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15 Cards in this Set
- Front
- Back
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1. Guess and Check
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Make a guess and check.
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2. Make and orderly list
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Where there are many possibilities, make an orderly list or table.
HHH THH HTH TTH HHT THT HTT TTT |
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3. Draw a Diagram
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Diagram or picture that represents the data
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4. Look for a Pattern
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Look at the ordered sequence and see if there's a pattern.
__,__,__,__,__=__ |
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5. Make a table
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Make a table reflecting the data
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6. Consider Special Cases
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Consider a sequence of special cases. May end up revealing a pattern.
(Pascal's Trigangle) |
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7. Use a variable
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If a problem requires a number to be determined, represent the number with a variable and set up an equation.
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8. Word Backward
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Start from the desired result and work backward step-by-step.
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9. Eliminate Possibilites
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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.
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10. The Pigeonhole Principle
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If m pigeons are place into n pigeonholes and m > n, then there must be at least two pigeons in one pigeonhole.
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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.
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12. Use Deductive Reasoning
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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. |
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Direct Reasoning
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If p then q....and p is true.
Therefore, q is true. |
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Indirect Reasoning
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If p then q......and q is false.
Therefore, p is false. |
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In a truth table that p ---> q, the only sequence that has a false p ---> q is:
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the sequence of:
p q p--->q T F F |
