| Solution
to prior Problem of the Week
For the week of October 24, 2002
The Problem
I unplug my computer
whenever there is a thunderstorm in the area. The thunder is not dangerous,
but the accompanying lightning can cause a power surge that is dangerous
to electrical equipment.
Light travels faster
than sound so we always see the lightning bolt before we hear the accompanying
thunder. When I see lightning, I start to count the seconds until I hear
the thunder. It takes five seconds for the sound of thunder to travel
one mile. How far away is the lightning if thirty-two seconds pass between
the flash of the lightning bolt and the sound of the thunder?
*CHALLENGE QUESTIONS*
1. Using the information from above, determine how far sound travels in
feet per second.
2. Another interesting fact about storms is that lightening strikes somewhere
on the surface of the earth about 100 times every second. How many times
would this be:
a. Per minute?
b. Per hour?
c. Per day?
d. Per week?
e. Per month?
f. Per year?
The
Solution
Although there were
many correct answers, there were fewer explanations that really clearly
described how and why students solved the task as they did. That is, the
criteria we are using to determine really strong explanations involve
determining if a classmate who was confused could read the explanation
and then understand why, in this case, it made sense to divide 32 by 5.
For example, both Ragan and Rachel explained that they counted by fives
because every 5 seconds represents another mile that the sound of thunder
traveled.
The second part of
the problem involved figuring out what to do with the remainder of 2.
Recall that when you divide 32 by 5 you get a remainder of 2. Jordon,
Amy, and Brass all explained how they got a fraction of 2/5 (or a decimal
of .4) very nicely.
Highlighted solutions
to original problem
Student's Name: Brass
Answer(or question to Mentor): The answer is 6 2/5 miles. The way I thought
about it was since I knew that 5 seconds from lightning to thunder means
that the storm is one mile away. So I divided 5 into 32 gettin 6 remainder
2 which is 6 and 2/5. The 2/5 means that it is 2/5 of another mile away.
And the final answer is 6 2/5 miles.
Student's Name: Rachel
Answer(or question to Mentor): Hey This is Rachel and this is my answer
to the problem. 6.4 miles or 6 miles and 2/5 of a mile. I got this because
if you count by fives till you get to 30 and count how many fives there
are you get the answer. I did this because it takes five seconds to go
one mile. There were six fives so that would mean six miles. Then you
have two seconds left and that is two seconds out of five seconds so that
would 2/5. ok well I gtg bye.
Student's Name: Ragon
Hi Angelica! My name is Ragon. I am a eleven year old girl that is ready
to learn. Well, I think that the answer is 6 2/5 miles. How did I get
this answer, I said since there is one lightning bolt and five seconds,
I counted by fives, and you would have two left over. And that would be
2/5 of a mile. -Ragon-
Student's Name: Amy
Answer(or question to Mentor): Hi, here is the answer I got: 1)6.4 miles
away. I know this because it takes 5 seconds for thunder to travel 1 mile.
So 30=6 miles with 2 left over. The 2 converts to 2/5, which is 4/10,
which as a decimal is .4. So 6+.4=6.4. Meaning 6.4 is your answer.
Student's Name: Jordan
Answer(or question to Mentor): Dear Gretchen, Lighting is about 6 2/5
miles away. You would divide five into 32 because every five seconds is
a mile. She counted to thirty-two so there for you would divide five in
to thirty-two and it goes in six times. Six times five is thirty. That
leaves two left over so you would make that a fraction equaling two fifths.
So your answer would be 6 and 2/5. So I thing the answer is 6 2/5. ~Jordan~
Solutions to the
Challenge Problems
The answers to the
challenge problems were:
1. The answer is:
sound travels 1,056 feet per second.
Explanation: From the original problem, we know that sound travels at
1 mile per 5 seconds. So, the question asks for how many feet per 1 second.
Well, we can find out that there are 5,280 feet in one mile, so we can
say that sound travels 5,280 feet in 5 seconds. Well, we want to know
how far it travels in 1 second, which is 1/5 of the 5 seconds we have
now. So, 1/5 of 5,280 ft is 1,056 ft. So, sound travels at a rate of 1,056
feet per second.
2. This question
has many parts:
a) Answer is 6,000
strikes per minute. This is because there are 100 strikes per second
and there are 60 seconds in a minute. So, 60 sets of 100 = 6,000 strikes
per minute.
b) Answer is 360,000 strikers per hour. This is because there are 6,000
strikes each minute, and 60 minutes in an hour. So, there are 60 sets
of 6,000 strikes in an hour, or 360,000 strikes per hour.
c) Answer is 8,640,000 strikes per day. This is because there are 360,000
strikes per hour, and 24 hours in a day. So, there are 24 sets of 360,000
or 360,000*24 = 8,640,000 strikes per day.
d) Answer is 60,480,000 strikes per week. This is because there are
8,640,000 strikes per day * 7 days per week.
e) This one had multiple answers (any of which would have sufficed as
long as you explained how many days you used to define a month). For
each one, you multiply the number of hours in a day * the number of
days in the month as follows:
A month with 28
days has: 241,920,000 strikes/month
A month with 29 days has: 250,560,000 strikes/month
A month with 30 days has: 259,200,000 strikes/month
A month with 31 days has: 267,840,000 strikes/month
f) Answer is 3,153,600,000
strikes per year. This was obtained by multiplying the number of strikes
per day (8,640,000) times the number of days in a year (365, unless
it is a leap year!).
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