How weighting is used to calculate grades is not always clearly understood. This explanation should be helpful. In the example, there are three weighted categories: Homework, Tests, and Final. Each is weighted 30%, 50%, and 20% respectively.
The figure to the right illustrates that a student's average for the Homework and Tests categories is 60% and 70% respectively. Since there is no score for the final exam, that category will not be used in calculating the student's average. The weight of each category used is multiplied by the student's average for that category. Those products are summed together and divided by the total of the weighted categories in use (80% as pictured above). In this example, the student has earned 53% of a possible 80% for an average of 66.25%. How that percent grade converts to a letter grade is based on the teacher's grading scale.
This is how the overall grade is achieved. Within a category, the total points possible and the total points earned are tallied together, and a percentage is calculated. If a student earns a 8/10 and a 9/12, then their category is 8+9=17 points out of a possible 10+12=22.
17/22 is 77.27%
This method of calculation accounts for the fact that one assignment is worth more than the other, as opposed to an average of averages, where each assignment is worth the same.
Q: How can my student's grade go down when they get a high score on an assignment?
A: Remember that grades are weighted by category. So if the score on the assignment is lower than the average for that category, the overall grade will go down.
Example: Student’s current overall grade is 90% for all categories (tests, homework, etc.) and they get a 92% on the next test. Intuition tells us that their grade should go up. However if their test average is 95% then the weighted average for the Tests category will go down and therefore their overall grade will go down as well.
Q: My student received 100% on an assignment and their grade went down - how is that possible?
A: The student had over 100% in that category, most likely due to extra credit.
Example: A student has turned in all of their homework and has some extra credit points, putting their average for the category at 110%. If the student receives a 100% on their next graded assignment, their weighted average for the Homework category will go down because 100% is less than 110%.
Q: My student did some additional extra credit but their grade went down. Shouldn't extra credit always raise their grade?
A: Not necessarily. Adding a new extra credit assignment will change the total points possible in the extra credit category and could lower the student’s percentage in that category.
Example: The extra credit category is set to give a student a 5% boost in their grade. So far the student has scored 10/10 on the one extra credit assignment, giving them 100% in the extra credit category, and therefore boosting their grade the full 5%. Now you assign another extra credit assignment worth 20 points and the student earns 5/20. Her total for the extra credit category is now 15/30 or 50%. Her boost has now gone down to 2.5%.