Handshaking

Your class has 28 students. If each student shook hands with ever other student, how many handshakes would there be?

Alternatives

Use the number of people in the class. On the first day of a class, ask everyone to introduce themselves and shake hands with everyone else before posing the problem. If the class is too large for that, divide it in halves or other pieces and have them shake hands with all those in the same piece.

Approaches

(28)(27) = 756

represent by acting out

represent with vertex-edge graph

Try for simpler problem.

(28)(27)/2

Why? (Each handshake is between two people; 28C2; number of edges in complete graph with 28 vertices)

respond: Why? explanation: each of 28 shakes with 27 others; respond: good thinking about "for each" multiplication, but please verify that your method works somehow, perhaps with a smaller group

try smaller problems and look for patterns (1, 3, 6, 10); see how "the next number" is being added each time

respond: Why?

act it out, perhaps with smaller problems

respond: Are you sure you counted them all? What's a number sentence describing your method of counting?

draw a picture, perhaps with smaller problems

respond: What's a number sentence describing your method of counting? introduce idea of complete graph

count pairs

respond: introduce idea of combination, elicit ideas for systematically counting combinations

Simulation

Interact with a small group of virtual students as they work on this problem.