Heads or Tails?

First graders have been exploring the relationships among combinations of numbers up to ten, as well as solving problems in which only the total and one part are known.  Two games that they recently played are "Heads or Tails?" And "How Many Am I Hiding?"  For each game they used a known total of objects.  In "Heads or Tails" they found many different combinations for a given amount by shaking and dropping their coins, always double checking that their numbers still added up to the original amount; and in "How Many Am I Hiding?" their partner would hide part of their objects and they needed to solve for the missing part.