Does this get you there?

=SUMPRODUCT((Sheet1!B1:B10)*--(LEFT(Sheet1!A1:A10,3)=LEFT(A1,3))*(OR(LEFT(A1,3)="mon",LEFT(A1,4)="mon ")))
Gives me 4 with A1 having "mon", "mon ", "mon xxx". Gives 0 with "xxx mon", " mon", "abcd", etc.