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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.
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
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