Problem Solving Tactics and Strategies
"First guess, then prove. ... All the great discoveries by Archimedes, Gauss, Newton were conceived this way". George Polya, 1966 (see the video with him below).
Draw a Picture  James Tanton

Solve a Simpler but Similar Problem  James Tanton

Make a Diagram and Construct a Table to Keep Track of Your Data
The question: 12 people are at a party. If everyone shakes hands once, how many handshakes are made? Go here to see a diagram.
How about 73 people? or maybe 200? Do you see a pattern? Can you generalize to make a formula, given the pattern?
Go here to see a table (Word file).
Go here to see a table (screenshot).
Hint: What shape do these numbers seem to represent?
The question: 12 people are at a party. If everyone shakes hands once, how many handshakes are made? Go here to see a diagram.
How about 73 people? or maybe 200? Do you see a pattern? Can you generalize to make a formula, given the pattern?
Go here to see a table (Word file).
Go here to see a table (screenshot).
Hint: What shape do these numbers seem to represent?
Find a Pattern  Richard Ruscyzk

Work Backwards  Richard Ruscyzk

Guess and Check
Using a List or Table (to help stay organized) 
Make a Table

Reasonable Guessing Using Analogies  Watch the master, George Polya (Hungarian, 1887 1985) in action.
Use Logical Deduction to Figure Out the Problem
The Census Taker Problem

Other Approaches
