GACE MATH

rational number

A number that can be written as a fraction

Rational numbers are

natural numbers , whole numbers and integers (-1,-2,1,3,0), mixed numbers

Natural Numbers

The set of numbers 1, 2, 3, 4, ... Also called counting numbers.

whole numbers

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

Intergers

The set of whole numbers and their opposites

irrational numbers

Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating.

Irrational numbers are

Non-perfect squares, numbers with Pi, numbers that have a decimal going on forever and never repeating

magnitude

Greatness of size, strength, or importance

less than or equal to

comparison can be less than or equal to

greater than or equal to

a value that is "at least" as big as another value

has a closed circle

comparing negative numbers

left is less

right is greater

comparing decimals

Line up the numbers and fill in the missing zeros

Counting by ones

basic form of counting 1,2,3,4,5

skip counting

counting by twos, threes, counting only even or odd numbers, or counting by other multiples

counting on

Counting up from the lesser number to the greater number to find the difference of two numbers.

counting backwards

A math strategy that is a prerequisite to subtraction

counting collections

a collections of various objects that student can count to help develop numb sense and number relations

number line

A diagram that represents numbers as points on a line.

absolute value

The distance a number is from zero on a number line. ALWAYS POSITIVE

Cardinality

the number of elements in a set

Multiplicative Identity

When any number is multiplied by 1, the product is the number

Associative Property

The way in which numbers are grouped does not change their sum or product (a x b) x c = a x (b xc)

Communicative Property

Numbers can be added or multiplied in any order. That is: Commutative Property of Addition and multiplication it states that changing the order of addends does not change the sum or product.

Distrubutive Property

a(b+c)= ab+ac, where a,b, and c are real numbers

divdend

the number being divided (a)

divisor

the number that divides the dividend (b)

quotient

the answer to a division problem (c)

prime number

A whole number that has exactly two factors, 1 and itself. 3,5,7,11,13,17,&19

even number

An even number can be shown as 2 equal parts.

An even number has 0, 2, 4, 6, or 8 in the ones place.

odd number

A whole number that is not a multiple of 2

perfect square

A rational number whose square root is a whole number

multiplication key words

times, double, triple, product, of, multiplied by, twice, multiple

Division Key Words

Distribute, share, average, per, out of, percent, and quotient

Subtraction Key Words

How much more, less than, fewer than, exceeds, difference, and decreased

PEMDAS

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction

factor

a number divided into another number without leaving a remainder

composite number

A number with at least three factors

place value

The value of a digit based on its position within a number

Base 10 Number System

a number system in which all numbers are expressed using the digits 0-9

what are base ten blocks use for ?

help understand place value and and assist with counting large numbers

standard form

actual number

expanded form

A way to write numbers that shows the place value of each digit.

decimal

A number with one or more digits to the right of the decimal point

common factor

A number that is a factor of two or more numbers

rectangle, square

all squares are rectangles but not all rectangles are squares

Natural Numbers

The set of numbers 1, 2, 3, 4, ... Also called counting numbers.

ordinal numbers

numbers that describe position or order (first, second . . .)

compass

tool to draw a circle

rounding numbers

means changing them to the nearest ten, hundred, thousand, and so on

Counting up method of subtraction

An alternative subtraction process that can be used to subtract or to check your work after having subtracted through standard processes. For each place value of the second number, count up to the next 10, 100, 1000. Once reaching the last place value of the higher number, add any remainder (ex. 327 - the remainder would be 27). Add all values together for the answer.

Volume

The amount of space an object takes up

Volume of a rectangle

L x W x H

symmerty

balanced proportions

line of symmetry

a line that divides a figure into two halves that are mirror images of each other

vertices

The point of intersection of two sides of a polygon. The point of intersection of three edges of a space figure.

corners of shapes

line

connects two points has no thickness and extends indefinitely in both directions beyond points

line segment

part of a line with two endpoints

ray

A part of a line, with one endpoint, that continues without end in one direction

whole numbers

Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

How to multiply decimals

1. Multiply as usual.

2. Count the number of digits above the line and to the right of all decimal points.

3. Place the decimal point in your answer.

Addition Property

If a=b, then a+c=b+c

proper fraction

a fraction with a numerator smaller than the denominator

improper fraction

a fraction whose numerator is larger than the denominator

numerator

the top number in a fraction

denominator

The bottom number in a fraction

long division

Divide, Multiply, Subtract, Check, Bring Down (Repeat)

DOES McDONALDS SELL CHEESE BURGERS?

area model

A model of multiplication that shows each place value product.

one-to-one correspondence

is the concept use when children relate a numeral to one item they can see and touch

quadrilateral

a four-sided polygon

Parallelogram

A quadrilateral with two pairs of parallel sides

Trapezoid

A quadrilateral with exactly one pair of parallel sides

addends

numbers that are added together

adjacent angles

Two angles that share a common side and have the same vertex

complementary angles

Two angles whose sum is 90 degrees

perpendicular lines

Lines that intersect to form right angles

Coplanar

points that lie on the same plane

coordinate plane

A plane that is divided into four regions by a horizontal line called the x-axis and a vertical line called the y-axis.

Radius

A straight line from the center to the circumference of a circle or sphere.

diameter

A straight line passing from side to side through the center of a circle or sphere.

The bar in a fraction represents:

division

equivalent fractions

Fractions that have the same value

unit fraction

a fraction with a numerator of one, it names one of the equal parts of a whole

How to multiply fractions

1. Multiply the numerator.

2. Multiply the denominator.

3. Reduce to lowest term if necessary.

How to divide fractions

keep change flip 22/5 / 1/2 = 22/5 x 2/1 = 44/5

perimeter

the sum of the lengths of the sides of a polygon

How angles are measured

In degrees.

360 degrees

full circle

180 degrees

half of a circle

90 degrees

quarter circle

acute angle

an angle that measures less than 90 degrees

right angle

an angle that measures 90 degrees

obtuse angle

An angle that measures more than 90 degrees but less than 180 degrees

mixed number

a number made up of a whole number and a fraction

number line

A diagram that represents numbers as points on a line.

additive and subtractive identity

zero

equivalent fractions

Fractions that have the same value

metric system

The decimal measuring system based on the meter, liter, and gram as units of length, capacity, and weight or mass.

1 foot = ____ inches

12 inches

1 yard = ____ feet

3 feet

1 mile = ____ feet

5,280 feet