1. TRIANGULAR NUMBERS BIG IDEA How can we apply number pattern techniques to determine rules for patterns in Geometry?

2. HERE’S A PUZZLE TASK: How many 2-person conversations are p possible at a party of 30 people? # People 12345…n # Handshakes

3. TRIANGULAR NUMBERS Today’s Objective: During today’s lesson, you will determine a rule for generating the n th term in a sequence of triangular numbers by using a table of values and doubling/tripling before factoring.

4. The triangular number sequence appears in many geometry problems. Ancient Greeks were the first to work with these numbers. Let’s find a way to determine a rule for this sequence.

5. EXAMPLE A: DOUBLE- FACTOR METHOD

6. TERM 1 2 3 4 5 6 … 20200 … n VALUE 6 10 15 21 2836-?- YOUR TURN: DOUBLE-FACTOR METHOD

7. EXTENSION: Patterns in Geometric Shapes Apply the number pattern techniques you have practiced to determine a rule for finding the total number of triangles formed in 15-sided polygon:

8. FINAL CHECKS FOR UNDERSTANDING FINAL CHECKS FOR UNDERSTANDING Use what you have learned about triangular number sequences, combined with the data obtained at the start of class, to complete this task. How many 2-person conversations are possible at a party of 30 people? # People 12345…n # Handshakes

9. Final Checks for Understanding: 1, 3, 6, 10, 15, 21…, Given the sequence, 1, 3, 6, 10, 15, 21…, determine the next term in the sequence, then find a rule for determining the 15th term of the sequence. TERM 1 2 3 4 5 6 …15200 … n VALUE 1 3 6 10 1521-?- In this sequence, it is easy to find the next term, but not so easy to find the rule. 5 minutes

10. HOMEWORK Triangular Numbers WS, plus select problems from Patterns in Geometric Shapes WS (Spiral Review)