There are lots of ways that fish in an aquarium can wow us. They could be huge, or spiky, or have a really weird shape. But often fish amaze us just by being incredibly colorful, and one of the most beautiful is the mandarinfish. As you see here, it’s blue with wild orange and white patterns, spots of purple and green, and frilly edges to its fins and tail. Unfortunately, the mandarinfish is as smelly as it is good-looking: to keep other fish from eating it, it covers itself in a thick mucous (like the goop in your nose) that tastes and smells terrible. As pretty as this fish might look, it won’t be a tasty snack.
Wee ones: If a mandarinfish sports blue, orange, white, green and purple, how many colors does it have? (You may count white as a “color” here.)
Little kids: The tiny mandarinfish is only a couple of inches long. If you have 3 mandarinfish each 2 inches long, how long a chain do they make if they swim end to end? Bonus: If they leave 1 inch of space between one’s tail and the other’s nose, now how long a chain is it?
Big kids: Mandarinfish can live in a saltwater aquarium. If your aquarium has 8 mandarinfish, twice as many clownfish, and 10 tangs, how many fish do you have? Bonus: If you put 5 mandarinfish in a little aquarium that’s 10 inches long and 6 inches wide, how deep does the water need to be to have at least 120 cubic inches of water for each fish? (Hint if needed: The volume of a box, i.e. the space inside it, in cubic inches is length times width times height.)
The sky’s the limit: Suppose an unknowing big fish is chasing a bad-tasting mandarinfish. If the mandarinfish starts 2 feet ahead of it, and darts to safety at 10 inches per second to hide in the coral 5 feet ahead, but the bigger fish swims 18 inches per second, will the mandarinfish make it to the hiding spot in time – and if not, where does the big fish catch up? (Assume the predator, mandarinfish, and coral are all in one straight line.)
Wee ones: 5 colors.
Little kids: 6 inches. Bonus: 8 inches, since they need just 2 gaps: one between the 1st and 2nd fish and another between the 2nd and 3rd.
Big kids: 34 fish (8+16+10). Bonus: 10 inches deep, since you need 600 cubic inches total.
The sky’s the limit: To get to safety, the mandarinfish needs to swim 60 inches, which at 10 inches per second will take 6 seconds. In 6 seconds the big fish could swim 108 inches, which covers the 2 extra feet (24 inches) plus the 5 feet (60) plus more, so he’s going to catch him. We can show where each one will be at any time t, and set those distances equal:
24+10t = 18t
24 = 8t
t = 3
So the big fish will catch him 3 seconds from the start, and will have swum 54 inches, which is 30 inches past the mandarinfish’s starting point…and in 3 seconds the mandarinfish will in fact have swum 30 inches.