each part of the state
(northern, eastern, southern, western) so I raised my guess from 50 to
300. I bet Tennessee has a lot of piano tuners because they are near the
Grand Ol Opry house where music is very important, therefore the pianos
better be in tune!
5: That sometimes that most complex and bizarre looking objects,
can really be made up by something completely simple. From the
experiment with the tube and strings, my group was in awe of how it
worked and we were tying knots in the middle and doing all this crazy
stuff. Then we found out that the answer was to overlap the two strings
in the middle and it worked! It was one of those situations when you
work so hard to reach the answer, get stumped, find out what the answer
really is, and then feel stupid because it was so easy.
6: Once pop has been sitting out for awhile, where/how does the
carbonation go? (why does it become 'flat')
lecture preflight 01
1: Find the mass of the full jar and subract the mass of the
empty jar. Then divide the answer by the mass of a jelly bean. Make a
mold of the jar take it home and fill it with the same kind of jelly
beans and count those.
2: Well, you could pull out all the beans and still not have two
of every color. Just because there three different colors does not mean
that they are all equally distributed. They could be all bluu with one
yellow and one red.
3: Again, you may have to pull ou tall of the beans. If there
were only one red bean in the jar, it may be the last one you pull out.
4: Well i would take the population of a large city and calculate
using that how many there would be in the US. My guess is 100,000.
5: The question to ask is not how is the model working, but what
can I ask to figure out how the model is working.
6: What is the deal with the "new" planet?
lecture
preflight 01
1: Well if the handful is big enough to fill the jar, then I
would fill it and count the jelly beans. But if there are not enough
then i would find a smaller cup, fill it with water, and see how many
times a cup of water could fit into the jar. Then I would fill the cup
with jelly beans and count how many there are in the cup. Then multiply
the number of jelly beans by the number of cups of water.
2: Four. If the first three are all different colors, then the
fourth would match one of the three.
3: all, it depends how many reds there are. If only one is red
and is at the bottom then you wont get it untile you take all the others
out.
4: 100,000, i would say and average of 2,000 tuners per state.
5: that the more people we had counting the number of noodles in
the cup, the more accurate we would be by finding the average.
6: Why was Pluto determined to not be a planet?
lecture
preflight 01
1: Well i'm assuming that the handful of jelly beans is not
enough to fill the empty jar to approximate how many jelly beans are in
the full jar. In this case I would fill a small cup with the handful of
jelly beans and count how many are needed to fill it. Then I would fill
the jar with water and pour the water into the cup until it is full;
determining how many cups of water are in the jar. If it ends up being
around 2 and a half (for example) I would multiply the number of jelly
beans I found to fit in the cup by 2.5.
2: Each time that you pull out a jelly bean you have a 1/3 chance
of picking a specific color. So in order to be guaranteed of picking a
specific color you'd need to pick at least 3 jelly beans. Therefore one
would need to pick 6 jelly beans in order to have at least two of the
same color on the desk in front of you.
3: You would need to pull out three jelly beans because you have
a 1/3 chance of pulling out a red jelly bean.
4: I think there's maybe 200 piano tuners in each state, so
200*50 amounts to 10,000 piano tuners in the United States.
5: The first activity with the strings in the tube I thought was
really neat, i had never seen that before... its a good trick to know!
6: Now that its snowing... I was wondering how salt melts ice on
the roads.
lecture preflight 01
1: I would first count how many jelly beans are in my possession.
I would then put my handful of jelly beans into the empty jar. From
there I would figure how much of the jar is full. Let's say (1/6) I
would then multiply the amount of jelly beans that are in the jar by the
number 6 and that should give me an estimation of how many jelly beans
it takes to fill the jar up thus giving me the correct answer to win the
contest.
2: Four because red, blue, and yellow all have an equal
probability (1/3). On the fourth pull you are guaranteed to get one of
the colors that you already have in your possession.
3: 3 because red, blue, and yellow all have an equal probability
(1/3).
4: 20,000 Based off of the population of the world and the amount
of people that own, care about the mainteance of their pianos, and
actually use them.
5: Sometimes the answer to a problem may be fairly easy and
simple, it is not good to always over think and analyze questions and
puzzles.
6: I m just curious about what is the best way/method to answer
question one?
lecture preflight 01
1: I would eat the jelly beans and walk away happy. Just
kidding... One way to estimate would be to put jelly beans in a cup
(counting them first), then see how many cups it takes to fill the jar
and do the math. This is pretty much how we estimated the macaroni going
into the big cup. Another way would be to assume that the store used
full bags of their own brand of jelly beans. So to figure out the
answer, get one bag of their brand of beans, count how many are inside,
then estimate using the method above.
2: Well, it depends. You could pull out six beans and have two of
each color in front of you. But the chances of that happening are small.
You have a one in three chance of getting the bean you want on your
first try and after that, it depends which bean you picked... I will say
it takes 36 tries to get two of each color.
3: I guess you could pull out one and have it, or two, or three,
or twelve. This is a tough question. It has something to do with
probability, right?
4: I am going to guess that about one tenth of the U.S.
population are piano tuners, so roughly 30,000,000 people in the U.S.
are piano tuners.
5: There are two other vegetarians (at least) in our class!
6: The only question that came to mind was "What DO piano tuners
have to do with science"? I'm assuming we'll talk about this on
Wednesday.
lecture preflight 01
1: 1. You could count the number of jelly beans given to you.
Then, you could place the beans in the jar. You would then see how much
space that number of jelly beans takes up in the jar. By seeing this you
could think of how many times you would have to put a handful in. Do the
multiplication and there you are!
2: You would only have to pick out 4 jelly beans. For the first
three jelly beans you could possibly pick out one of each color, but
after that you would have to pick one of the colors you had previously
picked.
3: I think that to ensure that you have two of the same color,
you would have to pull out around 2/3 of the jelly beans in the jar. I
think this because that way you would be sure that you had taken all of
the blue and yellow beans out of the jar.
4: I would guess that there are 2500 piano tuners in the United
States. There are 50 states in the United States, and I guessed there
would be around 50 in each state on average. It really is just a wild
guess though.
5: I thought it was interesting to know that to calculate the
total difference, you can take the square root of the number of times
the event occured and add or subtract it. That could be very useful.
6: Why does the sky appear to be the color blue.
lecture
preflight 01
1: Using the handful of jelly beans and the empty jar, I would
count the number of the jelly beans that I was given. I would then fill
the empty jar with the handful of jelly beans. I would then estimate how
many handfuls I would need to fill the jar and multiply the amount of
handfuls by the number of jelly beans given to get an estimate of how
many jelly beans are given in the big glass jar.
2: I would need to pull at least 4 jelly beans to have at least
two of the same color because you can pull 3 assuming that those 3 are
the 3 different colors given. Then I would pull a fourth jelly bean
because it would have to be a replica of one of the colors from the
first three jelly beans selected.
3: Considering we aren't given ratios of the colors of the jelly
beans, I would assume you would have to at least pull three jelly beans
to get a red bean. Logically speaking, it may be possible to select a
red bean one out of three jelly beans selected.
4: Assuming there are roughly 100 counties in Illinois, I would
guess that there is about 1 piano tuner per county. That would make 100
in the state of Illinois. So I would guess that there are roughly 100
per state, so my estimate would be 500 piano tuners in the U.S.
5: It was interesting to learn that there are several ways to get
a measurement for the same object. It was interesting when one group
decided to measure Winnie the Pooh using a thermometer. However, it is
difficult to take the temperature of a stuffed animal, so the group
decided that Winnie the Pooh was the length of about 2 thermometer's. I
thought this was very innovative!
6: Why do sparks come out of electrical outlets sometimes?
lecture preflight 01
1: well, since you are only given a handful of jelly beans, and
not enough to fill the second jar, i would put the jelly beans that you
do have, in the jar, and measure the hight. Count how many jelly beans
it took you to reach a certain height. Figure out how tall the jar is,
and what number you need to multiply your jelly beans by to have a full
jar. That number would be a fast way to get a close answer. For this to
work, you would need enought jelly beans to cover the whole bottem of
the jar, the more you have, the more accurate your answer would be.
2: 4. If there are only three colors, you are bound to get
atleast two that are the same color after pulling out 4 beans.
3: every one. Unless more specific, there could be only one red
bean in the entire jar, so you could, but highly unlikely, have to pull
every single bean out to get the only one at the bottem of the jar.
4: well, there are about 300 millions people in the US (i think),
so guessing that one in 1000 people have a tuner, and there is one tuner
per 100 pianoes, my guess in 3,000.
5: this is not physics related, but the sweet boxes that we got
are pretty cool. I've never seen ones that latch on the sides like that!
6: when placing telephone poles (although many times these days
the wires are underground), how do designers decide how far apart to put
the poles. Is is based on the weight of the wire, or how low of a dip in
the wire can have, or does it deal with tension and pressure?
lecture preflight 01
1: I will first count how many jelly beans that I was given. Then
I would put it into the jar. Using a ruler, I would measure how far up
the jelly beans were. Then I would estimate how many times that
measurement would be to where the real jellybean was filled. I would
take that number and multiply to the number of jelly beans I had to come
up with an estimate.
2: 6 because there is a possiblity of picking each color twice.
3: 3 because there is a chance to pick one of each color.
4: 2500 if there was five in each state.
5: I thought doing the "Mystery Tube" was interesting and made me
think of characteristics that are important for the tube that I did not
think of.
6:
lecture preflight 01
1: I would find a scale, and weigh a jelly bean. I would then
weigh the empty jar that is identical to the one that the jelly beans
are in. Next, I would weigh the jar with the jelly beans inside of it. I
would subtract the weight of the empty jar from the weight of the jar
with the jelly beans inside, and then divide the number by the weight of
the single jelly bean.
2: You would need to pull out a LOT of jelly beans to be
"guaranteed" two of the same color; just because there is a 1/3 chance
of pulling out a yellow does not necessarily mean that you're going to
pull out a yellow jelly bean every third time. In fact, there would have
to be absolutely no more red or blue jelly beans inside of the jar for
you to be guaranteed to pick a yellow.
3: Once again, you would most likely have to pull out a lot,
because you aren't guaranteed to pull out a red jelly bean at any point.
In the end, 1/3 of the jelly beans you pulled out WILL be red, but you
could pull out all of the yellow and blue ones before even touching the
red.
4: 200. I don't think that the demand for piano tuners is very
high.
5: I learned how to make a mystery tube!
6: How did people decide how time was going to be organized? Why
aren't there 8 days in a week, or 9, or 6? Who decided that we were
going to think of time in term of "week", "month", "year"?
lecture preflight 01
1: You can count put the jellybeans that you are given into the
empty jar and then see how much it fills the jar. Say it makes 2 layers
of jelly beans. You know that your handfill say has 20 jellybeals in it.
KNowing that 20 jelly beans makeys 2 layers or rows in the jar you can
count how many rows are in the original jar of jellybeans. Say there are
10 rows in the original jar, and you know that 2 rows has about 20 jelly
beans then you know that you should mulitpy 20 times 5 (5 sets of 2
rows) and make an educated guess from that!
2: I think that you need to pull out at least 2 and the max 4. I
tried to use the probability rules that i learned in high school but
that failed. So then i began to think: We'll you have to at least pull
out 1 (to get started) you could pull out the same color on the next
one. If you didn't then you would have to pull another one if you didn't
get this one you would pull out your third jelly bean but this time you
would have 2 chances (colors) to match it to. If still no matches occur
then your 4th pull is guaranteed to be a match because there are only 3
original colors.
3: You need to pull out 3 in order to be guaranteed to get a red
one. There are only 3 colors so you would not need to pull out more then
that and you would have at least have to pull out 1 (you could get it on
your first try).
4: Okay, well alot of people play piano but not i do not think
that all of them would know how to tune a piano becuase it's not like
playing a guitar where you do it everytime you play. I would guess that
there are prolly 1,500,000 piano tuners in the world. decided that an
average town in illinois is 30,000 people. If you took all the piano
tuners in one state and put them into a town there would be about 30,000
(this is just my guess) if you multiply that by 50 (the number of
states) then you get 1,500,000.
5: I learned what a Caliper was and that it measures in
centimeters and millimeters.
6: What is inside of a ruiny nose and how does your body produce
it.
lecture preflight 01
1: Use a small cup (like the Dixie cups we used in class) and
measure out how many jelly beans fit in the cup--count them
specifically. Then, find something similar to jelly beans (real beans,
macaroni, etc) and count, using the dixie cup, how many cups fill up the
empty jar. Then, multiply the number of cups by the number of jelly
beans that fit in a single cup. An alternate way would be to find a type
of food or small objects that have a size comparable to a jelly bean,
filling up the jar with those objects and counting how many objects are
in the jar (the jelly bean estimate would be similar to this if the
objects are of similar size to jelly beans)
2: If I were to pull out four different beans, I would be
guaranteed to have at least two beans of the same color. Since there are
only three colors, there would have to be one bean that repeated a
color. It is possible that this could happen with two or three beans. It
is only guaranteed, however, with four beans drawn.
3: This question is unable to be answered because of the data
given. Although it is stated that there are three different colors of
jelly beans, it does not state how many of each color there are or if
there are equal numbers of each color. For example, there could be only
one red bean in the entire jar, while there are 150 yellow beans. It
would be a higher probability of drawing a yellow bean than a red bean
in this situation. Therefore, I am unable to state how many beans should
be pulled out to guarantee one red bean.
4: 30,000 There are about 300 million people in the US, and I'd
take a wild guess that there is about 1 piano tuner for every 10,000
people. This means that there is about 30,000 piano tuners in the United
States.
5: I thought it was really interesting to find that one of the
groups measured the pooh bear with color, and that another did
temperature, while I think I would have used the color strips or
thermometer for a measurement in length (using the unit of 3 "color
strips" or 5 "thermometers" for example). It was interestingn to see how
different groups used their tools in a different way than I would
have--and it reveals that there are often many methods to solve a
problem or answer a question.
6: What are some science concepts to teach children who are
younger than elementary age (age 3-6)?
lecture preflight 01
1: I would use my handful of jelly beans to fill the entire
bottom of the empty glass jar. I would then count the number of jelly
beans, and measure with a ruler the height of that one layer of jelly
beans. I would then measure the height of the glass jar with the ruler,
and based on that height figure out how many layers of jelly beans would
fit in the jar. I would then multiply the number of layers by the number
of jelly beans in one layer. Depending on the size of the jar, I would
adjust my guess (for example, if the jar gradually gets smaller at the
top).
2: You need to pull out at least 4 jelly beans to have at least
two of the same color jelly bean. Even if you pick a different color
jelly bean for each of the first three picks, the fourth will definitely
have to be a repeat of yellow, blue or red.
3: I am not sure about this answer. I would want to say if you
pick three times you are likely to get at least one red, but there is no
guarantee. Even after 10 picks, you might still not be guaranteed a red
jelly bean. Those ten can be just blue and yellow beans. It seems like
there is no right answer for this question.
4: I would guess about 15 in each state, so about 750 tuners in
the U.S.
5: I liked learning about percent difference between an
individual prediction and the actual data. It is cool to see how
near/far one is from the correct answer.
6: I know this may sound like a stupid question, but in the
formula for percent difference, why did you have it multiplied by 100%?
To me, it makes me think that I am supposed to multiply it by 1 (because
100% is equal to 1, like .9 is equal to 90%). I know you multiply it by
100, but I was just confused why the percent sign was there? Also, what
is the actual math problem to find out the number of objects in a
container? I know there is one, but I am not sure of it?
lecture
preflight 01
1: I would put as many beans into the jar as filled up the bottom
of the jar completely and than multiply that by how many rows are in the
jar that is full.
2: You must at least pull out two beans in order to get two that
have the same color. However, in order to guarantee that you get at
least two of the same color you would have to pull out at least two
thirds of the beans.
3: You must pull out at least two thirds of the beans and one
more in order to have at least one red just in case every bean you
pulled out before then was the same color.
4: I would say that there are 5,000,000 tuners because that would
mean there is 1 piano tuner for ever 70 people in the US.
5:
6: How does a flashlight work?
lecture preflight 01
1: Draw a line down the middle of the empty identical container.
Place enough jelly beans into the bottom of the container so that
exactly half of the bottom of the container is coated with one layer of
jelly beans. Measure the height of the layer of jelly beans. Divide the
total height of the container by the height of the jelly bean layer and
multiply that number by the number of jelly beans it took to coat half
of the bottom of the container. Double that number of jelly beans and
subtract 10 for good luck.
2: You will need to pick only four beans to ensure that you have
at least two of the same color on the desk in front of you. This works
because if you pick one red, one blue, and then one yellow, the fourth
bean that you pick has to be either a red, a blue, or a yellow.
3: You will need to pull two thirds of all of the beans, and then
one more bean. This is true because you can pick all the blues and
yellows, two thirds of the beans, and still have no reds. But if you
pick one more you will have to have picked a red.
4: I would guess that there are 5,000 piano tuners int he United
States. I would guess this by saying that there are about one piano
tuner for every 300 pianos. I came to this number by assuming that most
piano tuners were not full time tuners and had other jobs. And I guessed
that there would be 1.5 million pianos in the United States.
5: There are many different ways to measure a Winnie the Pooh
6: Does the weight of a carbonated drink change as the
carbonation dimishes?
lecture preflight 01
1: You could use the jelly beans that you are given and pour them
into the identical jar. After seeing how much it fills up the jar, you
can estimate how many more groups of jelly beans you would have to add
in order to fill the jar. This would provide a good estimate of the
amount of jelly beans that can fit in the jar.
2: You would have to pull out four jelly beans to guarantee that
you will have at least two of the same color. You may pick out one of
each color, but then the fourth bean will have to match one of those
colors.
3: In order to guarantee that you will have a red jelly bean in
front of you, you may have to take out 2/3 of the jar. It would be very
rare, however it could happen where all of one color comes out (1/3),
all of the second color comes out (1/3) and only after that can you
guarantee that the next jelly bean will be red.
4: 1500 piano tuners, it is a somewhat rare profession.
5: I thought it was interesting when we measured a mysterious
object because most of the groups were given tools that would have
typically never been used to measure the bear, but it was still possibly
depending on what you decided to measure.
6: What exactly makes a rainbow occur?
lecture preflight 01
1: A first way that could be used to determine how many jelly
beans are in the jar is to put the handful of jelly beans in the jar and
then estimate what fraction of the jar it takes up. From the estimation,
multiply the number of beans from your handful by how many more parts of
it you would need to fill the jar. For example, if you have 25 jelly
beans in your hand and it appears as if they fill 1/4 of the jar, then
multiply 25 times 4 to estimate 100 beans are in the jar. A second
method of estimating how many jelly beans would fit in the jar is by
measuring volume. First I would choose an average sized jelly bean and
measure its volume by displacement. Then, I would determine how much
volume the jar can hold, and then divide that by the volume of the jelly
bean to estimate how many jelly beans will fit into the jar.
2: You would need to pull out 4 jelly beans to be guaranteed to
have two of the same color jelly bean on the desk in front of you. Since
there are only 3 colors of jelly beans in the jar, if you pull out 4,
even if you pull out one red, one yellow, and one blue, the fourth one
will be the second of any color that you will already have on your desk,
guaranteeing to give you at least two of the same color jelly bean.
3: It is uncertain how many jelly beans will be needed to be
pulled out until you are guaranteed to have at least one red bean on the
desk in front of you because we do not know the distribution of red,
blue, and yellow jelly beans in the jar. If there is only one red bean
at the bottom of the jar, then we would have to take out all the beans
just to get that one red bean. Therefore we do not know how many beans
needed to be pulled out to be guaranteed to have at least one red bean
on the desk.
4: I would estimate that there are about 3000 piano tuners in the
US. Since piano tuners are a rare profession, I would estimate that
there is one for every 100,000 people in the US. Since there are 300
million people in the US, I think that 3000 piano tuners is a good
estimate.
5: This week I really liked the analogy between the process we
went through to figure out the mystery tube in relation to models of
cells, atoms, and the solar system. We wrote down several ideas to
figure out how the tube worked, not realizing how simple the inside of
the tube actually was. I thought it was interesting that models of the
solar system started out complex also, and was narrowed down to the
simpler model we know of our orbiting solar system today.
6: How does a curve ball (in baseball) curve?
lecture
preflight 01
1: Depending on how many jelly beans I was give I would place
them in the jar to see how much space it takes up, then estimate how
many more handfuls I can fit in the jar. Finally I would multiple the
number of jelly beans by the number of handfuls for the answer.
Otherwise I would find an object the same size and fill it with those
and count them or go out and buy jelly beans to fill the jar with and
then count them.
2: It depends on how many beans there are and how many of each
color. However, I would guess nine because you have a third chance of
pulling out each color and multipling that by another third equals one
ninth which can mean you will get the two of the same beans by pick
nine.
3: Again inorder to do this mathmatically you need the exact
amount, you could possible go through 2/3 of the jar before picking a
red one. But if they are mixed I will assume five just purely on the
fact that you will probably have to pick one red after you pick 2 of
both other colors.
4: 17,521 because I estimated 300 a state and added a couple more
because I under estimate everything.
5: I learned how the tube worked and how there are other options
but it doesnt work as well (with a knot) which relates to the solar
system and cells which is why so many people have different opinions and
often change there ideas.
6: Why spend so much time studying something that you may never
know the answer to that doesn't affect you in this life or the next?
lecture preflight 01
1: First, I might find the mass of both the empty jar and the
jelly bean filled jar. I would then subtract the mass of the empty jar
from that of the filled jar, leaving just the mass of all the jelly
beans. Then I would measure out ten jelly beans on the balance. I would
take the mass of all the jelly beans and divide it by the mass of the
ten jelly beans. Then I would divide that number again by ten. Another
way I might try to figure out the number of jelly beans is by measuring
how tall the jar is with a ruler. Then I would take a much smaller
increment (maybe a half inch) and see how many jelly beans it would take
to reach that point on the ruler. I would then divide the entire height
by one half inch and multiply that number by the number of jelly beans
it took to reach a half inch.
2: You need to pull out 4. You could possibly pull out 3
different colored jelly beans, but when you pull out the 4th, it would
have to match up with one of the three already pulled out.
3: Since it is possible, though unlikely, to pull out 50
consecutive blue and yellow jelly beans without pulling out a red one, I
would say that it is unknown exactly how many you need to pull out to be
guaranteed to have at least one red bean.
4: My estimate would be 66,000 piano tuners because the
population of the U.S. is roughly 300,000,000 people and the population
of Champaign is roughly 67,000 people. So in the U.S., there are about
22,000 times as many people as there are in Champaign. Since there are 3
piano tuners listed in the phone book from Champaign, I multiplied that
by 22,000 and got 66,000.
5: The simpler the better.
6: How does this FutureGen or "clean (green) coal" work?
lecture preflight 01
1: Count the handfull of jellybeans, and pour that into the empty
jar. Then estimate how many handfuls it will take to fill the jar. Then
multiply the number of handfuls you think it might take, by the number
of jellybeans in one handful.
2: In order to pick out two marbles of the same color, you would
only need to pick out 4 jellybeans. This is becasue even if you pulled
out 3 different colors on your first three trys, the fourth pull you
would pull out one of those colors.
3: In order to get a red bean on your desk, you would need to
pull out at least 2/3 of the beans in the jar (the other colors would
then be gone).
4: My wild guess would be around 15,000. I guessed that there
would be around 300 piano tuners in each state.
5: To estimate the total difference, you should take the square
root of the amount of times an event actually happened.
6: How many gallons of gas does it take for a rocket to launch
into space?
lecture preflight 01
1: i would count the amount of jelly beans that are in the
handfull given to me. I would then put them in the empty jar. Then i
would estimate how many more of those handfulls could fit in the jar.
Then i would multiply the number of jelly beans handed to me by my
estimate of how many more handfulls would fit in the jar to get my final
estimate.
2: I do not think you can be guaranteed but if i had to guess i
would say you have a 1/3 chance of pulling out a certain color. To pull
out that same color again is another 1/3 chance. Therefore you would
mulitply 1/3 by 1/3 to get a 1/9 chance of pulling out two of the same
color jelly beans. therefore you would need to pull out nine to be
guaranteed.
3: I do not think you have a guaarantee once again but i would
have to go with three because you have a one third chance of pulling out
a red so you need to pull out three
4: I would say that there is at least one in every town and 20 in
every big city and say there are 50,000 towns and 50 major cities, then
i predict there are 51,000 piano tuners in the US.
5: how to make that cool mystery tube! that even though you
cannot see how things are made on the inside you can figure it out by
experimenting with the things on the outside.
6: how can you measure the weight of air. how can you contain it
to measure it?
lecture preflight 01
1: I would count the handful of jelly beans and then put them
into the container to see the impact that the handful of jelly beans has
in filling the jar. Then, once they're in the container I'd measure the
height they have in comparison to the height of the jar. Then I would
divide to two heights to see how many more handfuls would be needed to
fill the jar. Then multiply how many handfuls are needed by how many
jelly beans were in a handful. This should give me a relatively close
answer.
2: Four. If there are three colors I may get each color once on
my first three pulls. But on the fourth there must be a duplicate of a
color.
3: An undetermined amount. I could keep pulling yellows and blues
for a long time before I pull a red out of the jar.
4: My guess is 5,000,000. If there are one or two for every
relatively large town, there should be about 5,000,000 in America.
5: That even if I can't see the answer to a problem, I can
develop an answer based on information I can discover. The answer does
not need to be obvious in order to come to a conclusion.
6: Because my concentration is biology, I was wondering if there
is a relationship between biology and physics aside from both being
types of sciences?
lecture preflight 01
1: Count out how many jellybeans fill one inch of the jar.
Measure the height of the jar in inches. Multiply the number of jelly
beans by the number of inches to get your estimate.
2: You should pull out four jellybeans from the jar. Since there
are three colors possible, you are guaranteed to have at least two of
the same color.
3: It depends how many beans of each color are in the jar because
this determines the probability of chosing each color.
4: A piano tuner does not seem to be a popular profession so out
of the entire United States, so I predict there are about 10,000.
5: I learned that there are many different ways to use a
measuring device, even if it is not using its original purpose.
Sometimes you must be creative to measure an object.
6: Why is artificial sugar (in diet coke) so much lighter than
regular sugar (in regular coke)?
lecture preflight 01
1: I would fill the identical jar full of the same type of jelly
beans and then merely count the beans. However, I would do this
experiment multiple times and then take the average of the tests.
2: I would need to remove four beans in order to ensure that I
received two of the same color. Yet, depending on what color of bean I
draw, it could take less time.
3: In this situation since I do not know the number of each
color, I would have to get rid of all the blues, yellows and plus one to
ensure that I pick a red.
4: I am just guessing 100,000 piano tuners, and I am looking
forward to Wednesday.
5: I really liked the experiment with the rope. I couldn't
believe that the strings were not knotted in the middle of the tube.
Simplicity is better than complexity in all areas of life.
6: Why do we see our breath when it is cold outside?
lecture preflight 01
1: First I would count the hanful of jelly beans. Then I would
take the handful of jelly beans and put it in the empty jar. Then I
would try to guesstimate how many handfuls it would take to fill the
entire jar.
2: At least 6, because there are 3 different colors.
3: I don't think there is an exact number. You can be pulling out
a lot and not get to a red one.
4: Since piano tuners are a pretty rare profession and not
everyone has a pianos, I don't think the number would be that high. I
would say there are about 10,000 piano tuners in the US.
5: When measuring, sometimes it doesn't matter if you're off by
one gram.
6: How is petroleum jelly obtained?
lecture preflight 01
1: you can put a known amount of jelly beans in the "testing"
jar. If the jars are exactly the same size you will then know
approximately how many jelly beans will fit in the contest jar. If a
handful isnt enough to fill up the jar then you can see how much of the
jar the handful fills up and estimate about how many times of that known
amount in the handful would it take to fill the jar.
2: There is no way to figure this question out since the amounts
of each color jelly bean are not given. For instance if they said there
were equal amounts of each color you could find the probability. Since
the amount of each is not given, there could for example be only 1 red
jelly bean and 20 of the other colors and then you could not gaurantee
pulling two reds out at all.
3: As mentioned in the last question, you would need to know how
many of each color there were in the jar. There may only be one red
jelly bean total!
4: I don't actually know what a piano tuner is but I would have
to estimate about how many people own pianos or find out how many pianos
have been made and there should be a tuner in each piano. I could take a
random sample of the population and use that to represent the population
of the world and poll them as to whether they have a piano or not. The
sample would have to be representative of the worlds population though
and that would be hard.
5: I learned that its much easier working a team. 4 minds are
always better than 1! I would never be able to figure out that tube
experiment without my group!
6: whats the cornstarch for?
lecture preflight 01
1: One way us that you can bring your own small container that
can be filled with a handful of jellybeans and fill it up to the top.
(You may eat any extras). Count the number of jelly beans that fill your
container. Then, you can find out the volumes of the container and the
identical jar. Make sure they are in the same units. Then, divide the
volume of the identical jar by the volume of your small container. Take
the answer and multiply it by the number of jelly beans that fit in your
container. As a reward for all your hard work, you can eat the rest of
the jelly beans!
2: By the time you pull 4 jelly beans from the bag your are
guaranteed to have at least two jelly beans of the same color because
these are the only things that can occur: 2 jelly beans of one color and
1 of each of the other colors, 2 of one color and 2 of another color, 3
of one color and 1 of another color, or all 4 the same color.
3: It is difficult to determine the answer to this question,
since the number of each color was not given. The only time that you
could be 100% guaranteed of picking a red is when all of the yellow and
blue jelly beans are gone. However, it is likely that by the 7th pick
you will get a red jelly bean if they are evenly distributed because by
then you would have already picked several of the other two colors.
4: 5,000. I think that there are around 50 piano tuners in each
state and 50 x 50 = 2500. I know that they are not that common, so I'm
guess in a small number, like 50 per state.
5: I learned that something as simple as a cardboard tube and 2
strings can help children to understand how scientists arrive at
solutions and discoveries. For example, you can can compare this type of
problem solving to that of an astronomist. Astronomists often discover
objects in space because they detect the effects its gravity on another
object. What we did was similar. We saw how the strings were affecting
eachother to predict what was going on inside.
6: What is the first the first standard unit of measurement that
was ever invented and who invented it?
lecture preflight 01
1: To educate my guess, I would count a number of jelly beans and
drop them in the empty jar. I would then measure their height with a
ruler. I would probably then count out a number twice as large, drop
into the jar, and again measure. If the second number was close to twice
the first, I would simply measure the total height of the jar, and then
scale the total height with the number of beans that filled a fraction
of the height. Maybe not a perfect procedure, but solid.
2: 4, because if the first 3 are different colors, the 4th has to
be the double of one of the colors. Could be less (the first two blue),
but at the most 4.
3: There is no guarantee you will ever see a red bean. It should
be one out of 3, but you could keep pulling out blue and yellow.
4: I'd say 1,000, because that number is still a really small
portion of our nation's population. And there aren't really that many
cities that would create a market for a piano tuner or several.
5: The PVC tube/string apparatus was an interesting toy. I plan
on making a "classy" version to market as a desk toy for executives.
6: How a diesel engine can be converted to run on vegetable fat
from chinese restaurants/deep fryers?
lecture preflight 01
1: I would use the handful jellybeans and put them into the jar
to see how much of the surface area of the bottom they cover. I would
then estimate about how many of those handfuls you would need to cover
the entire bottom of the jar. You would take the number of jellybeans in
the handful times the number of handfuls your approximate needing. THen
i would take one jellybean and measure how many went up the side of the
jar. I would take this number times the number found earlier and make my
estimate.
2: according to probability you would need to pull out 4, because
if three colors are evenly distrubuted throughout the jar, you would
have a 1 in 3 chance of pulling out any given color, therefore the next
jellybean your chose would be a match to an already pulled jellybean.
However, because probability is just that, PROBABLE, no one can say for
sure how many need to be pulled out until a match is reached.
3: same as above. Probability states that you should only have to
pull out three to guarantee getting a red bean, but that's not definite
by any means.
4: 2500, fifty in each state, give or take
5: 1. that being clear about the particular unit of measurement
being used is important 2. alternate ways to measure things
6: How do defrosters in cars work?
lecture preflight 01
1: First, I would count the number of jelly beans given to me and
then place them in the identical jar. I would us a caliper or ruler, to
measure the height of the jelly beans in the jar. Then I would measure
the height of jelly beans in the full jar. I would then find out how
many "rows" of jelly beans it takes to fill up the jar (divide height of
handful of jelly beans by the the height of full jelly beans in jar).
Then I would guesstimate with the numbers I came up with.
2: 2/3 of the jar. Because if you pull out only reds or only
yellows, you are guaranteed that the rest will be only blue.
3: 1/3 of the jar.
4: Well, I think that there are MANY people who are able to tune
GUITARS, because there are a ton of people who can play guitar. On the
other hand, thinking about pianos, there are a less amount of people who
can play piano, but not all of them can tune pianos. So I would say
about 25,000.
5: The tube experiment was a lot of fun and very interesting. I
learned how to think outside of the box in order to find out things that
I cannot see.
6: What creates smells?
lecture preflight 01
1: One way I would try to estimate would be to count the number
of jelly beans I was given and put them in the empty jar to see how much
room they take up. I could try to estimate how many times that handful
would fit in the jar and then multiply the number of jelly beans by the
number of times it would fit in the jar. Another way would be to look at
the jar and divide it into like four sections. I could estimate the
number of jelly beans in one section and multiply it by four.
2: I don't think this would be possible to know because you could
pick the same color for example ten times in a row. I would think that
the more jelly beans you pull out, the better the chance you would have
to pick at least two of the same number. It is possible, however, to
pick two of the same color in your first and second picks. It's hard to
determine what you will get.
3: This is kind of the same answer. It would be hard to tell
because it would be possible to pick either blue or yellow jelly beans
and not red. But like in #2, the more jelly beans you pick, the greater
the chance to pick a red. However, it is possible to pick red on the
first try. It's too hard to determine exactly which one you will pick.
4: I think there are about 300 million people in the U.S. I
estimated about 175 million have at least one piano. A piano tuner
probably tunes about 100 people's pianos. If you divide 175 million by
100, the answer is 1.75 million. So I think there are about 1.75 million
piano tuners in the world.
5: I really enjoyed the part of the lab where we tried to figure
out how the strings in the PVC pipe were "placed." I liked making our
own samples this by trial and error. It was a great feeling when I
figured it out. I thought it would be really complicated inside the
pipe, but I was completely wrong. Simpler is better.
6: When you eat or drink something really hot and it burns your
mouth, why does your mouth hurt for days?
lecture preflight 01
1: Fill the jar with water, measure how much water is in it, put
the sample beans into the jar and measure the amount of water that is
displaced. Next, multiply the amount of beans in the sample times the
amount of displaced water units it would take to fill the jar up.
2: all but one bean would be the max. amount of beans to insure 2
colors. This would mean there is only one red, one blue and the rest
yellow(or other combos).
3: All of the beans. if there is only one red bean then you would
need to pull all of the beans.
4: 15,000, I only know one tuner, but I come from a musical
family. families are average 5 people. Say 20% of families own a piano.
each tuner can tune 4 a day time 200 working days 800pianos per tuner a
year. (298,444,215/5)x.2=11937768.6. divide by 800= 14922.21, about
15000
5: what a caliper is.
6: How do plasma and lcd t.v.'s work different than tubes?
lecture preflight 01
1: I would take the handful of jelly beans, count them
individually, and then place them in the jar. Then I would measure the
how high up the jar the jelly beans go. I would also measure the height
of the total jar, then use those two numbers to determine roughly how
many jelly beans are in the jar.
2: You need to pull out at least 6 in order to get two of every
color. However, it is also possible (although not as likely) that you
could pull out every blue and every yellow jelly bean before you pick
out even one red.
3: It can be as little as one. You might get red on the first
try. On the other hand, you could potentially pull out every blue and
every yellow jelly bean before you pick out a red jelly bean.
4: Let's assume that 1 piano tuner is responsible for tuning 40
pianos each. Although pianos aren't as easy to find as, say, guitars,
they are still abound. Of the 250 million or so people in the United
States, let's say that 1 out of every 50 people play the piano. That
would leave 5 million piano players. 5 million divided by twenty would
equal 125,000 piano tuners.
5: I enjoyed learning about what made the PVC pipe lab experiment
work. I found it very fascinating to try to to emulate how that
particular experiment worked.
6: We talk about various units (SI, English). My question is: how
and why did America decide to remain stuck on English Units?
lecture preflight 01
1: I would lay some jelly beansto fill up the base of the jar
evenly. After I have a flat layer of jelly beans I would count how many
jelly beans it takes to cover up the base. Then I would take a piece of
regular tape that is cut exactly to the measurement of the height of the
jar. I would see how many jelly beand fit oin that strand of tape. Afetr
i get my number i would multiply it with the amount of jelly beans on
the base. This should give me a real good estimate of how many jelly
beans are in the jar.
2: You need to pull out four jelly beans in order to be guranteed
that you will have two that are alike. There are only three diferrent
colors so the fourth one is bound to match one of the other three.
3: The answer for this question can not really be determined
because we do not know if there is an equal amount of all three jelly
beans. For example there could be 70 blue, 15 yellow and 3 red, so it
may take longer due to probability to get atleast one red jelly bean on
the table.
4: I would say at least 10,000. This is just a random guesstimate
because i have never thought about this question.
5: I learned that measurements for things can vary depending on
how they are being measured. There is not only one way to measure
things. For example: When measuring Winnie the Pooh, we all came up with
different measurements depending on the tool we were given, although we
were given the same object to measure. I had never really thought about
this.
6: Can air be measured in a cylinder?
lecture preflight 01
1: I would count the number of jelly beans you are givern to use
in the second jar and then see how much space they take up in the second
jar. I would then multiple the number of jelly beans I used by the
number of times I thought it would to take to fill the jar with that
number of jelly beans.
2: You need to pull out four beans to be guaranteed to that you
will have at least two of the same color because there are only three
different colors so even if you pull out one of each color first, by the
fourth bean it has to be one of the three colors that has already been
pulled.
3: If the ratio of red to yellow to blue jelly beans was equal,
then you could possibly have to pull 1 more than 2/3 of the jelly beans
to ensure that you have at least one red, on the off chance the you pick
only yellow and blue first. Most likely you would have to only pull 3
beans before you would get a red one.
4: I guess that there are 2,500 piano tuners in the United
States, figuring that many towns have one or more piano tuners and each
state have a couple hundred, but there are probably areas where there
are not many piano tuners.
5: I learned that the same scientific techniques of guessing and
checking and other methods are used to solve problems of all sizes.
6: What is the rarest element on earth?
lecture preflight
01
1: line the bottom of the jar with the handful of marbles you are
given. Then turn the jar on its side and make a line of marbles on the
side of it. Multiply the two numbers together to get an estimate. OR
just count a row of marbles up and down in the already full jar and then
count how many are on the bottom of the jar and multiply those two
together.
2: You are guaranteed to have two of the same color after at the
most four tries. Even if you pull one of each color on the first three
tries, the next one you pull out will be one of those three colors.
3: It could be any number of tries. You could get it on the first
try, or you could keep pulling blue and yellow ones any number of times.
4: 10,000...its just a wild guess! I have no idea how to actually
figure this one!
5: I was so glad that I figured out that tube with the strings!
When I was first presented with it, I had no idea what to do, but
through trial and error, I was the first one to get it in my group...I
suprised myself!
6: Why can people be in the same room and one be hot, one be
cold, and one be just right? Does that really only have to do with body
mass and body fat?
lecture preflight 01
1: Weigh the jar that contains all the jelly beans. Then weigh
the empty jar. Also, weigh one jelly bean. Subtract the weight of the
empty jar from the weight of the jar containing the jelly beans. Then,
divide the resulting number with the weight of one jelly bean. That
number should be a good estimate of how many jelly beans are contained
in the first jar.
2: You cannot possiblely GUARANTEED to have two of the same
color. There may be just one of those colors in the jar; you don't know
that there are equal numbers of red, blue, and yellow jelly beans.
3: Probability suggests that after pulling out three beans, one
of these beans should be red. This is not a guarantee, just what is
probable to occur.
4: Just assuming that there are 300,000,000 people that live in
the United States, I assume a relative estimate would be around 6,000
piano tuners.
5: I learned that you can make use of even the strangest
measuring devices. (Ex. Finding some way to measure a stuffed animal
using a beaker.)
6: Why do metal objects remain more slick than the concrete when
there is ice on the sidewalks?
lecture preflight 01
1: Count the handful of jellybeans you are given and then put
them in the empty jar. Measure the volume that handful takes up as well
as the total volume. Find out how many times the bean volume must be
mulitplied to reach the total jar volume and multiply. Then multiply
that number times the original number of beans you put in and that is
your estimation.
2: You are never guaranteed to have 2 of each color until 2
colors run out. Statistics tells us that this probably would not happen,
but it could and there are no guarantees of selecting different colors
early on in the process. It may happen after pulling 12 beans or it may
take many more times. There is no way of making a guarantee until after
2 of the colors run out.
3: As I said before, it is not likely, but you may not get a red
bean until the blue and yellow are gone.
4: I would estimate that after averaging out the populations of
different states, there are about 20 piano tuners in each state, making
my guess 1000. This takes into account that there probably aren't more
than a few in states like Alaska and there may be say 50 or 60 in
Illinois.
5: That people actually try and estimate how many aliens are in
the solar system.
6: What if we lived in a vacuum?
lecture preflight 01
1: I would put enough jelly beans in the identical jar to form
one single layer of beans. I would use a ruler to measure how tall this
layer was. Then I would see how tall the jar is and multiply the height
of the layer of jelly beans by another number to equal the height of the
jar. Then I would multiply the number of jelly beans in that layer by
the number used to get the height of the jar.
2: I don't think you can ever guarantee two of the same color,
but I think that if you grab a handful, there is a great possibly that
you will get at least two of the same color.
3: The same goes for this- there is no guarantee you will pull
out at least one red bean, but with a large jar, there is a great
possibility you will grab at least one red bean when you grab a handful.
4: There are approximately 700000000 piano tuners in the United
States. There are around seven billion people in the United States. I
divided that by fifty (for the fifty states) and got 140000000. I figure
maybe ten percent of these people are piano tuners, so that would be
14000000 per state. For fifty states the answer would be 700000000.
5: The concept of dealing with things you can't necessarily see
(i.e. the string in the tube experiment.) You must sometimes experiment
to get the right answer. I'm more of a visual person so guessing without
seeing was difficult for me.
6: I think we should talk about how to properly estimate the
number of jelly beans in a jar, and the best way to get the more exact
estimate. There are many contests where you are asked to do this, and I
think it would be cool to win one.
lecture preflight 01
1: You could count the jelly beans that you are given and then
fill the empty jar with them. Judging by how much that amount of jelly
beans fills up the jar, estimate how many more handfulls it would take
to fill it completely. Then, multiply the initial number of jelly beans
by the number of handfulls to get an estimate of the total number of
jelly beans in the jar.
2: 4 is the number of jelly beans that you need to pull out until
you are GUARANTEED to have at least two of the same color. Although by
pulling out only two jelly beans it is possible that they would be the
same color, by pulling out four, it is GUARANTEED.
3: 3 is the number of beans that you need to pull out until you
are guaranteed to have at least one red bean on the desk. Again, there
is a chance that on the first or second try you will pull a red one, but
three pulls would GUARANTEE it.
4: 50,000 piano tuners - One thousand coming from each of the
fifty states.
5: That something as simple as 2 strings looped over each other
can create what seems to be a complex experiment. Often what seem to be
complex problems can be solved with a simple solution.
6: How do you measure a Winnie the Pooh stuffed animal using a
thermometer??
lecture preflight 01
1: count how many jelly beans are in your handful- put it in the
empty jar, measure how they fill the jar/how much volume they take up.
calculate the volume of the jar. Estimate based on that.
2: 4 beans is the most tries it can possibly take. If you draw a
red, blue, then yellow, not matter what color bean you pull out on the
4th try, it matches one of the other colors.
3: All of them. There only needs to be one red bean in the jar to
fit the description in problem 2, you can't be guaranteed you have a red
bean until all the beans are on the desk.
4: 1 per every 6,250 people. There are approximately 300 million
people in the United States. 48,000 piano tuners in the USA.
5: how to estimate standard error.
6: what causes dizziness?
lecture preflight 01
1: I would count the number of jelly beans I was given, and place
them into the identical jar. Then I would estimate about how full the
jar is, and how many more sets of the number of jelly beans I already
put in the jar I would need in order to fill the jar. Then I would take
the number of jelly beans in the jar and multiply it by how many sets of
those jelly beans I thought I needed to fill the jar. That would give me
my estimate of how many jelly beans are in the jar.
2: I would need to pull out four jelly beans to be guaranteed at
least two of the same color on the desk in front of me. By only pulling
out three jelly beans, I could end up with a red, a blue, and a yellow.
If I then pull out a fourth bean, however, I know that I will at least
have two of one of the colors.
3: Honestly, I don't really know how many beans I would need to
pull out until I am guaranteed to have at least one red bean on the desk
in front of me. I don't really even know how to go about solving this
problem. I would guess 25 just because I think in that many trials a red
jelly bean would have shown up.
4: Even though my family has a piano, I have never met a piano
tuner, so I dont think that there are very many out there. I am just
going to guess that there are about 20 per state, so 20 multiplied by 50
will give me 1000. I guess I would say that there are about 1000 piano
tuners in the United States.
5: I thought learning about the plastic tube with the strings was
really interesting. I had no idea that just two strings intertwined like
that would work in that way.
6: Why are snowflakes symmetrical?
lecture preflight 01
1: I would weigh the empty jar and the full jar and subract the
empty jar weight from the full jar so I only have the weight of the
jelly beans. Then, I would weigh ten jelly beans from my handful and
devide the total weight by that weight to get an estimate.
2: You would have to pull out four jelly beans because the first
three could be all different colors but the fourth would have to be one
of the same colors.
3: You would have to pull out two thirds of the jar because you
could pull out all of the yellow ones at once and then all of the blue
ones next so after all the yellow and blue are gone than you are
guaranteed a red.
4: 50,000 because that would give about one thousand per state
and that sounds pretty good.
5: I learned that you need to think through your observations
because it can be very different than it appears.
6: Why doesn't America switch to the metric system?
lecture
preflight 01
1: I would count a hand how many can fit in my hands and try to
pick up the same amount of jelly beans each time. I then would multiply
the number of handfulls by the numer of jelly beans. Therefore it wont
be tooo boring but will be close to the correct answer.
2: i think that it will depend on how many beans of each color
are in the jar because if there is more of one color than the others
then it will take longer for you to pull out two of the less same color
beans if, but it might take you a few chances to get two of the majority
of beans.
3: I think that this is the same case- if there is more red beans
then it will take less time, but if there are more red beans than the
other two then it will not take as long
4: i believe that there are 200 piano tuners in the US. I think
so because there are 50 states and some smaller states might have one or
none, but the larger states will have more within them to cover the
larger areas.
5: I enjoyed the first lab- trying to figure out how the tube
worked without looked inside of it and really having to think and try to
build it a few times to make sure it works properly.
6: is the lab we did in class with the balloons the same reason
why balloons shrink when let go into the atmosphere?
lecture
preflight 01
1: Given the handful of jelly beans, you can count them and then
place them in the empty jar. You can then observe the the jar and see
how times more of the same amount of jelly beans it would take to fill
the jar. So if I counted 10 jelly beans, and that filled up about one
inch of the jar and the jar was about 6 inches tall, then I would guess
60 jelly beans.
2: 9 times. There is a 1/3 probability of you pulling out a red,
blue, or yellow jelly bean at any time. Therefore, by the ninth time,
you should be able to have two of the same colors in front of you.
3: 3 times. Since there is a 1/3 chance, by the third time, you
should have a red in front of you.
4: 500,000. I estimated ten per city, estimated that there are
100 cities in a given state, and then 50 states.
5: That we tend to think the center of an object is usually how
things work, but given the tube experiment, that was not the case.
6: Why has it been so warm lately during the winter months and
what affect is global warming going to have in recent years?
lecture preflight 01
1: I would dump in all of the jelly beans into the jar and
estimate what fraction of the jar it fills up. I would then count those
jelly beans and multiply it by the denominator of the fraction and come
up with an estimate.
2: I could possibly have to pull out all of the jelly beans
because while there are three different colours of jelly beans, I do not
know how many of each colour there are in the jar. (For example, there
could be 300 jelly beans total, 200 blue, 99 yellow and one red.)
3: I could possibly have to pull out all of the jelly beans
because while there are three different colours of jelly beans, I do not
know how many of each colour there are in the jar. (For example, there
could be 300 jelly beans total, 200 blue, 99 yellow and one red.)
4: 1000. 50 states, 20 per state
5: I LOVE physics!! My roommate thinks the professor is HOT! Her
name is Neha Shah, nshah3
6: Are we alone in the universe...
lecture preflight 01
1: I would fill up a small dixie cup with the jelly beans. I
would then count the # of jelly beans in the cup. Next, I would fill the
jar up with jelly beans by pouring them into the jar from a dixie cup. I
would repeat this until the jar was full, keeping track of how many
times I poured jelly beans from the dixie cup.
2: Before you are GUARANTEED to have 2 of the same color, you
need to take out 5 jelly beans. If the first four are all different
colors, then the 5th one will have to be a duplicate color.
3: You would have to empty 75% of the jar before you are
guaranteed to have a red bean. By chance, you could continue randomly
pulling out all of the jelly beans that aren't red before actually
pulling a red one.
4: What is a piano tuner? Is it a person who tunes pianos, or is
it a tool that tunes pianos?
5: A calloper measures VERY accurately. (1,000th of an inch)
6: A pro wrestler once dove off a 16 foot tall platform and
crashed through a table that was about 3 feet tall. How could we measure
his velocity as he was free falling?
lecture preflight 01
1: First, I would count how many jellybeans I was given to "play
with". Then I would use a small cup that when putting the handful of
jellybeans in, it fills up all the way. I would pour the jar into the
empty identical jar and observe how much space one cup of jellybeans
takes up. Then I would estimate how many cups it would take to fill the
entire jar and multiplying by the number of jellybeans that I was given
in my original handful.
2: I would need to pull out 4 jellybeans in order to be
guaranteed to have at least two with the same color. This is because
even if I pulled out one of every color on the first three pulls, no
matter what color I pulled out on the fourth pull, it would match with
one of the jellybeans.
3: Since we do not know how many jellybeans are in the jar, nor
how many red beans, yellow beans and blue beans are in the jar, the only
guarantee of having a red bean on the table is to pull out ALL the
beans, since there is no way of telling how long it could take to pull a
red bean. For instance, there could be one red bean and 400 blue and
yellow beans which makes it very unlikely that a red bean will be pulled
soon, or there could be 1 blue and 1 yellow bean and the rest red making
it extremely likely for a red bean to be pulled.
4: There are 50 states in the US. Since the job of a piano tuner
seems like a rare job to me, I am going to assume that there is 75 piano
players per state. Although there are very small states and large states
and it is unlikely that each state has the same number of piano tuners,
the larger states like Florida and California and Texas make up for
states like Massachusettes, Rhode Island and Delaware. Therefore, I am
going to estimate that there are 3,750 piano tuners in the US because 50
times 75 is equivalent to 3,750.
5: I learned what a caliper was and how to use it to measure
objects such as POOHBEAR!
6: Why does a curve ball curve?
lecture preflight 01
1: I would take the jelly beans that were given to me and make a
flat layer at the bottom of the empty jar. I would make sure the layer
was completely flat, and fills the entire bottom of the jar, and then I
would take a ruler and measure how tall that flat layer is in the jar.
After I have written down that measurement, I would count the number of
jelly beans that I used to make the flat layer in the jar. Then, I would
take my measurement of the height of that layer and see how many
measurement heights are in the entire jar. Once I have the two
measurements (height of jar based on jelly bean height and number of
jelly beans per layer), I would multiply the two numbers together, and
that would give me an estimation to how many jelly beans are in the jar.
2: Since there are three different colors of marbles in the jar,
you would have to pull out at least four marbles to get at least two
marbles that are the same color. However, there is a chance that this
could happen on the second or third try, but for a guarantee of two
colors, you would have to pull out four marbles. For instance, you could
pull out a red, then a yellow, then a blue, but the fourth try will be
one of those three colors.
3: There is not enough information to know when you are
guaranteed to have at least one red bean on the desk in front of you.
This is because the problem does not say how many different color beans
there are, or how many beans are in the jar. For instance, there may be
500 black beans, and only one red bean in the jar, so you are guaranteed
to pull a red one after 499 tries. Also, the jar could contain only red
beans, so you would be gauranteed to pull out at red bean on the first
try.
4: If I were asked this question, I would first estimate about
how many piano tuners there are in each state. I would assume that there
are many more in certain states than others, but overall, I would guess
that there are about 500 per state. Then, I would take 500 and multiply
it by 52 states and would come up with about 26,ooo piano tuners in the
United States.
5: I learned that many times you cannot see all the parts to a
problem and you need to think creatively to be able to solve it. For
instance, the first part of the lab using the strings, you could not see
how the original product was made, so we had to test it out and come up
with some different ideas. Creativity is a great thing to teach to
little children so they can be encouraged to come up with new ideas
about things.
6: I would like to figure out how the forensic scientists on CSI
Miami can figure out what material, or what substance is on just about
anything in this world. I think it is so interesting how they can solve
all the parts to a crime by doing all the things they do in their
laboratories. For instance, they can test what drugs are in a persons
system, or figure out what type of substances are in a certain object,
and much more. I always wonder how they figured out how to do that.
lecture preflight 01
1: One way that you could use to estimate the number of jelly
beans is to use the jelly beans that you are given as your resource.
Count how many there are in the amount given to you. Then put the jelly
beans in the empty jar so see how much space that it takes up. From
there, you can estimate how many jelly beans that it would take to fill
up the entire jar by seeing how many layers of the jelly beans that it
takes to fill to the top. Then you mulitply how many layers by the
number of jelly beans in the ones given to you to get an estimation. I
actually used this method before at a jelly bean contest at a bank many
years ago and won the jar!! Since you can use any tool or equipment that
you can think of, maybe you could bring in a scale and weigh the jar.
Then weigh the empty jar and the number of jelly beans that you already
have. Plus you will need to weigh a single jelly bean. Then you could
estimate how many jelly beans are in the jar by seeing how much more
weight that you need to make the jars equivalent.
2: I think that the answer would be 4 jelly beans because even if
you pull out one of each color in the first 3 times, then the fourth
pull would be one of the 3 colors you already have. Therefore, if you
pull a red, blue, then yellow, then the fourth jelly bean will either be
red , yellow, or blue making it so that you have 2 of the same color in
front of you.
3: I am guessing that it could take more than 4 times to pull out
a red because you could pull out all blues or yellows. So I am guessing
that 6 would be a good number that you would have a red by because due
to the random selection, it is more likely than not that you will get a
red in 6 times of pulling out jelly beans.
4: I'm going to guess that there are about 5 thousand piano
tuners in the United States. I think that because there are 50 states in
the US that each state has to have about 100 or so piano tuners. Just
from my social background, I have never heard of a persons occupation to
be a piano tuner; therefore, the nuber has to be significantly low. So,
I am guessing 5,000 piano tuners. 100 for each state.
5: One interesting thing that I learned in the lab this week is
that estimation is a great way to discover how many small items occupy
the space in a large container. Surprisingly, my groups estimation was
very close to the classes average. I think that I'm going to use my
estimation skills more often.
6: How do hairs like those on the legs or in the nose consistenly
grow back after they are shaved or trimmed?
lecture preflight 01
1: I would probably fill up the bottom layer of the jar so if
covered the entire bottom. Then I would count how many layers it would
take to reach the level that the other jar was at. Then multiply the
number of jelly beans in that level by how many levels to get to the top
to make my estimation. Then eat them.
2: You need to pull out however many there are in the jar
multiplied by 2/3 plus 2, so that way if the slim probability that, all
of one color is at the bottom or that you just will not pull one of a
certain color until everything else is gone, is true, you will still be
guaranteed at least two of every bean.
3: You need to pull out however many there are in the jar
multiplied by 2/3 plus 1 so that way if the slim probability that, all
of the reds are at the bottom or that you just will not pull one until
everything else is gone, is true, you will still be guaranteed at least
one red bean.
4: I would say there are 7500 piano tuners in the US, estimating
that there are probably 150 in Illinois (or a little more, but there
will be less in smaller states, so it works out) and multiplying that by
50 states.
5: I learned that most times the simplest answer is the right
one!
6: How did the "fathers" or "grandfathers" of science know how to
start investigating and experimenting?
lecture preflight 01
1: First, I would count the jelly beans and then take the handful
of jelly beans i was given and cover the bottom of the empty jar. I
would then try and estimate how many "layers" of jellybeans would be
needed to fill the jar. I would then multiply the number of beans from
the beginning with the number of layers i estimated, and would hopefully
have a close number. or.. i would go buy the same kind of jellybeans
(since we can use any tools or equipment that we want..) and fill the
jar until i knew how many beans it took to fill it.
2: You would need to pull out four jelly beans to be guaranteed
at least two of the same color, because there are only three separate
colors, so the fourth one is guaranteed to be one of the three previous
pulled colors.
3: You would have to pull out all the beans to guarantee at least
one red bean, because it is possible to keep pulling out the same two
colors of beans without them being red until the very end. Maybe there
was only one red bean in the whole jar, and it was the very last bean to
be pulled.
4: 50- one in each state. actually, i have absolutely no idea and
can't think of a way to figure it out... sorry!
5: I learned how to do something "blindly"k and still make it
successful!
6: Has El Nino actually significantly impacted our weather
patterns? (warm->snow->warm..)
lecture preflight 01
1: If you count the handful you are given and then pour that
handful into the jar you can guess how many times you would have to put
that same amount in the jar to fill it. Also you could try to count the
"layers" of jelly beans in the filled jar and then find out how many it
would take to cover the bottom "layer" with the jelly beans you are
given.
2: The minimum amount would be 4 if you picked had already picked
one of each color for your first three drawings.
3: Possibly just one, but it could take a lot more than that.
There is not a set number because it depends on how many of the other
colors you pick out before your first red bean.
4: I would say 50,000 piano tuners because I'm going to assume
there are about 1,000 tuners/state. I have no good reasoning behind
this, but I would think that a piano tuner is a rare job.
5: You can measure a Winnie the Pooh stuffed animal in a
beaker...and it is about 3,000 mL :)
6: When you step down a stair, is it you pushing toward the step
or gravity pulling you to the step?
lecture preflight 01
1: You could count about how many jellybeans there are in a
hanful and see how many times you think that handful would be needed to
fill the jar.Than multiple the number of jelly beans in the handful by
how many times you think that would fit in the jar to get an
approximation of the total number of jelly beans in the the jar
2: You must pull out at least 4 jelly beans to be guarenteed that
there are two of the same color. If you happen to pull out three and
they are all different colors than that means no matter what color you
pick for the fourth jelly bean it will be a color that you have already
picked since there are only three different colors in the jar.
3: There is not enough information to answer this question
because I would need to know how many of each color bean there was.
Technically I could pull all of the blue and yellow jelly beans before I
pull a red one even though this would be very unlikely.
4: I would guess that there are 1000 piano tuners in the United
States. SInce there are 50 states and I am assuming that there are about
20 piano tuners per state. This allows for some states to have more and
others to have less.
5: I learned that by experimenting and guessing and checking our
group was able to come up with a decent model of the tube that we were
given in class.
6: How does a drinking straw work?
lecture preflight 01
1: First, I would count the number of jellybeans that I'm given.
Then, I'd put them into a jar and use a ruler to measure how many
mm/cm/inches they fill the jar. Whichever unit of measurement I use, I'd
then continue to use that unit and mark off the measured amount all the
way to the top of the jar. Finally, I'd multiply the number of layers I
marked off by the number of jelly beans I initially counted, and that
would be my estimate!
2: You would need to pull out 4 beans to guarantee that you have
atleast 2 of the same color. If you pull out 3 beans and you get one
red, then one blue, then one yellow, the next bean you pick will have to
be one of those 3 colors and then you will have 2 of the same color.
3: although it's very unlikely, I think you'd have to pull out
all of the colors but one because there's a chance that there is only 1
red and that you may not pick it out until your very last pick.
4: I'd guess that there are about 200 piano tuners in each state,
and since there are 50 states i'd multiply 200 by 50..so my guess is
about 10,000 piano tuners
5: two people in my class can lick their elbows.. and to estimate
the likely hood of an event happening, take the square root of the
stated number and that will provide you with an estimate of the total
difference
6: why does pop(soda) become flat
lecture preflight 01
1: You can count how many jelly beans are in that handful and
then put them in the jar. Estimate about how many times you would have
to add the same amount to fill the jar to guess how many jelly beans are
in the full jar.
2: You would have to pull out four because even if you get one of
each color the first three times, the fourth one has to be the second of
one of the colors.
3: You would have to pull out however many blue and yellow beans
together plus one, because all of the red ones could be at the bottom.
4: 25,000 piano tuners. There are 50 states and I have absolutely
no idea how many are in each state so I said 500, then multiplied those
together. It does not seem like too many piano tuners, but I have played
piano for about 14 years and I have only ever met one piano tuner that
had to travel 45 minutes to get to my house so they can't be too common.
5: I learned that scientists seriously try to figure out how many
alien colonies are in the galaxy. I had no idea people actually would do
that. Oh, and I learned how to measure a Pooh Bear with a thermometer.
6: How in the world could you possibly find out how many alien
colonies are in the galaxy?!?
lecture preflight 01
1: One obvious way is to fill the identical jar with jelly beans
and count how many jelly beans fit. Another way is to use a smaller jar
and count how many fit in there and then to count how many times you can
pour the jelly beans from the small jar into the big jar and calculate
about how many jelly beans you put into the jar through mathematics
instead of counting.
2: YOu need to pull out four jelly beans because if you have
three, they could be one of each color, but the fourth bean must be
exactly the same as another color bean that you had already pulled.
3: There is not enough information about how many jelly beans are
in the jar to figure out how many you need to pull out. Say there were 6
beans versus 600, then you would need to pull a different number to be
guaranteed at least one red bean. Also, you need to know if there are
exactly the same number of each color bean in the jar.
4: To find this, you should approximate how many piano tuners
there are for example in your town of a certain amount of people and
then figure out the "equivalent fraction" for the number of people in
the town to the number of people in the United States and then from
there you can estimate how many piano tuners are across the US.
5: I found the PVC lab experiment extremely interesting-
especially when we compared it to the work of scientists working with
extrodinarly small particles such as atoms. I never thought about the
work that they are required to do and cannot see, but yet make educated
guesses about what to do.
6: Why do apples fall from trees?
lecture preflight 01
1: I would use the handful of jelly beans that I am given and
measure them against the empty jar. I would see how many it takes for
the circumference and then i would also measure how many jelly beans
from top to bottom. Then calculate the volume of the jar and estimate
how many can fit inside. I would also use the handfull i have and put
them in the empty jar and see how full the jar gets. Then i would see
how many are in the jar and how much space they take up. I would
estimate the remaining space based off of that.
2: You would need to pull out 4 beans to get two of the same
color. For example you do three trials and pull one yellow one blue and
one red. Since there are only three colors on the 4th trial you would
have to pull out either a red blue or yellow making you have two of one
color.
3: This question is a little more ambiguous because you do not
know if the colors of beans are evenly distributed. There can only be 5
red beans, 100 yellow beans and 50 blue beans. Therefore you have a much
greater chance of pulling the yellow beans and the blue beans over the
red ones. It can take few trials or many to get a red it depends on your
luck.
4: 500. i have no idea but i guess about 10 per state.
5: There can be more then one right answer when you measure
things.
6: why is snow white?
lecture preflight 01
1: 1 - Take a handful of jelly beans, count them, put them in the
jar, estimate how many more handfuls it would take to fill the jar, and
multiply by that number, 2 - Weight 5 jelly beans and then the jar. Then
weigh the full jar, subtract the original weight of the jar. The number
you have is then divided by the weight of 5 jelly beans, and that number
is divided by 5 for the number of jelly beans in the jar.
2: 4. It is possible to pull out one of each color before a
second, but after 3 there are no new colors so the 4th must be a double.
3: It depends on how many total jelly beans, but lets say 100 of
each. To guarantee a red, 201 because there is a small chance you pull
out every blue and every yellow before any red.
4: I would guess 1,000. A few in every major country, more in the
Western countries
5: Whinnie the Pooh does not have a fever
6: Don't really have any
lecture preflight 01
1: I would try to do something like we did in lab today. My tool
would be a small cup, just big enough to fit all the jelly beans that I
was allowed to investigate/play with. Then I would estimate how many of
those cups fit into the big glass jar and multiply.
2: four
3: There is not enough information to tell.
4: I estimate that there are 500 piano tuners in the United
States. I picked this number because I decided that each state has about
100 piano tuners. States like Rhode Island and Hawaii have less than
that average but it'll make up for states like Texas and California that
probably have more than 100.
5: I learned how to find a percernt difference by dividing my
total difference (average class prediction minus my prediction) by the
average class prediction. This helps give a more accurate estimation.
6: Why does the sun make me sneeze?
lecture preflight 01
1: there are several ways to approach this problem. none of them
will give the exact answer but an estimation. i would take the handful
of jelly beans and pour them into the empty jar. i would measure how
high the jelly beans filled up the jar and then mutiply that number by
how tall the entire jar is.
2: four times at maximum. after you pull out three jelly beans of
different colors, the next jelly bean will have to be one of the colors
you already chose.
3: you are not guaranteed a red jelly bean until you have
randomly selected all of the green and blue jelly beans. without knowing
these quanities, i can not place a number on this.
4: in my town of about 30,000 there is probably two piano tuners
or one piano teacher for every 15,000 people. assuming this is constant
for the entire united states of population 300,000,000. i would estimate
there are approximately 200,000 piano tuners in the united states. this
seems reasonable to me.
5: the most intriging part of ab for me this week was the
metaphor created by the tube and string activity. this was a great
activity for children to understand how scientist use the effects to
figure out what is happening although they can not observe it
themselves.
6: how and why does gravity work?
lecture preflight 01
1: One way that I would estimate the number of jelly beans in the
big glass jar would be by first filling up a cup all the way to the top
with jelly beans. Once the cup is filled, I would then count how many
jelly beans filled the cup. I would record how many jelly beans fit in
one cup. Then I would see how many cups of jelly beans it takes to fill
up the entire jar. I would try to have the jelly beans fill up the cup
as close to the same way each time. I would count how many cups it takes
to fill up the entire jar with jelly beans. Finally I would multiply the
number of cups it takes by the number of jelly beans that fill one cup
in order to get my estimate of the number of jelly beans in the big
glass jar.
2: This question depends on the number of each of the different
colors of jelly beans there are. There is no exact number for this
answer because we do not know how many red jelly beans they are, how
many blue beans there are, and how many yellow jelly beans there are.
3: Once again, we cannot determine this from the information
because we do not know how many of each color jelly bean there is. There
can be a majority of red beans so you may only need a couple of trials.
At the same time, there could be just one red jelly bean and that could
take a lot of trials.
4: 50,230
5: I learned that sometimes things are more simple than they seem
like with the string object. We had a couple of complicated trials, but
then with our third trial we made it very simple and it worked the best.
6: How do you stop hiccups?
lecture preflight 01
1: I would probably find out the weight of the jar and the weight
of one jelly bean. Then I would weigh the jar full of jelly beans find
the mass. I would subtract the weight of the empty jar from the total
weight of the jar full of jelly beans. Finally, I would divide the
weight of the the jelly beans inside the jar by the wieght of one single
jelly bean, and this should give you a close estimate of how many beans
are in the jar.
2: You would have to pull out at least 6 because although it is
very unlikely there is a slight chance that you might get two of every
color without havign to pick out extra trials.
3: You should pull out at least three since there are three
colors. However, this does not mean you will get one red with having
pulled three beans. There is still a chance that none of the beans would
be red.
4: I would say somewhere around 450. However, in order to find
out the answer i think people can estimate the number of tuners that
there are in a couple of states and then multiplying it by 50.
5: I really liked the PVC tube experiment. I think it is a cool
way to teach students that no matter how simple things seems physics is
everywhere, even in things we would not expect.
6: A question that popped into my head was how would you estimate
the mass of a single macaroni without actually using any sort of
equipment.
lecture preflight 01
1: You could count how many jelly beans you are given (from the
handful) and then place them into the empty jar. From there, estimate
the amount of the empty jar that appears fill. For example, say the
handful of jelly beans fills up 1/4 of the jar. From there, you can
estimate that the number of jelly beans in the handful multiplied by
four would fill the jar. You can assume this because it makes sense that
the handful fills up a fourth of the jar, so four handfuls would fill up
the whole jar.
2: For this question, you must assume that there are equal
amounts of each color of jelly beans, because without that this question
does not have enough information to answer. But let's say we assume
that. First you need to find the probability of pulling one color (1/3).
Then from there, you have another 1/3 chance of pulling that same color
again. So, in order to pull the same color twice you should draw nine
jelly beans (1/3 x 1/3 = 1/9). I got this answer using basic probability
and also by assuming that there were equal amounts of each color jelly
bean in the jar.
3: Again, there is not enough information to answer this question
without assuming that there are equal amounts of each jelly bean color.
But if that is assumed, then you have a 1/3 chance of pulling a red
jelly bean, because there are three colors total.
4: There are a lot of things to take into consideration with this
question. I would think that anyone who plays the piano would have a
piano tuner. Also, you have to think about the piano tuners being sold
in stores, and sitting in factories. If I had to take a wild guess, I
would say there are about 20 million piano tuners in the world. If
anything, this number is too small considering there are about 300
million people in the United States.
5: You can measure anything by using a variety of tools. For the
third part of the lab (the mystery object), my group received the
thermometer. The first thing that came to our heads were 'how are we
going to find the length with this'? But, we were to measure for
temperature, not length. There are so many things to be measured;
length, color, temperature, weight, volume, etc. I learned to think
outside the box and really use the tools I was given.
6: Why is it that when the Earth is closest to the sun, it is
winter for us?
lecture preflight 01
1: put the jellly beans tat u have in the empty jar and use the
number of jelly beans that you have to see about how man are in the jar.
2: 5 beacause u will have all of the areas covered, with room for
error.
3: 3 beause u have to take into acount that there are an equal
amount of the 3 different jelly beans and they could be doubles of the
other jelly beans already.
4: 1 because there is only one scale that it can be tuned by and
they must all follow it to be the correct tune!
5: The tube thing was really cool, but i really liked that Mats
is so into his class. JUST WANTED TO SAY THANKS FOR THE EXPERIENCE! :)
6: ok so my mom sometimes does not pay to much attention to dates
on food, beacut there are so many differnt things now that are like
expiration dates, good by, sell by, best by, fresh until, and so on....
SO what is really the rule of thumb. I throw away everything the day on
the package... i hate being so wasteful! THANX:)
lecture preflight
01
1: You could place the jelly beans in the empty glass jar and
estimate how many more equal handfuls of jelly beans it would take to
fill up the jar. Count the number of jelly beans and then multiply this
number by the number of piles it would take to fill up the rest of the
empty jar. This should give you a rough estimate of the number of jelly
beans in the jar.
2: There is no guaranteed number because there might not be an
equal number of each color of jelly beans in the jar. For example,it is
possible that there are 100 blue jelly beans and only 5 red and yellow
jelly beans.
3: Again, there is no guaranteed number because there might not
be an equal number of each color of jelly beans in the jar. It is
possible that there is an uneven number of each color of jelly beans.
For example there may be 100 blue and 100 yellow jelly beans and only 1
red jelly bean.
4: I think there are about 250 piano tuners in the United States
because I extimated that there were about 5 piano tuners for each of the
50 states.
5: I learned that you can measure the same object (Winnie the
Pooh) with a variety of different tools.
6: How do microwaves work?
lecture preflight 01
1: I would count and then fill the empty jar with the jelly beans
provided. After observing how much the jar is filled, I could compare
the full and partially filled jar and make a guess. For example, if 50
beans filled half the jar, I would guess the whole jar contained 100
beans.
2: Six beans need to be pulled out. This is the minimum amount of
beans that could give you two beans of the same three colors. There is
no guarantee here though. To be 100% sure, every bean should be pulled
out.
3: Pulling out just one bean could be enough. However, this first
bean could be yellow or blue. To be 100% sure, every bean should be
pulled out.
4: 5,000. A piano tuner is not a very popular profession. I just
guessed about 100 tuners per state and multiplied by fifty.
5: I learned that the simpliest answer is usually correct.
6: Is the light from the stars that we see millions of years old?
lecture preflight 01
1: I would first put enough jelly beans in the identical jar so
that the bottom layer would be covered. I would then measure the height
of a jelly bean and then the height of the jar to see how many layers of
jelly beans would fit in the jar. Then I would multiply the number of
jelly beans per layer times the number of layers. This should be a
decent estimate even though some jelly beans might be standing upright
instead of laying horizontally.
2: In order for a guaranteed two jelly beans the same color, you
need to pull out four jelly beans. For example, if you first pull a
yellow, then a blue, then a red, then the next jelly bean will be one of
those three colors giving you two of the same color. This is assuming
that you will not pull out four of one color, but even in that case at
least two of the jelly beans are the same color.
3: You would have to pull out 2/3 of the jelly beans plus one.
This is assuming that you may pull out all the yellows and all the blues
first because then the last one you will pull out is red because it is
the only color left.
4: 25000, estimating around 500 per state.
5: That you can use several different objects in order to measure
(I never thought of paint strips as a way of measuring because it is
somewhat "outside of the box").
6: How does the inside of an orange form (referring to the "pulp
sacks")?
lecture preflight 01
1: I would count the sample amount of jelly beans and then place
them in the identical jar. I would then estimate how many 'servings' of
these sample beans it would take to fill the jar. I would then multiply
by this number by the number of jelly beans.
2: You would have to pull atleast 4 jelly beans (it could be as
little as two) because if you pull 4 jelly beans and there are only 3
colors there has to be AT LEAST two beans that are the same color.
Although you could pick 2, or 3 and have two of them be the same color.
But picking 4 guarantees there are at least two of the same color.
3: This is much more difficult to estimate, if there is one red
bean in the entire jar than to guarantee this you would have to pick the
entire amount of the jar (entire amount of jar - 1-number of red beans).
To guarantee you are going to pick a red bean you would have to pick at
least the amount in jar minus 1-the amount of red jelly beans.
4: Ok lets say there are 300 million people in the United States,
I would guess that for every million people (with variation in the
suburbs, urban areas, etc) there are 50 piano tuners. That would be
saying there are 50 piano tuners in Chicago (approx. population of 3
million). So 50 x 100 - I believe there are 5,000 piano tuners in the
United States.
5: I thought it was very interesting how students used the
different instruments to measure Winnie the Pooh. I don't believe I
would have thought of measuring the bears length with the beaker (saying
he is 1 1/2 beakers long) or using the thermometers for the length as
well. It was an unconventional way of using the measuring instruments.
6: (not that I'm an alcoholic in the slightest but...) Why don't
vodka and other hard alcohols freeze?
lecture preflight 01
1: One way to estimate the number of jelly beans in the jar would
be to take the empty jar and put the handful of jelly beans in it. Then,
you could use a marker and draw a line on the outside of the jar to show
how high the jelly beans go. Then, you could try to estimate how many
similar layers you can make and multiply the exact number there is in a
handful of jelly beans times the number of layers. You could also
compute the volume of the jar and find the volume of a jelly bean. By
dividing the volume of the jar by the volume of a jelly bean, you can
find out about how many jelly beans would fit in the jar.
2: You need to pull out 4 jelly beans to guarantee to have at
least two of the same color. There is a chance that after you pull out 2
jelly beans that they are the same color. There is a bigger chance that
after you pull 3 times that you have two fo the same same. But in order
to guarantee two of the same color you must pull four times because
there is a chance with the first three pulls you got one of each color,
but by the fourth pull you have to get a double of a color.
3: You would have to pull out every jelly bean to guarantee to
have at least one red bean. You may pull a red bean out on your very
first try, but if there are very few red beans, it could take a lot more
pulls to get one.
4: I would guess that there is about 12,500 piano tuners in the
United States. I would guess that each state has about 250 piano tuners,
some will have more, some will have less. I multiplied 50 states by 250
tuners per states and think there is about 12,500 piano tuners in the
United States.
5: One interesting thing I learned in lab this week was the trick
with the tube and the strings. This is very similar to the trick
magicians use with the tube and the poms on the strings. I never knew
how it worked until today, and now I feel kind of ridiculous for never
knowing how it worked.
6: Someone was telling me that if you sneeze with your eyes open,
your eyes would pop out of your skull, is this true?
lecture
preflight 01
1: You can count the nuber of jelly beans you are given, then put
them into the identical jar and see how much they fill up. From there,
you can estimate about how many more jelly beans you will need from that
initial amount.
2: There is no correct answer to this question, becuase it is all
chance what color of jelly bean you pull out. But, I would say that if
you pull out ten jelly beans, you are guaranteed to have two of the same
color. Because the odds of you pulling out more than nine of two colors
and only one of the third is very low.
3: In order to just have one red jelly bean, since there are only
three colors, if you pulled out six jelly beans, I think you would be
guaranteed to have at least one red one. You could be lucky and the
first one you pull out could be red, but there is no skill involved.
There is a high likelihood that a red will come out in the first six
because there are only three colors.
4: Well, I have no idea what the answer may be, but if you try to
think how many pianos there are in the United States, that may help. So,
I'm guessing there are about 1 million pianos in the US, so there are
probably around 500,000 piano tuners.
5: I learned that there are many ways to measure an object with
just one type of tool. For instance, my group was given a thermometer
and we could measure temperature as well as length to some degree.
6: What does the white color on the tips of your nails mean?
lecture preflight 01
1: I would try to estimate the number of jelly beans in the jar
by first filling a small cup with a specific number of jelly beans that
I counted out. I would then continue to dump cup-fulls of jelly beans
into the identical jar until it looked about as full as the original. I
would multiply the number of jelly beans I had to begin with in the
small cup by the number of times I dumped a new cup-full into the jar. I
believe this would be both a less time consuming and accurate way to
estimate the number of jelly beans in the candy store's jar.
2: Assuming that there is approximately a third of each color in
the jar, ideally, one in every three jelly beans should yield a
different color. In order to pull two of the same color, you would have
pull out at least four jelly beans.
3: Assuming the same conditions as the previous question, you
would need to pull out at least three jelly beans to be guaranteed to
have at least one red bean on the desk.
4: I would guess that there are about 5,000 piano tuners in the
United States. I estimated that about 1 in 25 houses have a piano and
that one piano tuner surves about 200 houses. I assumed there are about
a billion people in the U.S., and after doing the math, I figured about
5,000 piano tuners are in the U.S.
5: There are many ways to measure one item (ie Winnie the Pooh),
and there are also many ways a measuring device can be used to measure
something.
6: What causes a rainbow?