It may not seem like the case, but math never changes. School curriculum often adds perspectives and processes, but basic math concepts are always consistent. Understanding these terms helps students internalize math concepts and build on them in later grades. Keep reading for definitions of basic elementary math terms.

# Basic Math Terms for Elementary Students Explained

## Basic Math Terms and Their Meanings

The Common Core standards separate elementary math concepts into five categories: *counting and cardinality, operations and algebraic thinking, number and operations, measurement and data, and geometry*. While there are specific terms associated with each concept, a strong mathematical education bridges math skills across them all. Check out the common terms found in these concepts and see if they help you understand mathematics a little better.

### Counting and Cardinality Terms

*Counting and cardinality* is primarily a preschool and kindergarten skill. It’s a building block to higher math skills, such as order of operations and geometry. Terms found in counting and cardinality include:

**array**– set of numbers or objects in rows and columns**cardinal numbers (cardinality)**– number words that mark quantity (e.g.*one, two, three*)**digit**– 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 number 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 basics of these skills before they move on to more complex algebraic functions. They need to know the following operations and algebraic thinking terms:

**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)**counting on**– addition strategy in which learners start from one addend and add the second addend by ones to find the sum**decompose**– taking a number apart into sets of ones, tens, hundreds, etc.**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)**factor pair**– two numbers that multiply into one product, and are evenly divided by that product (e.g. 3 and 4 are factors 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)**make a ten**– addition strategy in which you solve an equation by making a ten-group**mental computation**– working out a mathematical equation mentally**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)**parentheses**(also**brackets**or**braces**) – symbols that indicate multiplication in an equation, or group numbers to be calculated first in the order of operations**PEMDAS**– acronym used to remember the order of operations in algebra (Parentheses, Exponents, Multiplication, Division, Addition, Subtractions)**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

Number and operations concepts in elementary school include both *base ten *and fraction skills. Older elementary learners work with* place value* and *decimals* as well. Here are some number and operations terms that elementary math students should know:

**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**bundle of ones**– place value technique in which learners decompose a ten into ten ones**bundle of tens**– place value technique in which learners decompose a hundred into ten tens**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**estimating**– problem-solving strategy in which learners find a general, inexact solution to an equation without fully working it out**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 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**rounding**– form of estimation in which a number less than five “rounds down” to the nearest zero, and a number greater than or equal five “rounds up” to the higher zero (e.g. 77 rounds up to 80; 33 rounds down to 30)**skip counting**– any counting process that is not counting by ones (e.g. counting by twos, fives, tens, etc.)

### Measurement and Data Terms

Measurement and data includes measuring the attributes of a shape to find its *area, volume, mass*, or *perimeter*. But it also includes measuring time, creating bar graphs, and calculating amounts of money. Check out these measurement and data terms:

**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**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**put-together/take-apart problems**– addition problems that often have an unknown addend**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

Geometry knowledge doesn’t start in high school. Elementary students start by identifying shapes and move on to *coordinate planes* and *vertices*. See how many elementary geometry terms you know, and learn more about the rest:

**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**– straight path that extends in two directions, joining various points along the path**line of symmetry**– dividing line that splits a shape into two equal, symmetrical parts**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

Elementary students study* ratios* and *proportional relationships *starting in sixth grade. They continue the concept in secondary school, and apply the concepts to *statistics* and *probability*. Some elementary terms 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

## Teaching Math Vocabulary

Students should have a strong understanding of math vocabulary throughout their education. Young learners who know about the relationship between major math concepts go on to find success as mathematicians, engineers, physicists, technicians, computer scientists, and more. Find new ways to teach math terms in the classroom with these helpful math vocabulary lesson plans.

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