Jim Mezzanotte

posted this on May 15, 2012 07:39 AM

ANI would like to thank Russell Beauchemin, from ANI client Roger Williams University, for his contributions to this article.

If you have set up Gradebook2 for weighted categories, you may want to determine how the course grade is calculated--both at the end of a term, when all items are scored, and during the term, when you have not yet entered scores for all items.

How items are weighted in the gradebook

First, let’s review how an item is weighted in the gradebook. We can determine an item’s weight with the following calculation:

relative weight in category × category weight in gradebook = item weight in gradebook

This item weight is displayed in the gradebook:

So if an item is worth 25% of a category, and the category is worth 30% of the gradebook, the item’s weight in the gradebook will be:

25% x 30% = 7.5%

How scores for weighted items are calculated

Next, let’s review how the score for an item in a weighted category is calculated, assuming the gradebook is points-based:

earned points ÷ possible points × item weight in gradebook = weighted score for item

So if you score an item 80 points out of a possible 100, and the item is worth 7.5% of the gradebook, the item’s weighted score will be:

80 (earned points) ÷ 100 (possible points) = .8

.8 × 7.5 (item weight in gradebook) = 6

If you have scored all items in the gradebook, the course grade will be the sum of all weighted scores (plus any extra credit that is included). But what happens when you have not yet graded every item? Read on for an explanation of how this “course grade to date” gets calculated.

How course grade is calculated when all items are not scored

When you have not yet entered scores for every item in the gradebook, the CLE must make some adjustments to weights. To calculate this “course grade to date,” the CLE will:

- Ignore categories in the gradebook with no scored items, and increase the weights of categories with scored items to equal 100% of the gradebook.

- In a category, ignore unscored items and increase the relative weights of the scored items to equal 100% of the category.

While you won’t see any of these adjustments displayed, they will change an item’s weight in the gradebook--and therefore change the calculated weighted score.

Scenario #1--All categories do not include scored items

Let’s say you have four categories in your gradebook, weighted as follows:

- Participation--10%
- Homework--20%
- Quizzes--30%
- Tests--40%

Next, let’s assume you haven’t yet scored any items in the Tests category--so the CLE ignores this category and proportionally increases the weights of the other categories:

To determine how the weights of the categories with scored items are increased proportionally to equal 100%, you would follow these steps:

- Add the weights of the categories with scored items:

10 + 20 + 30 = 60

- Divide the weight of each scored category by the resulting sum:

10 ÷ 60 = 0.1667

20 ÷ 60 = 0.3333

30 ÷ 60 = 0.5

- Multiply each quotient by 100:

0.1667 x 100 = 16.67

0.3333 x 100 = 33.33

0.5 x 100 = 50

So in this case, if the Tests category contains no scored items, the weights of the categories with scored items will be adjusted as follows:

- Participation: 16.67%
- Homework: 33.33%
- Quizzes: 50%

Of course, these increases in category weight will change each scored item’s weight in the gradebook--and therefore its weighted score for a course grade to date.

Scenario #2: All items are not scored in an equally weighted category

Let's assume that all categories in the gradebook include at least one scored item, so category weights are not being adjusted. One of the categories is worth 30% of the course grade and is set up for equally weighted items.

The category contains four items, so each item has a relative weight in the category of 25%. If all items are scored, each item’s weight in the gradebook will be: 25% x 30% = 7.5%

But now let’s assume that, for this category, you entered scores for only two of the four items. The CLE ignores the unscored items and increases the relative weight of the scored items to equal 100% of the category:

Since the category is set up for equally weighted items, the CLE increases the weight of each item equally, to 50%. So the relative weight of each scored item in the gradebook is: 50% × 30% = 15%

If a student earns 80 points for the first item and 75 points for the second item (out of a possible 100), the student’s total weighted score for the category, to date, will be:

Item 1 score |
80 ÷ 100 = .8 .8 × 15 = 12 |

Item 2 score |
75 ÷ 100 = .75 .75 × 15 = 11.25 |

Category total |
12 + 11.25 = 23.25 |

Scenario #3: Only one item scored in a weighted category

What if you only enter a score for one item in a category? In this case, the CLE increases the relative weight of the item to 100% of the category--so its weight in the gradebook is identical to the category weight.

Using the example from scenario #2 (with all categories containing scored items), let’s assume you have only entered a score for one item in the category. Since the category has a weight of 30% in the gradebook, the scored item will have the same weight--30%.

If a student earns 80 points (out of a possible 100) for the item, the student’s total weighted score for the category will be:

80 ÷ 100 = .8

.8 × 30 = 24

Scenario #4: All scores not entered in a category with unequally weighted items

Again, let's assume that all categories in the gradebook include at least one scored item, so category weights are not being adjusted. The Homework category is worth 20% of the course grade, and it is set up for unequally weighted items.

This category contains four items, with the following relative weights:

- Assignment 1: 20%
- Assignment 2: 30%
- Assignment 3: 45%
- Assignment 4: 5%

We can determine each item’s weight in the gradebook by multiplying its relative weight in the category by the category weight in gradebook. So if all scores are entered, the weight of each item in the gradebook will be as follows:

- Assignment 1: 20% × 20% = 4%
- Assignment 2: 30% × 20% = 6%
- Assignment 3: 45% × 20% = 9%
- Assignment 4: 5% × 20% = 1%

Now let's say you have entered scores for the first three items--but not for Assignment 4.

The CLE ignores this unscored item and proportionally increases the relative weights of the three scored items to equal 100% of the category. Each scored item will then have an increased weight in the gradebook:

In the same way that we can calculate how category weights are adjusted, we can determine how the relative weights of the scored items are increased proportionally to equal 100% of the category, by following these steps:

- Add the relative weights of the scored items in the category:

20 + 30 + 45 = 95

- For each scored item, divide its relative weight by the resulting sum:

20 ÷ 95 = .2105

30 ÷ 95 = .3158

45 ÷ 95 = .4737

- Multiply each quotient by 100:

0.2105 x 100 = 21.05

0.3158 x 100 = 31.58

0.4737 x 100 = 47.37

So in this case, if Assignment 4 is not scored, the relative weights of the other scored items in the category will be adjusted as follows:

- (Assignment 1) 21.05%
- (Assignment 2) 31.58%
- (Assignment 3) 47.37%

Lastly, we can determine the adjusted weight in the gradebook for each scored item by multiplying each item’s relative weight by the category weight:

- (Assignment 1) 21.05% x 20% = 4.21%
- (Assignment 2) 31.58% x 20% = 6.32%
- (Assignment 3) 47.37% x 20% = 9.47%

Scenario #5: All items not scored in a category/all categories do not have scored items

So far, we’ve considered scenarios in which all items are not scored in a category, but each category in the gradebook has at least one scored item--so category weights do not change. But what happens if some categories contain no scored items?

In this case, the CLE makes the following adjustments to a category with scored items:

- Increase the relative weight of each scored item in the category
- Increase the weight of the category in the gradebook

Let’s consider a category that has a weight of 30% in the gradebook. The category is set up for equally weighted items, and only two out of four items are currently scored. The CLE ignores the unscored items and increases the relative weight of each scored item equally, to 50% of the category.

When all categories in the gradebook contain a scored item, this category has a weight of 30%, so the weight of each scored item would be:

50% (relative weight in category) × 30% (category weight) = 15%

But now let’s assume that all categories do not contain scored items--and the CLE increases the weight of this category to 50% of the gradebook. So the actual weight of each scored item will be:

50% (relative weight in category) × 50% (category weight) = 25%

Calculating course grade with categories set up to drop lowest score items

If you have set up a category to drop lowest score items, keep in mind that these items get treated in the same way as unscored items: the CLE ignores “drop lowest” items and increases the relative weight of the other scored items to equal 100% of the category.

Let's assume that all categories in the gradebook include at least one scored item, so category weights are not being adjusted. One category is set to drop the two lowest score items. Items in the category are equally weighted, and the category has a weight of 30% in the gradebook. The items in the category have been scored as follows:

- Item 1: 70
- Item 2: 80
- Item 3: 75
- Item 4: 85

The CLE drops items 1 and 3 as the two lowest-score items--and then increases the relative weights of items 2 and 4 equally, so each item has a relative weight of 50% in the category. The weight in the gradebook for items 2 and 4 will then be:

50% (relative weight in category) × 30% (category weight) = 15%

Calculating course grade when extra credit items are included

When you set up your gradebook for weighted categories, the total possible points an extra credit item can contribute is determined by the item’s weight in the gradebook. So you can determine the total possible extra credit points for an item with the following calculation:

relative weight in category × category weight in gradebook = total extra credit points

Let’s say an extra credit item has a relative weight of 10% in a category, and the category has a weight of 30% in the gradebook. The total possible extra credit points the item can contribute will be:

10% (relative weight in category) × 30% (category weight) = 3 extra credit points

The way extra credit points get calculated, however, will depend on how you have set up extra credit. There are two basic approaches you can take:

- Include an extra credit item in a category that is NOT set up for extra credit.
- Create a category that is set up for extra credit.

Extra Credit Scenario #1: extra credit for a category not set up for extra credit

If you take this approach, keep in mind the following:

- An extra credit item cannot contribute more than the total possible points for the category. So, depending on the item’s total possible contribution, as well as the score being entered, the extra credit points may be capped. In addition, the extra credit points will not exceed the grade scale.
- The total possible extra credit for an item will increase if all categories do not contain scored items. In this case, the CLE ignores categories with no scored items and increases the weights of categories with scored items to equal 100% of the gradebook. If a category weight increases, so does the weight in the gradebook (and therefore the points) for an extra credit item.

Let’s consider a non-extra credit category that has a weight of 30% in the gradebook. This category includes an extra credit item that has a relative weight of 10% in the category. If all categories contain scored items, this extra credit item can contribute a maximum of 3 points:

10% × 30% = 3 extra credit points

The course grade to date for a student includes 29 non-extra credit points for this category. To determine the total possible extra credit that can be added to this student’s course grade, we subtract total earned non-extra credit points (29) from total possible category points (30).

30-29 = 1

So even if this student earns the maximum possible score for the extra credit item, only 1 extra credit point will be added to the student’s course grade.

Next, let’s assume that all categories do not contain scored items--and the CLE increases the weight of this category to 50% of the gradebook. In this case, the extra credit item can contribute a maximum of 5 points:

10% × 50% = 5 extra credit points

Extra Credit Scenario #2: category set up for extra credit

If you take this approach, the contributions of extra credit items are calculated differently:

- The category contribution is fixed. When you set a category to be extra credit, the category weight in the gradebook determines its total possible extra credit points. Even if some categories do not contain scored items, this weight will not change.
- Extra credit points are not limited by the grade scale. When you enter scores for items in an extra credit category, those points are in addition to the contributions of the non-extra credit categories. Assuming you are using the default 100-point grade scale, the extra credit can result in a score greater than 100.
- The extra credit contribution of each item may change, depending on your gradebook setup. If you selected “scale extra credit” when setting up your gradebook, the CLE treats items in the category in the same way as items in a non-extra credit category: unscored items are ignored, and the weights of scored items are increased to equal 100% of the category.

Let’s consider an extra credit category that has a weight of 20% in the gradebook. This category can contribute a maximum of 20 extra credit points. The category contains two equally weighted items. So, with both items scored, each item can contribute a maximum of 10 extra credit points to the course grade:

If a student has a 90 for a course grade and earns the maximum possible points in this category, the student’s course grade will be:

90 + 20 = 110

This extra credit maximum does not change, even if some categories do not contain scored items. But how the extra credit items contribute to the maximum 20 points will depend on whether you select “scale extra credit” when setting up the gradebook--and whether you have scored all items in the category.

Let’s assume you do not select “scale extra credit.” In this case, the CLE makes no adjustments to the relative weights of items in the category, even if some items are not scored. So if you enter the maximum score for the first item, but do not score the second item, 10 extra credit points are added to the course grade.

But what if you do select the “scale extra credit” setting? In this case, the CLE ignores unscored items and increases the relative weights of scored items to equal 100% of the category. So, until you score the second item--and the CLE again adjusts the relative weights of both items--the first item contributes 20 extra credit points to the course grade.

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