For the Beginners, Dr. Root gave the students examples of what is stalemate and what is checkmate (using a King and Queen vs. King) as models first, on the demonstration board. Then Dr. Root said, “You have a king and queen. Your partner has a king. Set up 5 different positions that are checkmates and two positions that are stalemates.” Then they showed Dr. Root (one position at a time) the 7 positions they created.
For the intermediate and advanced, Dr. Root taught the Criteria Challenge activity from Science, Math, Checkmate: 32 Chess Activities for Inquiry and Problem Solving (2008, pp. 28-30). In each group, a mother came in asking for her child to leave early. In both cases, the child asked to stay to finish the challenge being worked on with a partner. The intermediate group finished two or three of the four challenges working in pairs. The advanced group pairs each finished all four challenges