Praxis II 0014 Mathematics

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This is a study of mathematics terminology for the elementary education content knowledge (0014) Praxis II exam.

Deductive Reasoning

process in which conclusions are made based upon prior knowledge, facts, and truths. it is a step-by-step process of drawing conclusions.

Inductive Reasoning

process of reasoning based not upon proofs but open observation. involves drawing conclusions based upon a set of observations. it does not provide valid or reliable conclusions, but is used to develop hypotheses or ideas. after ideas are formed, systematic methods are used to confirm or deny the ideas.

Adaptive Reasoning

process defined as ability to justify strategies and analyze the strengths and weaknesses of solutions proposed by others

Problem Analysis

the ability to apply and adapt a variety of mathematical strategies to solve problems

Integer

natural AND whole numbers AND the negatives of the natural numbers

Rational Numbers

all integers AS WELL as fractional numbers or fractions... any integer over any integer

Prime Numbers

any integer other than zero and one that has only 2 factgors: itself and 1; a number divisible only by itself: 3,5,7,11,13,17...

Complex Numbers

any numbers with "i" in them (6-2i)

Algorithm

routine process used to obtain a result to a problem without using extreme concentration (there are 4 of these for basic operations)

Factor

prime or composite number that is multipled to obtain a product

Factors of 18

1,2,3,6,9,18

Factor Rules

2 is a factor of all even numbers; 10 is a factor of all numbers ending in 0; 5 is a factor of all numbers ending in 0 or 5; 3 is a factor of a number if it is also a factor of the sum of the individual digits within the number; 9 is a factor of a number if it is also a factor of the sum of the individual digits found within that number; 11 is a factor of a 3-digit number if the middle digit is the sum of the 2 outside digits

Associative Property

states that numbers can be grouped or regrouped in an operation in any manner without changing the answer (examples are addition & multiplication)

Commutative Property

states that numbers in an operation can change order without changing the end result (examples are addition & multiplication)

Distributive Property

states that one operation may change to another. this property can be used when multiplying with parentheses

Transitive Property

states that when an operation is applicable between successive numbers in a sequence then it also applies to any 2 numbers taken in order (whenever a=b and b=c, then a=c)

Perimeter

Rectangle- P=2l+2w; Triangle- P=a+b+c; Square- P=4s; Circle- P= (pi)(d)

Area

Rectangle- A=lw; Triangle- A=1/2 bh; Square- A= s (squared); Circle- A=(pi)r squared

Pythagorean Theory

a squared + b squared= c squared

Formula for finding TIME

distance/rate

Formula for finding DISTANCE

rate x time

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