Believe it or not, there are a lot of words in math — and if you don’t know them, it’s going to be hard to work with the numbers they describe. An understanding of basic math terms goes a long way, no matter if you consider yourself a “math person” or not.

## Counting and Cardinality Terms

Counting and quantities are building blocks to higher math skills, such as order of operations and geometry. Terms found in a counting and cardinality list include:

**array**- set of numbers or objects in rows and columns**cardinal numbers (cardinality)**- number words that mark quantity (e.g.*one, two, three*)**digits**- numerals found in all numbers; includes one-digit numbers (e.g. 0, 7, 4) and multi-digit numbers (e.g. 12, 284, 5746)**equal**- having the same value**greater than**- having a higher value**less than**- having a lower value**numeral**- written symbol that indicates a value (e.g. 1, 2, 3)__one-to-one correspondence__- understanding that numbers correspond to quantities (e.g. five apples, sixteen cars)**ordinal numbers (ordinality)**- number words that mark an item’s position in a sequence (e.g.*first*,*second, third*)**sequence**- collection of numbers or objects in a particular order

## Operations and Algebraic Thinking Terms

Addition, subtraction, multiplication, and division are known as the order of operations. Students need to know the basic terms for these skills, including:

**addend**- the two numbers added together in an addition problem**addition**- combining two numbers to make a new total (sum)**algebra**- branch of mathematics in which students solve for the value of variables (symbols or letters)**arithmetic**- the study of numerical quantity using counting and operations (addition, subtraction, multiplication, division)**associative property**- mathematical property by which three or more numbers can be grouped in any way and still have the same sum (addition) or product (multiplication)**average**(**mean**) - the sum of numbers divided by the count of numbers**commutative property**- mathematical property that states that numbers can be added or multiplied in any order and still have the same answer**compose**- putting a number back together from sets of ones, tens, hundreds, etc.**composite number**- any number that can be divided by more numbers than 1 and itself (opposite of a prime number)**difference**- the result of a subtraction problem**distributive property**- mathematical property by which the sum of two numbers multiplied by a third number is equal to the products of the first two numbers individually multiplied by the third number**dividend**- number being divided into parts**division**- process of dividing one number into a set number of parts**divisor**- number that divides the dividend into parts**equation**- number statement that shows two equal expressions on either side of an equal sign**even number**- any number that is divisible by 2**factor**- number that divides into another exactly (e.g. 3 is a factor of 12)**formula**- equation that describes the consistent relationship between variables (e.g. the formula for volume: V = lwh)**identity property**- mathematical property by which the sum of any number and 0 is itself (in addition), and the product of any number and 1 is itself (multiplication)**integer**- whole number (including zero)**minuend**- the top number in a subtraction equation; the number that is subtracted from**multiplicand**- each number in a multiplication problem**multiplication**- repeated addition of one number a set amount of times**odd number**- any number that can’t be divided by 2**operation**- addition, subtraction, multiplication, or division**order of operations**- the order in which you solve an algebraic equation (Parentheses, Exponents, Multiplication, Division, Addition, Subtractions — also known as__PEMDAS__)**parentheses**(also**brackets**or**braces**) - symbols that indicate multiplication in an equation, or group numbers to be calculated first in the order of operations**product**- the result of a multiplication problem**prime number**- number that is only divisible by itself and 1**quotient**- result of a division problem**remainder**- the amount left over when a divisor does not divide evenly into a dividend**subtraction**- one number minus or taking away another number.**subtrahend**- the number subtracted from the first number in a subtraction problem**sum**- the result of an addition problem**variable**- letter that represents the value that one must solve an equation to find**whole number**- a number without fractions; a number that has all the parts of a whole

## Number and Operations Terms

Basic number and operations concepts include base ten, fractions, place value, and __decimals__. Math terms in this glossary category include:

**algorithm**- a procedure that carries an operation out in steps**base ten**- number system (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) in place value positions**decimal**- real number from the base 10 number system that represents a fraction using place value (e.g. 2.73, 0.453)**denominator**- the bottom part of a fraction; how many parts are in a whole**equivalent**- equal in value or amount**expanded form**- way of writing out a multi-digit number by its place value (e.g. the expanded form of 736 is 700 + 30 +6)**exponent**- superscript number that indicates repeated multiplication of a number**fraction**- a number that is not whole; one part (numerator) is present over the whole (denominator)**irrational number**- number than cannot be expressed as a decimal because its digits are infinite (e.g. π)**mixed number**- whole numbers combined with fractions (e.g. 3 ¼)**non-zero**- number that is not zero**number line**- line with__positive and negative__numbers assigned to various points**numerator**- top part of a fraction; the part present of a whole**place value**- numerical value of a digit based on its position in a number (e.g. tens place, hundredths place)**rational number**- number that can be expressed as a fraction or decimal

## Measurement and Data Terms

Measurement and data includes measuring the attributes of a shape to find its area, volume, mass, or perimeter. It also includes measuring time, creating __bar graphs__, and calculating amounts of money. Common measurement and data terms include:

**analog clock**- traditional clock face with hour, minute, and second hands**area**- two-dimensional space taken up by a shape (measured in square units)**bar graph**- visual representation of data using bars of different heights or widths**cubic unit**- unit cube; unit for measuring volume in three-dimensional spaces**data point**- unit of information that can be graphed**data set**- collection of data points that can be graphed**digital clock**- clock that displays the hour and minute digitally**distance**- measurement of space between two objects or locations__extrapolation__- the process of estimating an unknown value that exists outside a sequence of data points**height**- vertical measurement between the base of an object and its top**length**- measurement of a figure or object from end to end**line plot**- number line graph that shows frequency of data**measurable attribute**- characteristic that allows a shape or object to be measured (height, width, depth)**money math**- math equations that use units of money**perimeter**- total distance around a shape**picture graph**- graph that uses images or symbols to represent data points**time interval**- amount of time between two set points, indicated in units of time (seconds, minutes, hours)**unit conversion**- converting a unit of measurement into another unit with multiplication or division**unit square**- square unit; unit for measuring area of a two-dimensional shape**volume**- measurement that indicates how much space an object occupies**width**- horizontal measurement that indicates how wide an object or figure is

## Geometry Terms

Sharpen your geometry knowledge by __identifying shapes__ and learning basic terminology:

**2-D shapes**- flat figure with two dimensions (length and width); also known as a**figure****3-D shapes**- solid figure with three dimensions (length, width, and depth)**angle**- two rays that share the same endpoint and are identified by their degrees (e.g. right angles measure exactly 90º, acute angles measure less than 90º)**axes**- the perpendicular lines on a coordinate plane (*x*-axis and*y*-axis)**circumference**- total distance around a circle**coordinate**- an ordered pair of numbers that notes a point’s location on a coordinate plane (e.g. -4, 6; 3, -7)**coordinate plane**- plane created by two perpendicular lines (axes) that meet at the origin; area where students can graph coordinate pairs**defining attributes**- characteristics that define a specific shape (e.g. number of sides or angles)**degree**- unit of an angle’s measure noted with the º sign (0 - 360º)**fourth**- one piece of four (the whole); half of a half; a quarter**geometry**- study of shapes and sizes of figures, as well as their lines, angles, and properties**half**- one equal part of a shape or number divided into two parts__line__**line segment**- straight path with two endpoints**non-defining attributes**- characteristics that don’t define a specific shape (e.g. color, size)**orientation**- position of a shape or figure**parallel lines**- two lines that are always the same distance apart and never intersect**parallelogram**- four-sided figure with opposite parallel sides**perpendicular line**- two lines that intersect at a 90º (right) angle**plane**- flat surface joined by a set of points**point**- a position on a plane, joined by a line**polygon**- shape created by connected line segments**quadrant**- a quarter of a plane that’s divided into four sections**quadrilateral**- four-sided figure**radius**- length of a line segment between the center of a circle and its perimeter**ray**- straight line with one endpoint**side**- line segment between two vertices of a two-dimensional shape, or a face of a three-dimensional shape**vertices**- angular points of a shape

## Ratios and Proportional Relationships

Ratio and proportional relationship terms apply to statistics and probability later on. Some math words relating to ratios and proportional relationships include:

**event**- an outcome of probability**frequency**- number of times an event can occur in a period of time**linear association**- proportional relationships between two variables in which one change affects each variable equally; when graphed, these variables form a straight line**negative association**- proportional relationships in which one variable changes in the opposite direction as another variable**nonlinear association**- proportional relationship in which a change in one variable does not equally affect another variable**odds**- likelihood of an event happening, measured in a ratio (the likelihood:total possibilities); also known as**probability****outliers**- data point that differs from the behavior of the rest of a data set**percent**- parts of 100 (the whole); fraction with 100 as the denominator**probability**- likelihood of an event happening; also known as**odds****proportional relationship**- connection between two variables with equivalent ratios**positive association**- proportional relationship in which a change in one variable causes its value and the value of another variable to increase**rate**- occurrence of an event over a specified period of time**ratio**- comparison of values between two amounts**relative frequency**- number of times an event can occur divided by all possible outcomes**scatter plot**(scatter chart, scatter graph) - graph that uses dots to represent numeric variables between vertical and horizontal axes