What’s an example of some feedback that you think a teacher might consider giving, but is not the ideal response?

What feedback would you give this student on the page?

If you had five minutes to work with this kid one-on-one, what would you talk about?

## 4 replies on “Centimeters to Meters”

A non-ideal response would be to either suggest that the student is a blithering idiot or to simply correct the error.

I would suggest asking the student what “centi-” means. If s/he doesn’t know, that might suffice to explain the mistake. Because clearly the student grasps that something here is 100 times greater than something else, but appears not to know (or at least not to be sure of) which unit is 100 times greater than the other. So the issue may be more linguistic than mathematical.

Of course, it may be both. But without some grounding in those relevant roots/prefixes, it’s pretty hard not to screw this sort of problem up royally.

The worksheet seems to be poorly designed. Fortunately, the worksheet does tell the students to always use units, not just numbers. The easiest way to do most unit conversions is to multiply by one, and then cancel matching terms from the numerator and denominator. For example, 120 cm = 120 cm * (1 m / 100 cm) = 120 m / 100 = 1.2 m ; 160 cm = 160 cm * (1 m / 100 cm) = 160 m / 100 = 1.6 m

If the student randomly (or accidentally) tries 120 cm = 120 cm * (100 cm / 1 m) , they have not made a mistake. 120 cm^2 / m is still correct — it is just not what they are aiming for. If they get to this point, teach them to recognize that they accidentally made things more complicated, but they can go back one or two steps and try doing the conversion “the other way”.

Every student should do a self-check at the end of the problem. In order to do a self-check with units, it helps to be familiar with the units. If the students are in America (or another country that uses inches and yards): Show them a yard-stick and a meter-stick. Let them compare the sticks. Hopefully they will remember that the meter-stick is about as long as the yard-stick. Maybe they will remember that the meter-stick is a bit longer than the yard-stick. Let them do the “its this big” comparison to their wing-span and height. Do the same thing with a short metric ruler (for centimeters), a short American ruler, a penny, and a quarter. If the moon is in the sky, dare them to hold a quarter at arm’s length, and compare its size to the moon. (Warn them that the sun is too bright for doing this trick — the sun will hurt their eyes.) And of course teach them the common metric prefixes (like centi — 100 cents are in ).

I experience this confusion with fourth graders all the time. I’m convinced that the problem lies in the fact that we don’t use the metric system, so converting within is irrelevant to students. They don’t use it in their daily lives, so it’s unlikely that they will self-check. As a coach, I see teachers do a good job with teaching “centi” and place value. U.S. students have no practical application, so it becomes a rote paper and pencil task.

Or it could be correct if they’re European and write American 1.200 as 1,200 instead?

Assuming they multiplied by 10 instead of dividing by 100, I would think the kid ought to get some actual measuring experience in the classroom. There should be some image of people’s heights being a meter or two based on familiarity with what a meter stick looks like, and a lot of emphasis on the habit of checking the answer against some kind of estimate.