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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 stepbystep.


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 