# Resources for Unit Conversions

I am working with a college student who was placed into a pre-college level math class. She's in a unit that covers a lot of unit conversions (simple ones, like 5 km = ___ miles or 3 yards = ___ cm ). She says she's confused by what the teacher showed her in class so I spent time working with her to reinforce the method they learned in class (the "Train Track Method" is what she calls it). I like the idea because to me it makes a lot of sense. Organizing the conversion this way helps the students focus on cancelling the units first, before filling in the numbers. For example, for 3 yards, I want to cancel the yards, so I know I'd multiply by feet/yards to get yards on the bottom of the fraction to cancel. Then to get to inches I'd multiply by inches/feet, then finally cm/inches. Then once all the units are cancelling out properly, then I can worry about filling in the numbers and handling them.

Well, after two different 1-hour long meetings with her, she still isn't getting it. She says it's totally foreign to her. Every other student I have shown this idea to or practiced it with was able to get it and do very well on this class's unit conversion quiz. But she is still stumped. She emailed me asking me for other helpful resources for these kind of problems, but everything I Google seems to be a re-hashing of the same method, or the exact same explanations I was already saying to her.

What are some good resources (handouts, webpages, videos, etc.) to help a student that is really struggling with basic conversions?

• $1$ yard is $3$ feet, but to convert from yards to feet, the relation $y = 3f$ is incorrect. For example, substituting $f = 3$ gives 9 yards = 3 feet. The correct relation is actually $y = f/3$. Oct 21 '20 at 23:14
• @TobyMak I see what you are saying: she shortens the textual expression "1 yard is equal to 3 feet" to "1y = 3f", where "y" and "f" are dimensions, and confuse it with algebraic expression "1y = 3f" where "y" and "f" are values respectively in yards and feet. Oct 22 '20 at 18:05
• @TobyMak ah ok, I didn't understand what you were referring to until RustyCore rephrased. I don't think that's the girl's mistake, since she isn't trying to manipulate things algebraically with variables. This is a very low level math class, they haven't started to use variables yet. Oct 22 '20 at 19:01
• The videos that seem like exactly the same explanation to you might seem different to her. It is worth pointing her to a few good ones to see if any of it helps. Oct 22 '20 at 19:16
• The concept of units is powerful. Unfortunately in the U.S. this concept is not introduced early enough. Worse, it's actively abused at the lower levels. My youngest grandchild had a word/picture problem that showed "3 violins + 1 trombone = ?" My answer was A Bad Quartet . Dec 13 '20 at 17:28