Weighted Grading

This is the first post of two about grading issues.

I use weighted grades when teaching Math 20. Most confusing to students is that there are two midterms, and for each student the midterm they do worse on is worth 10% of their overall grade but their better midterm is worth 20%. How does the math work?

Imagine a student who scores 12 out of 15 on the first midterm, and 9 out of 15 on the second midterm.

First, change the scores to percentages. The student got 80% correct on the first midterm and 60% correct on the second midterm.

Next, separately multiply those percentages by their appropriate overall "weight". For the worse midterm we get 0.60 × 10 = 6 overall points. For the better midterm we get 0.80 × 20 = 16 overall points.

Finally, add the results. This student earned 6 + 16 = 24 overall points (out of 30 possible) from midterms.

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Note that some instructors use a simple version of weighted grading that simply assigns more points to more important items. For example, maybe the final is graded out of 50 points, the midterm out of 30, and homework out of 20.

This is indeed simpler, but cannot create my "your better midterm should count more" situation.