Problem of the Week September 26th

Lower Elementary:

Question: A red-eyed tree frog has 4 toes on each front foot and 5 toes on each back foot. How many toes does a red-eyed tree frog have?

Upper Elementary:

Question: Luke says he saw a piranha that was 4¾ inches long. Howard says he saw a piranha that was 4.7 inches long. Who saw the bigger piranha?

Middle School:

Question: A kapok tree is 200 feet tall. A vine growing up the trunk of the tree overtakes 10% of the tree’s remaining height each week. How high does the vine reach after 3 weeks?

Algebra and Up:

Question: A biologist is monitoring a flock of toucans. The biologist determines that the number of toucans in the flock can be estimated using the function f(n) = 22 + 3n, wherein n is the number of toucan nests that the biologist counts in the flock’s territory. If the biologist counts 5 nests, what is the estimated number of toucans?

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Lower Elementary Answer:

Answer: 18 toes

Solution: The frog has 4 + 4 = 8 front toes and 5 + 5 = 10 back toes. That makes a total of 8 + 10 = 18 toes.

Upper Elementary Answer:

Answer: Luke

Solution: One way to solve this problem is to write both measurements as decimals. Since ¼ is equal to 0.25, ¾ must be equal to 0.25 + 0.25 + 0.25 = 0.75. That means that a piranha that is 4¾ inches long is 4.75 inches long. Since 4.75 is greater than 4.7, Luke saw the bigger piranha.

Middle School Answer:

Answer: 54.2 feet

Solution: On the first week, the vine grows 10% of 200 = 20 feet, leaving 200 – 20 = 180 feet untouched. On the second week, it grows 10% of 180 = 18 feet, leaving 162 feet untouched. On the third week, it grows 10% of 162 = 16.2 feet. So, in total, the vine has grown 20 + 18 + 16.2 = 54.2 feet up the tree.

Algebra and Up Answer:

Answer: 37 toucans

Solution: If the biologist counts 5 nests, then n = 5. So, f(5) = 22 + 3(5). That’s 22 + 15 = 37. That means that f(5) = 37 toucans