The teacher orchestrates a class discussion about the numbers in the table. Most students quickly detect a pattern of growth and are prepared to predict the answer for a 5times5 geoboard—20 different segments—because (2 + 3 + 4 + 5) + 6 = 14 + 6 = 20. In fact, many students are prepared to state a more general conjecture: The number of segments for an NtimesN square geoboard is the sum 2 + 3 + ... + (N + 1).