Google Classroom now comes with its own built-in gradebook.

To set it up, create gradebook categories under Class Settings:


screenshot of gradebook settings

You can then choose whether you want to assign a total number of points for the categories or use the weighted mean:


Screenshot of gradebook category totals and weights

screenshot of weighted mean option


Now, when you create an assignment, you will be able to assign it to one of the categories you have created:


Screenshot of category choices


Here is some more information on setting up and using the Gradebook.