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.