triangular numbers big idea how can we apply number pattern techniques to determine rules for...
TRANSCRIPT
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