Help creating a half hot switch: 3 sets of wires
Some wires need to be marked here (on both ends)

The white wire that is with the blacks is not a neutral.  It has been assigned to be a hot, and as Code requires, it's being used for the "always-hot". As such, Code also requires it be marked with colored tape, paint or shrinktube, and I recommend black.  Like any marking, it should be done on both ends.  

Now, I am a big fan of also marking the switched black wire "red", so it's clearer that it is the switched wire.  That's not mandatory, but it does make things a lot clearer in the box.  

At this point, this gets super easy: just break the tab on the "hot" side of the recep, and connect one screw to red (switched-hot) and the other screw to black (always-hot).