Test 1 Math

Problem

Has no immediately obvious solution

Problems should be…

imbedded into the curriculum as real life situations

Four principles of Polya’s problem-solving method

1. Understand the problem

2. Devise a plan

3. Carry out the plan

4. Look back

The difference between consecutive numbers is…

always the same

Algebra

Used to generalize arithmetic.

Variable

A symbol, usually a letter, use to represent an unknown quantity.

Algebraic expression

contains at least one variable and possibly numbers and operations.

Arithmetic series

A sum in which the addends are consecutive terms in an arithmetic sequence.

Equation

A statement that two expressions are equal

Inductive reasoning

Drawing a conclusion based on information obtained from specific examples

Conjecture

A statement that seems to be true, but not yet proved true or false.

Counterexample

An example that disproves a statement.

Deductive reasoning

Using statements and logical reasoning to reach a conclusion

Statement

A declarative sentence that is either true or false, but not both

Compound statement

Two statements connect by “and” or “or”

In a valid argument…

The hypothesis guarantee the stated conclusion

Rules of direct reasoning

Hypothesis - If p, then q : p is true

Conclusion - Therefore, q is true