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15 Cards in this Set

  • Front
  • Back
1. Guess and Check
Make a guess and check.
2. Make and orderly list
Where there are many possibilities, make an orderly list or table.

HHH
THH
HTH
TTH
HHT
THT
HTT
TTT
3. Draw a Diagram
Diagram or picture that represents the data
4. Look for a Pattern
Look at the ordered sequence and see if there's a pattern.

__,__,__,__,__=__
5. Make a table
Make a table reflecting the data
6. Consider Special Cases
Consider a sequence of special cases. May end up revealing a pattern.

(Pascal's Trigangle)
7. Use a variable
If a problem requires a number to be determined, represent the number with a variable and set up an equation.
8. Word Backward
Start from the desired result and work backward step-by-step.
9. Eliminate Possibilites
If the problem has a guaranteed solution, use the data of the problem to decide which outcomes are IMPOSSIBLE. If one of the possibilities is not ruled out, then it is the correct answer.
10. The Pigeonhole Principle
If m pigeons are place into n pigeonholes and m > n, then there must be at least two pigeons in one pigeonhole.
11. Inductive Reasoning

(Mathematical Statements)
(Representational Reasoning)
Look at several examples and check that the solution holds in other examples. Try to find a counterexample. If it holds in EVERY example, then make a generalization that the property is true.
12. Use Deductive Reasoning
If p is true, then you can deduce that q is true by direct reasoning.

If q is false, then p leads to a contradiction, then p is false by indirect reasoning.
Direct Reasoning
If p then q....and p is true.
Therefore, q is true.
Indirect Reasoning
If p then q......and q is false.
Therefore, p is false.
In a truth table that p ---> q, the only sequence that has a false p ---> q is:
the sequence of:

p q p--->q
T F F