Math Glimpse: Kit Canright, MWS Math Tutor

Noticing the relationship between numbers is key to both simplifying basic arithmetic and delving into deeper math in the upper grades and beyond. In tutoring, we pay attention to facts that neighbor facts they already know: for 3+4, think about 3+3 or for 7+9, think about 7+10. Once they notice the relationship of the numbers, the problem usually becomes easy; they just may not have noticed that relationship before. Similarly, when working on multiplication tables, looking for patterns in the tables is key. Once the pattern is discovered, songs and other mnemonics can help cement the table in memory, but it’s recognizing the pattern that transforms multiplication from a hundred random facts to something both understandable and with an “Oh!” factor.

In the 7 th grade, we’ve begun working on ratios and proportions while also reviewing fractions and percent. The heart of all these topics is relationship. Solving these problems can involve using a process, methodically going through the memorized steps – sometimes that’s the only way to solve them. But often they can be solved more easily by observing the relationship. 7/21 = 5/x becomes easy once you notice that the bottom number in the first fraction is 3 times the top number. As with any puzzle, it’s looking for the key element that makes things fall into place. I once asked high school math and science teachers what they wished incoming students knew better. Their answer was ratios. The value of understanding numeric relationships, though, goes beyond high school chemistry class.

It helps when evaluating the reasoning put forward by political leaders, when deciding how much bleach is needed in your odd-sized container, and when altering a recipe because you only have two eggs and the store near you is closed for the night. Whether it’s that the relationship between the circumference and diameter of a hula hoop is the same as that of the equator (π) or that the Fibonacci sequence can be found in seashells and sunflowers, there is wonder as well as usefulness in number relationships.