# A Canadian Marking with the 7-point Scale

Something that has boggled my mind is the 7-point marking system used in Chile. If you grew up in Canada as I did, you may be used to thinking in a few different systems, metric and imperial –which in the Canadian experience works out to feet and inches for height, ounces and pounds for weight (except when buying groceries when metric is also posted). Moving away from footage and weight, exams and assignments in Canada are always marked in percentages, with 50% normally signalling minimum achievement and working all the way up to 100% for a perfect mark (which is never given). Now, it’s true that these percentages have “always” been converted into some letter based system, but this has always been at the end of the course, semester, or the school year –and so Canadians (as previously mentioned) understand and mainly think along the lines of a percent based marking system.

As can be deduced from above, being asked to mark using this 7-point scale has sometimes been awkward. It doesn’t help that Chilean teachers I’ve spoken with don’t work with percentages at all, some of which mark in what can only be termed qualitatively rather than quantitatively (a huge problem IMHO. Gd, I’ve been asked to be on Chilean “university” evaluative boards where rubrics weren’t required and certainly weren’t standard, but I’m getting off topic). Formulas to which you can input percentages –usually in the way of a spreadsheet– are sometimes provided by institutions. They usually consider more than just a percent to 7-point scale conversion but also provide a curve. Many institutions do not provide spreadsheets with built-in conversion formulas, leaving it up to the teacher.

What in part makes the Chilean point system odd –although it’s a 7-point system– it really isn’t marked as having seven intervals because one can’t give a student a grade below 1, despite his or her performance. It’s thought that if they show up to class, as infrequently as this may be and as uncooperative as they may be, they at least deserve a “1”. In the case that they don’t come to class –depending on how far the institution has commercialized itself– it’s either the teacher’s fault (for not motivating the student, despite the limited influence teachers hold) which disallows giving a failing mark or –if the institute is of an academic standard– the student may be removed from the class roster. Either case demonstrates that a “0” is never given –but this is getting off topic again. Back to the point at hand, the Chilean system forces one to think in unusual fractions. What’s a 5.6? And how is a 5.6 different from a 5.7? Is this difference significant? And to ultimately come to the point of this article, how does one convert from percent to the 7-point system?

**Percent to 7-point scale conversion formulas**

Two provided by a boss (a math teacher) are as follows.

6 (constant)/total marks of test=factor

ie., 6/20=0.3

Amount of marks student achieved * factor

ie., 15 * 0.3=4.5

Add 1

ie., 4.5+1=5.5

Apparently using a “6” makes for a higher standard, thus the gratis “1” at the end. My boss also suggested –something to the effect of– using an averaged figure, between what she called the real and ideal average to figure out the factor –at least that’s what I understood but considering that I don’t recall real and ideal (I don’t teach math) I’ll leave that alone.

**One provided by my cousin, an accountant.**

Best possible 7 point mark/total marks of test*amount of marks student achieved

7/20*15=5.25

In trying to understand what my cousin was saying I made the following algebraic formula.

7/20=x/15

20x=105

x=105/20

x=5.25

It works, but I found the following really makes more sense, in that you know your student has 15 correct out of 20 and that this is comparative to something (x) over 7, your 7-point scale.

15/20=x/7

20x=105

x=105/20

x=5.25

**Fast way**

Lastly, the fastest way to get your 7-point mark is provided by wikianswers. It explains how to convert to a four point system . I’ve adapted it to the seven based one.

7 (seven point system) * Grade in decimal format (75% as .75) = 5.25

7*0.75 =5.25

This method allows for quick double-checking, by converting from the 7-point system back to percentage by simply dividing.

5.25/ 7 =0.75

You’ll notice, given the figures above, most formulas state that the 7-point mark is a “5.25”, written in Chile with a coma (“5,25”). A 5.50 was achieved by figuring out a factor and proceeding from there, but even this can be brought in line with the 5.25 result of the other formulas by using a 7 instead of the 6 –and thus removing the necessity of adding a one to the end result. In any case, you’ll start to associate percentages with the 7-point system after using any of the above conversion methods.

I hope this helps someone out there coping with weird marking systems. All these can be adapted to any scale by supplanting the 7 for whatever scale is being used. Of course, run it past your department head, supervisor, or what not before using. Use your own discretion, as math is not my area of expertise.

Maurice Cepeda

**Links of interest**

http://en.wikipedia.org/wiki/Academic_grading_in_Chile

http://en.wikipedia.org/wiki/GPA_in_Canada

http://wiki.answers.com/Q/How_do_you_calculate_Grade_Point_Average_GPA_from_percentages

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My girls are now using a 7 point marking system in their school, but the rubrics are important to the grading and required. As well, the final outcome is determined by a mode rather than a mean, which I think is the best way. Some teachers are giving percentages and then converting them to the 7 point system, which doesn’t work. They must use the rubrics and I think this is the best way for a student to get feedback on their work and actually learn from their mistakes. It took 3 years for me learn the system and I’m convinced it’s the best way for a school to grade.

Feedback is always important, regardless of the marking system. And I like rubrics. They’re not only useful to students but they economically streamline the teacher’s workload.

As for why you say the conversion from percent to 7-point system doesn’t work, why do you say that? All you’re doing is changing the scale and doing so proportionately. It’s just simple math.