Moodle's grade book enables you to arrange items in your grade book, add columns and categories, and customize how students' grades are calculated. To control these features, go to the Views section beneath Categories and Items in the grade book drop-down menu:
Simple view allows you to control the order of items and categories in your grade book, set the relative weight of a category as part of the final grade (for weighted average), and set the method used to calculate grades for categories and the overall course.
Full view contains the same options as simple view. Additionally, you can change advanced grading options for multiple assignments at once.
Note: The image below is of Simple view.
(Click to enlarge)

Add Extra Columns to the Grade Book
To record grades for offline activities that you want to factor into your grades, such as quizzes or exams, you must first add a column to your grade book be creating a new grade item. Adding a grade item does not add a corresponding activity for your students to submit (e.g. an online activity/assignment). Data can be added to this column manually or by importing a spreadsheet. For instructions, refer to Import Student Data into Moodle.
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To add a column to your grade book, create a new grade item by clicking Add grade item. The Add grade item screen will open.
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Name the item in the Item name field, and set its point value in the Maximum grade field.
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When finished, click Save changes
Arrange Columns & Categories
To change the order of columns in the grader report, you must be in Simple/Full view. Each grade category and grade item (equivalent to a column in the grader report) has a up-and-down arrow icon next to it. Clicking this button triggers the move action.. The element to be moved is highlighted and the word (Move) appears next to it. Rectangular boxes preceded by an arrow appear in places where you can move your selected item or category.

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You can cancel your action at any time using the "Cancel" button at the bottom of the page
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To select the new location of a category or item, click within one of the destination rectangles, your item will appear there when the screen reloads.
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If you move a category that contains items and/or categories, all its contents will also be moved to the new location.
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Note: Moving items and categories does not affect individual grades. However, it affects the scores aggregated by categories and, if these categories have special calculation formulas in place, also affects the scores aggregated under the course grade category (Course total)
Moving Multiple Items at Once
You can also move multiple grade items at once using the check-boxes located in the right-most column. (Click image for larger view)

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Check the boxes for items you wish to move
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Below the table next to Move selected items to, choose a category
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Once you select a category, all selected items will appear there when the screen reloads
Deleting Columns & Categories
If you find that you want to delete a column or category in your grade book, first go into either Simple or Full view.
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For categories or grade items that you have created in the grade book, you can delete them by clicking the delete button next to the item (Which looks like an "X").
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Note: If you delete a category that contains multiple items, those items will not be deleted but move up one level to the parent category (which in most cases would just be the course total).
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For grade items that are connected to activities, you cannot delete them from the grade book. You can hide them by clicking the hide icon (eye) and they will no longer be visible in student grade reports. To delete them entirely, you would need to delete the assignment from your main course page.