Grades?

The grade refers to the structure and appearance of the cancer cells, and the speed at which the cells are multiplying. 

Here's some info on cancer cell grading:

The Scarff-Bloom-Richardson system is the most common type of cancer grade system used today....Pathologists closely observe three features when determining a cancer's grade: the frequency of cell mitosis (rate of cell division), tubule formation (percentage of cancer composed of tubular structures), and nuclear pleomorphism (change in cell size and uniformity). Each of these features is assigned a score ranging from 1 to 3 (1 indicating slower cell growth and 3 indicating faster cell growth). The scores of each of the cells' features are then added together for a final sum that will range between 3 to 9.

• Tubule Formation (% of Carcinoma Composed of Tubular Structures)

>75%             Score 1

10% - 75%     Score 2

<10%             Score 3

• Nuclear Pleomorphism (Change in Cells)

Small, uniform cells                                   Score 1

Moderate increase in size and variation       Score 2

Marked variation                                        Score 3

• Mitosis Count (Cell Division)

Up to 7          Score 1

8 to 14          Score 2

15 or more     Score 3

• Grade 1 (lowest) Well-differentiated breast cells; cells generally appear normal and are not growing rapidly; cancer arranged in small tubules.  Score 3, 4, 5
• Grade 2  Moderately-differentiated breast cells; have characteristics between Grade 1 and Grade 3 tumors.  Score 6, 7
• Grade 3 (highest) Poorly differentiated breast cells; Cells do not appear normal and tend to grow and spread more aggressively.  Score 8, 9

*Scarff-Bloom-Richardson grade system

http://www.imaginis.com/breast-health/histologic-grades-of-breast-cancer-helping-determine-a-patient-s-outcome-2

I would not agree that grade 3 DCIS cells are the closest to being invasive, since invasive cancer cells, just like DCIS cancer cells, can be grade 1, grade 2 or grade 3. Additionally, it's believed that usually (although not always) if a grade 1 DCIS cancer cell becomes invasive, it will become a grade 1 invasive cancer cell.  Similarly, a grade 2 DCIS cell is most likely to become a grade 2 IDC cell and a grade 3 DCIS cell is most likely to become a grade 3 IDC cell.  What is true is that grade 3 DCIS is the most aggressive form of DCIS (the cells are growing the fastest and have the least resemblance to normal cells) and therefore grade 3 DCIS is more likely (than grade 1 or grade 2 DCIS) to evolve to become IDC more quickly. 

I'm not sure I wrote that very clearly so I hope it isn't confusing!