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Remeber
September 11
Let
It Begin with ONE
(n05)
Subject
Math
Objective
To
use math in understanding the scope of the 9/11
tragedy and how the world could be a better place
if ONE person does a good thing for two people
and then asks each one to do one good thing for
two OTHER people
Time
Needed
One
hour
Materials
Paper (large newsprint if possible), pens, calculator,
lyrics to "Let There Be Peace on Earth",
and access to a computer spreadsheet (if possible)
Lesson
Introduction:
Somewhere in our education, we all learned the
words to the song "Let There Be Peace on
Earth". Today would be a great day to haul
that song out of our memories and share it with
the students - many of them have already learned
it! Now think about the possibilities - if ONE
person does one good thing for two people, and
asks each one to do one good thing for two OTHER
people, how many steps would it take to do one
good thing for everyone on Earth (projected population
9/1/02 = 6,250,000,000 people).
Procedure:
We'll set a rule that "once you've had the
one good thing done for you, you are only allowed
to 'pay it forward', no one gets 'seconds'!"
Students may want to argue this point but it's
your game - set your own rules!!!
Predict
Answers
(estimation)
Experiment: Since this is a BIG problem, discuss
problem-solving strategies that might be used.
Remind students they will need to report their
work to other teams so their THINKING must be
shown! Let the students work in pairs to begin
their calculations.
Discuss:
Stop them after a few minutes to discuss their
findings so far - most students will decide that
"make a table/chart" process is most
appropriate.
Data Collection: Have them reorganize their data
into chart format, if they haven't.
step 0 = 1 person (performs good thing for two
people)
step 1 = 2 people (who then perform good thing
for two people each)
step 2 = 4 people etc.
Computation:
Students will balk at multiplying by 2 as the
number value increases. I like to have them sneak
in some multiplication practice so I would have
them multiply up to step 13 (my game - my rules!),
then allow them to use their calculators, but
they MUST record the data in their charts.
They will discover they must continue to the 33rd
step to have the value exceed the 6.25 billion
mark!! This is the point where you can introduce
the terms "base" and "exponent".
Each step is the exponent. The base number we
are using is 2. The exponent reflects how many
times the base 2 is used as a factor. Students
are often confused about the "2 to the zero
power". I remind them that numbers follow
patterns and ask if they can see the pattern in
the table (first column - number increases by
one as you proceed down the column, therefore,
the number decreases by one as you proceed up
the column.)
Connect
to Technology: This is an excellent time to introduce
them to the value of using simple spreadsheet
formulae to do the same computations in much less
time! (Two columns, the first begin with 0 and
add one to the value with each cell down; the
second, begin with 1 and multiply by 2 with each
cell down. Insert the formulae for the two above
steps and "drag" down through the cells
- be sure you have set your numbers to view with
separating commas or you will find yourself also
doing a lesson on scientific notation!! - Save
that for another day.)
Analyze:
Between what two "steps" on the spreadsheet/table
does the projected population fall (ordering of
numbers)?
Extension:
What if you did one good thing for FOUR people?
How many steps would it take then to reach all
the people? What if you did FIVE? TEN? This could
be a homework assignment or an extension for another
day to look at the power of exponents as the value
of the base number increases.
Enhancements
- Enrich
the environment with additional music. Link
to Suggested
Music.
Source:
Karen Maitland, McKelvie Middle School. Bedford,
New Hampshire 03301
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