Question: Is it possible for me to mark student assignments in the same order that they were received within Quercus? 

Answer: Yes, by using Speedgrader you are able to sort your assignments according to the order that they were received. To begin to change the sorting options, open Speedgrader from the assignment that you're marking. Next, click the gear icon in the upper left portion of the screen. You will now see a window entitled "Speedgrader Options". Within this window, select "the date they submitted the assignment" option from the "Sort student list" drop down menu. You can also choose to sort your assignments alphabetically or by their submission status (e.g., needs to be graded, not submitted).  

For a detailed guide on selecting different assignment sorting options within Speedgrader, please see "How do I sort the student list in SpeedGrader?"