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Math
Connections
Students may complete rain forest related
math puzzlers posed by Otis Reedy, one of the fictitious students going on
the adventure, by clicking on the Otis Reedy's Rain Forest Puzzlers
icon at the bottom of an Adventure Page. These puzzlers generally require
multiplication and division, but also may involve the following mathematical
skills: measurement, researching statistics, problem solving, formulating
solution strategies, rounding up and determining percentages.
Some of the puzzlers require one or two calculations while others are fairly
complex. Encourage teamwork for the more complex puzzlers.
Note: We recommend that you review the puzzlers before having
your students complete them, determining which meet your curricular objectives
and will fit in the time frame in which you are working. (Some may be too
advanced for your students or require more time than you might have available.
If so, simply skip them.) Go to the Adventure
Guide for Teachers for quick links
to the puzzlers for review.
Solutions to Otis Reedy's
Rain Forest Puzzlers
1.
The Tree Puzzler:
A. There are 5,280 feet in a mile. So, at 80'
per tree, it would take 66 trees to reach one mile. To reach 240,000 miles
(average distance to the moon) it would take 66 X 240,000, or 15,840,000 trees.
B. 15,840,000 (trees) divided by 500 (trees per acre) = 31,680 acres. C. 31,680
rounds up to 32,000. 32,000/40,000,000 is the fraction representing the number
of acres of trees cut down to reach the moon over the total number of acres
of rain forest trees cut down in one year, which equals 0.0008, which is 0.08%
(less than one tenth of one percent). D. Since it would take 32,000 acres
of trees (rounded up to nearest thousand) to reach the moon, it would take
64,000 acres of trees to travel back and forth. 64,000 goes into 40,000,000
625 times. So we could travel back and forth to the moon 625 times by stacking
all the trees cut down in one year on top of each other. (Note: there are
several ways to come to the same answer. For example, using the percentage:
0.08 X 2 = 0.16 >>> 100/0.16 = 625. Or, the long way: 40 million
(rain forest acres destroyed in one year) X 500 (large trees per acre) X 80
feet (average length of tree) divided by 5280 feet (one mile) divided by 240,000
miles (average distance to moon) divided by 2 (back and forth) = 631.31313131.
Note the difference since no rounding off is used in this solution - which
actually makes it a more accurate figure given the variables.) E. 625 X 2
(back and forth) = 1250; 1250 X 240,000 (miles to the moon) = 300,000,000
total miles. Or: 40,000,000 acres X 500 trees = 20,000,000,000 X 80 (feet
per tree) = 1,600,000,000 divided by 5280 (feet in a mile) = 303,030,303.03
miles. (Again, the difference is the result of not rounding off in this method.)
F. We could travel to Mars, take what's left, travel to Venus, take what's
left, travel to Mercury, take what's left, travel to the sun, and still
have enough trees left over to build thousands of houses.
2.
The Armadillo Puzzler:
131.25 pounds = 2100 ounces (X16) divided by 14
= 150
3.
The Leafcutter Ant Puzzler:
A. Find out the total number of students that attend your school. Divide this
number by 20. The result is the number of boys that would be in your school
if your school had the same ratio of boys to girls as leafcutter ant colonies.
Subtract the result from the total number of students at your school to find
out how many girls your school would have. B. Including antennae (2), pincers
(2), body segments (3), and legs (6), an ant has a total of 13 body parts.
So, multiply the total number of students in your school by 13 to get the
answer. C. i) Divide the total number of students at your school into 5,000,000
for the answer.ii) Divide 5,000,000 by 20 for the answer (250,000).
4.
The Tree Frog Puzzler:
A. 3 peeps X three frogs is 9 peeps/second X 60 seconds is 540 peeps/minute
X 60 is 32,400 peeps/hour X 24 is 777,600 peeps/day. B. 777,600 + 177 = 777,777
- a number made of all the same digit.
5.
The Sloth Puzzler:
A. 3000 (miles) divided by 100 (m.p.h) = 30 hours
or one day and six hours. B. If sloths can travel 1/3 mile in one hour, they
can travel one mile in three hours. 3000 (miles) X 3 (hours per mile) = 9000
hours. (Or 1/3 goes into 3000, 9000 times; or 3000 divided by 1/3 = 9000.)
9000 divided by 24 (hours in one day) = 375 days which is one year and 10
days.
6.
The Toucan Puzzler:
The best way to solve this problem is to
line your students up and have them pass the fruit (or something more accessible).
Better yet, break your class up into groups of six and challenge the groups
to come up with the solutions. The answers are: Even numbers , except for
ten [2,4,6 & 8] would result in the toucan in position #3
getting 4 of the ten pieces of fruit, or 40% - not bad! Odd numbers except
for 5 [1,3,7 & 9] would result in the toucan in position #3
getting 2 of the ten pieces of fruit, or 20% - not quite as good but more
equitable. Numbers 5 and 10 would shut toucan #3 out completely - not
good!
7.
The Beetle Puzzler:
20% = 1/5. Therefore: 320,000/x = 1/5.
Therefore: x = (320,000)5. Or: x = 1,600,000 known species.
8.
The Harpy Eagle Puzzler:
First Pass: Ten people pass the message to
ten others. (10 X 1 = 10); Second Pass: Those ten each pass the message to
ten more (10 X 10 = 100), for a total of 100 more people; Third Pass: Those
100 people each pass the message to ten more (100 X 10 = 1000), for a total
of 1000 more people; Fourth Pass: 1000 X 10 = 10,000; Fifth Pass: 10,000 X
10 = 100,000; Sixth Pass: 100,000 X 10 = 1,000,000; Seventh Pass: 1,000,000
X 10 = 10,000,000; Eighth Pass: 10,000,000 X 10 = 100,000,000; Ninth Pass:
100,000,000 X 10 = 1,000,000,000; Tenth Pass: 1,000,000,000 X 10 = 10,000,000,000
(ten billion). Since the world population is roughly six billion, everyone
in the world would have heard the message after the tenth pass. Note: Problem
illustrates usefulness of base 10 system: when multiplying a number by ten,
can add one 0.
