I made this worksheet today as well!  For years and years we have been teaching our students to add vertically, however, students rarely understand why.  When children add vertically are they truly understanding they are adding tens and ones?  I don't think they really are.  I think students are just learning... ok to add numbers vertically I just add down.  So they would look at 36+3 as...

From perhaps at least ONE student's perspective:

   36
+   3


OK my teacher tells me I add down...
1. lets add 6+3=9
2. ok lets move over to the left
3. lets add 3+0= 3
4. The answer is bring down the 9 and bring down the 3.. 39

However how can we truly know as educators if the student memorized the pattern of adding down or if he or she truly understands that the "3" they added to "0" is really "30" + 0 (tens) = 30

Cross Number Puzzles SHOWS PLACE VALUE!