Weighted Grades

Many teachers put assignments in a variety of categories and then "weight" them to calculate final grades. So finding the final "average" is not as simple as adding up the points and dividing by the total possible.

A similar scenario might be like the following problem. This is often how it might first be introduced to students.

You are driving to your grandmother's home which is located 100 miles away. On the way you certainly would not be able to drive at a constant rate because of many factors like traffic, rest stops, etc. So to find your average speed you take the total distance and divide by the total amount of time. Let's say it took 2 hours to get there and therefore your average speed was 50 miles per hour (100 ÷ 2 = 50). Simple enough!

Now your trip home did not go quite as planned as you had a flat tire along with the normal stops so it took 4 hours to get home. Just as before the distance, 100 miles, divided by the time, 4 hours, would yield an average speed of 25 miles per hour for the trip home.

But what is the average speed for the entire trip?

Here is the mistake most people make, (50 + 25) ÷ 2 = 37.5 miles per hour. So what's wrong with that? The average of 50 and 25 is 37.5!

The problem is that you spent a lot more time averaging 25 mph than you did averaging 50 mph. The 25 mph trip has more weight. If you really averaged 37.5 mph then the entire 200 miles should have taken you 200 ÷ 37.5 = 5.33 hours when it actually took 6 hours. So to find the actual average you must take the total distance, 200 miles, and divide by the total time, 6 hours. 200 ÷ 6 = 33.33 miles per hour. It is less than the average of 50 and 25 because the 25 has more weight and has a greater effect on the final average.

Weighted grades have the same impact. If tests are weighted more than homework than they will have a greater effect on the final grade.

How to calculate weighted grades

Another scenario

Think of the categories as boxes and each box can contains marbles. The maximum number of marbles that a box can contain is equal to its assigned weight/percentage. Since the total of the weights/percentages must equal 100% then all together the boxes can contain 100 marbles.

For example, use the following weights and categories.

Category
Weight (%)
Tests
30
Homework
40
Participation
10
Projects
20

So the maximum number of marbles in the TEST box is 30, HOMEWORK box is 40, PARTICIPATION is 10, and PROJECTS is 20. If all of the boxes are full then the student will have a grade of 100%

To calculate the number of marbles a student has in their boxes you do a simple proportion.

Let's say that over the course of a semester there have been a number of tests that have a total value of 350 points and that a student has earned 300 of them, or 300 ÷ 350 = 0.857 = 85.7%. The number of marbles in the TEST box would be 85.7% of 30 or 25.7 marbles.

Doing likewise for the other categories will give the number of marbles in each box and the total would be the final grade since there were 100 marbles possible.

Examples

These examples are using the weights/percentages from above.

Student A

  Points Possible Points Earned Percent Marbles
TEST
400
360
90
27
HW
250
224
89.6
35.84
PART
600
578
96.3
9.63
PROJ
200
150
75
15
      Grade
87.47

Student B

  Points Possible Points Earned Percent Marbles
TEST
400
250
62.5
18.75
HW
250
200
80
32
PART
600
578
96.3
9.63
PROJ
200
180
90
18
      Grade
78.38

Student C

  Points Possible Points Earned Percent Marbles
TEST
400
250
62.5
18.75
HW
250
100
40
16
PART
600
578
96.3
9.63
PROJ
200
180
90
18
      Grade
62.38

 

Students need to be aware that if they want to improve their grade then they need to look at the category that is causing them to have a low grade and improve there. If you have a low participation grade and a high homework grade then doing more homework will not do much to improve their grade, they need to participate.

If your box is full or nearly full of marbles then you cannot put any more in that box, you need to find the box that has more room.

Regardless of the grading system utilized students also need to understand that to influence their grade they must do something significantly different than they have been doing in the past. If a student has an 80% in a category, then doing 80% work will only keep the grade where it is. Even doing 85% work will have only a small impact on the grade as this is not much of a difference. To truly make an impact the difference must be significant.

Unfortunately, a zero (0) is almost always a significant difference and will have a dramatic effect in the wrong direction. Lesson - do not get zeros!

Why Weighted Grades?

Weighted grades require student to be fully engaged in all phases of the learning process. They need to realize that everything has value. It is not OK to neglect homework or refuse to participate just because you can score well on tests. There is a lot more to "earning a grade" than just taking a test.

Weighting grades also makes it much easier to recognize areas of weakness and strength. It becomes readily apparent if a low grade is due to poor test scores rather than lack of homework.