Problem of the Week: Dinosaur Edition!

Have your Mathlete give these paleo-problems a try!

Lower Elementary:

Question: A baby T-Rex weighs 3 pounds when it hatches. After a week, it weighs 6 pounds. At two weeks, it weighs 12 pounds. At three weeks, it weighs 24 pounds. If the pattern continues, how much will the baby T-Rex weigh when it is 5 weeks old?

 Upper Elementary:

Question: A paleontologist found five triceratops nests. The first nest had 12 eggs. The second nest had 14 eggs. The third nest had 12 eggs. The fourth nest had 16 eggs. The fifth nest had 21 eggs. What is the average number of eggs in a triceratops nest?

 Middle School:

Question: A pterodactyl’s wingspan is 30 feet. Its height is 6 feet. If a twelve-year-old kid is 5 feet tall, then how wide would their “wingspan” (the length from fingertip to fingertip with arms spread out) be if it were proportional to that of a pterodactyl?

 Algebra and Up:

Question: The Pachycephalosaurus was a dome-headed dinosaur that fought by running into its competitors head-first like a bighorn sheep. If two pachycephalosaurs run toward each other, each traveling 30 miles per hour, from a quarter mile apart, then how long will it take for them to collide?

(Solutions Below)

 Lower Elementary:

Question: A baby T-Rex weighs 3 pounds when it hatches. After a week, it weighs 6 pounds. At two weeks, it weighs 12 pounds. At three weeks, it weighs 24 pounds. If the pattern continues, how much will the baby T-Rex weigh when it is 5 weeks old?

Answer:  96 pounds

Solution:  The T-Rex doubles in weight every week---6 pounds is 3 doubled, 12 pounds is 6 doubled, 24 pounds is 12 doubled. If the pattern continues, then at 4 weeks, the T-Rex will weigh 48 pounds because 48 is 24 doubled. At five weeks, the T-Rex will weigh 96 pounds because 96 is 48 doubled.

 Upper Elementary:

Question: A paleontologist found five triceratops nests. The first nest had 12 eggs. The second nest had 14 eggs. The third nest had 12 eggs. The fourth nest had 16 eggs. The fifth nest had 21 eggs. What is the average number of eggs in a triceratops nest?

Answer:  15 eggs

Solution:  To find the average, we add up all the eggs and then divide by the number of nests. 12 + 14 + 12 + 16 + 21 = 75 eggs. 75 eggs ÷ 5 nests = 15 eggs per nest.

 Middle School:

Question: A pterodactyl’s wingspan is 30 feet. Its height is 6 feet. If a twelve-year-old kid is 5 feet tall, then how wide would their “wingspan” (the length from fingertip to fingertip with arms spread out) be if it were proportional to that of a pterodactyl?

Answer:  25 feet

Solution:  The pteradactyl’s wingspan is 5 times its height because 30 ÷ 6 = 5. So, to find out how wide the kid’s wingspan would be if it were proportional to the pterodactyl’s, we multiply the kid’s height by 5: 5 × 5 = 25 feet.

 Algebra and Up:

Question: The Pachycephalosaurus was a dome-headed dinosaur that fought by running into its competitors head-first like a bighorn sheep. If two pachycephalosaurs run toward each other, each traveling 30 miles per hour, from a quarter mile apart, then how long will it take for them to collide?

Answer:  15 seconds

Solution:  Since both pachycephalosaurs run 30 miles per hour, they cover a total of 60 miles per hour when they run at each other. To find the amount of time, we solve 60 mph × t hours = ¹/₄ mile and find that t = ¹/₂₄₀ hour. That’s equal to a quarter of a minute, or 15 seconds.