TRIANGULAR NUMBERS

BIG IDEAHow can we apply number pattern techniques to determine rules for

patterns in Geometry?

HERE’S A PUZZLE TASK:

• How many 2-person conversations are p possible at a party of 30 people?

# People 1 2 3 4 5 … n

# Handshakes

TRIANGULAR NUMBERS

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

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.

EXAMPLE A: DOUBLE-FACTOR METHOD

TERM 1 2 3 4 5 6 … 20 200 … n

VALUE 6 10 15 21 28 36 -?- -?-   -?- -?-

YOUR TURN: DOUBLE-FACTOR METHOD

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:

FINAL CHECKS FOR UNDERSTANDINGUse 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 1 2 3 4 5 … n

# Handshakes

Final Checks for Understanding:

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 … 15 200 … n

VALUE 1 3 6 10 15 21 -?- -?-   -?- -?-

In this sequence, it is easy to find the next term, but not so easy

to find the rule.

5 minutes

HOMEWORK

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