Goldfish and Koi - What's the Difference?

There’s something fishy about this week’s word problem—jump on in and give it a try (the water’s fine)!

Ben has a goldfish that is 3¼ inches long. Ruby has a goldfish that is 3.3 inches long. Who has the longer goldfish?

Check waaay below for the solution!

Fun Fact: The world's longest goldfish measures 18.7 inches from snout to tail-fin end. That’s almost as long as the average newborn baby!

My father was an architect and civil engineer. He loved ponds and pools. I lived in two homes that he designed with indoor sunken fish ponds. Not knowing anything about fishes, we experimented by stocking our first pond with inexpensive guppies, then added red and black sword tails, and tetris. They were a colorful sight to behold, a school of swirling color that swarmed and collected during feeding time. With that flush of success, we started buying more fish to stock our eco system. Once we bought koi carp. Now, they were a truely impressive sight to behold. The carp cruised gracefully around our pond like shark. We quickly realized they were sharks! Our population of colorful guppies plummetted drastically as the carp ate through their population! Back to the store they went!

We settled on fantail goldfish. Viewed from the top, the goldfish were big enough to be clearly visible and their wide fins were gorgeous. Finally, we had fish that were proportional to our pond size. Later I learned that goldfish are mutated carp, selected over generations for bizarre mutations that would normally doom a fish in the wild. So, our pond continued to suffer some occasional small fish loss due to the severely handicapped carp. Our pond was a lesson in Darwinism, the faster smaller fish surviving by keeping away from the slow lumbering giants! Feeding time was now in separated areas of the pond, the clear open spaces for the giants and hiding in the weeds were the smaller fishes.

Fractions and decimals are like dissimilar fish, but they are actually just representations, like koi and goldfish, of the same fish. Understanding numeric representation can be a slippery challenge to our students. Some try their hardest to just "know" decimals and avoid fractions, especially those exposed to calculators too early. They'll continually convert all fractional arithmetic into decimal forms. We patiently teach both forms as appropriate to a problem. In fact, we do need our students to become comfortable with fractions because it's fundamental to algebraic expressions.

This is a perfect problem for fluently moving between representations. The Mathnasium method is particularly effective because we teach each student individually. We're able to hold a two-way conversation where we discuss and verbalize the questions to make it concrete verbs and nouns rather than abstract symbols on a paper, or a droning one-way narration from classroom teacher to student. In this particular case of "Ben has a goldfish that is 3¼ inches long," we'll ask the student to verbalize 3¼ as "three and one-quarter." Then we might prod, "remember how many cents a quarter of a dollar is?" to bring up the relationship of quarter = 0.25 = 25-hundredth = 25/100. We may even draw a quartered-dollar bill to reinforce the concept further. Hence, Ben has a goldfish that is 3¼ = three and one-quarter = 3.25 inches. Ruby has a goldfish that is 3.3 inches long and this should clearly be the longer fish.

Going a little further 3.25 = three and 25-hundredth inches long; and 3.3 = three and 3-tenth = three and 30-hundredth inches long. And now that we have the same noun—hundredth—for the fractional part, it easy to see that Ruby has the longer goldfish by 5-hundredth of an inch. We feel that has a deeper meaning than a difference of point-zero-five inches!

Contact:
Ruby Yao and Benedict Zoe, Mathnasium of Fort Lee
201-969-6284 (WOW-MATH), fortlee@mathnasium.com
246 Main St. #A
Fort Lee, NJ 07024

Happily serving communities of Cliffside Park, Edgewater, Fort Lee, Leonia, Palisades Park, North Bergen, West New York, and Fairview.