Triangular Numbers

Materials: Handouts

Goals (you must fill in the blanks):

¨ Recognize the sequence of triangular numbers and be able to distinguish this sequence from arithmetic, geometric, and other sequences.

¨ Spply your knowledge of triangular numbers to applications such as the Handshake Problem, diagonals of polygons, and network connections.

¨ Prove the sum of the first n integers is _________.

¨ Illustrate triangular numbers with several different diagram s.

¨ Make connections between the formula (shortcut) for triangular numbers and a visual representation of that formula.

Step 1:

¨ Review the "Handshakes" exploration in Bassarear.

¨ Actively read Investigation 1.5: The Sum of the First 100 Numbers on pp. 23-25 of Bassarear.

¨ Do problem 28f on page 29 of Bassarear.

¨ Actively read Investigation 2.4: Triangular Numbers on pp. 86-87 of Bassarear.

¨ Do problems 48a on page 164 of Bassarear.

¨ Do "The Vertex Connection" of Activities from the Mathematics Teacher.

¨ Do Activity 6: Polygons and Diagonals from Mathematics Activities for Elementary School Teachers: A Problem Solving Approach.

¨ Actively read "Triangular Numbers" from Math for Fun.

¨ Explain how the two diagrams "Sums of Integers I and II" from Proofs Without Words illustrates the formula .