If month in this cell is in current month, count this other cell?

Hi - I've found similar posts which have helped me get a start on this (thank you), but still aren't quite right. I've attached a generic sample copy of my spreadsheet and noted in red what I'm trying to do. Essentially, whenever someone leads a class, they will enter it onto this spreadsheet with the date, the number of sessions held on that date, etc...

I need to provide Month-to-Date, Quarter-to-Date and Year-to-Date session count totals for each class. YTD is easy, but I'm getting stuck on the MTD and QTD formulas. I was able to apply a formula (in there currently for MTD on Class Type 1) that I thought would work until I realized it was counting the actual date cells, not the session cell for that date.

Any thoughts? Hopefully it makes more sense once you see the spreadsheet, but if not, let me know? Thank you in advance!