Math Vocabulary
Intermediate Grades (3 rd – 5 th )
Introduction
Research shows that students benefit from lessons that explicitly teach math vocabulary. The math words provided will not be the only math words that you and your students will use in the classroom. These words are provided as a starting point for each of the different standards. The words were compiled by using Building Background Knowledge by Robert Marzano, the KSDE assessment vocabulary document, and teacher input. We suggest, as you begin your study of a particular standard, that you pull the words appropriate for your students by using the standards as a guide. As you and your students explore the math concepts and the vocabulary with each standard, you will find that you may need to add words that have not been provided in this packet. We encourage you and your students to add those additional vocabulary words.
This document provides you with a list of mathematical words with their definitions for your level, a few vocabulary strategies, and pages of words that can be displayed. The list of words with the definitions is given for teacher support. Students are not expected to recite the definitions word-for-word, but are expected to understand the concepts of these words and how to use them in their written and oral language. The vocabulary strategies are just a few that you may decide to use when introducing some of the words with your students. The vocabulary pages are intended to be interactive and to be utilized as each unit is taught.
There are various resources that are beneficial to use as vocabulary concerns arise. We recommend any of the Great Source math resource books such as Math at Hand or Math on Call. There are also some excellent websites such as:
A Maths Dictionary for Kids (chers.ash.org.au/jeather/maths/dictionary.html)
which have definitions, pictures and interactive opportunities to assist students with their understanding of mathematical concepts or
Ask Dr. Math (hforum.org/dr.math/). These resources are also beneficial for family support in understanding mathematics.
EXPLORE MATH and HAVE FUN!
Math Words with Definitions
This list of vocabulary words with their definitions is to be used by the teacher as a resource. Students are not expected to memorize these definitions but they are expected to understand the concepts and apply them in mathematics.
(The letters after each vocabulary word indicate the other levels that this word is listed. P = Primary; M = Middle School; H = High School)
Click on “A Maths D i ctionary for Kids” for access to an interactive math dictionary website.
A
addend (P) – any number being added.
addition (P) – to join two or more numbers (or quantities) to get one number (sum).
algorithm (M,H) – a step-by-step method for computing.
angles (M,H) – two rays that share an endpoint.
acute - an angle with a measure less than 90°.
obtuse – an angle with a measure greater than 90° and less than 180°.
right - an angle that measures exactly 90°.
straight – an angle with a measure of 180°.
array (P,M) – an arrangement of objects in equal rows and columns.
attribute – a characteristic (such as size, shape, color, etc.)
axis (M,H) – a reference line from which distances or angles are measured on a coordinate grid.
B
base (M,H) – the bottom line of a plane figure or the bottom face of a solid figure.
C
circumference (M,H) – the distance around the outside (perimeter) of a circle.
combination (M,H) – a group of items or events. Placing these items or events in a different order does not create a new combination. (Example: Coins placed in various different positions does not change the amount of money.)
congruent (M) – having exactly the same size and shape.
coordinate grid/plane (Cartesian plane) (M) – A 2-dimensional system determined by the intersection of two perpendicular number lines in which the coordinates of a point are its distances from the number lines.
coordinates (M,H) - An ordered pair of numbers that give the location of a point in a coordinate grid.
D
data (P) – information (often numerical but can be words) that is usually organized.
data displays (concrete, pictorial, & abstract) – the final product when organizing data.
c hart – an organized list with headings and then lines separating the information.
frequency table (tallies) - A table that shows how often each item, number, or range of numbers occurs in a set of data.
graph – a drawing that shows a relationship between sets of data.
b ar graph – a diagram using labeled axes (categories and scale) with parallel bars showing the frequency of the data.
circle graph – a display using a circle divided into parts (like a pie) to represent the data in relation to the size of the whole circle.
line graph – the data points are connected by lines (most line graphs show changes over time).
picto graph – a display that uses pictures or symbols to compare the data.
scale – the numbers running along a side of the graph.
i nterval – the difference between the numbers from one grid line to another.
line plot – a diagram showing frequency of data on a number line (usually used to show the spread of the data).
single stem & leaf – this display organizes the data so that the numbers themselves make the display. The stem usually will show the numbers in groups of powers of 10 (such as 10’s, 100’s, etc.). The leaves are the numbers from the data set in numerical order running to the right of the stem.
input/output table – a T-table showing the relationship between one number and another.
Venn diagram – a drawing that shows relationships among sets of objects, numbers, shapes, etc.
data set (M) – a collection of related data.
d ecimal point (M) – a dot separating the ones and tenths places in a decimal number.
diagram (M,H) – a drawing that represents a mathematical situation.
diameter (M) – a line (chord) that goes through the center of a circle to touch both sides of the circumference.
difference (P,H) – The amount that remains after one quantity is subtracted from another.
digit (P) – any one of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
digital root (M) – the single digit sum when adding the digits of a standard whole number. (Example: To find the digital root of 524 add all of the digits together ~ 5 + 2 + 4 = 12. This is not a single digit yet so add the digits of that number together ~ 1 + 2 = 3. The digital root of 524 is 3.)
dividend – the quantity to be divided.
divisible (M) – when a quantity can be divided without a remainder. (Digital root gives you clues about the divisibility of a number.)
division – sharing or grouping a quantity into equal parts.
d ivisor – the quantity by which another quantity is to be divided.
E
edge – where two sides of a solid shape meet.
equal (P) – having the same value.
equation (P, M) – a mathematical statement where the left side of the equal sign has the same value as the right side of the equal sign.
equilateral (M) – a shape with all sides the same length.
equivalent (M) – having the same value.
estimation (M) – to find a number close to an exact amount.
even numbers (P) – whole numbers that are divisible by 2. Even numbers have 0, 2, 4, 6, or 8 in the ones place.
expanded notation (form) – a way to write numbers that shows the place value of each digit. (Example: 493 = 400 + 90 + 3)
F
face (M,H) – the flat surface of a solid figure.
fact family (P) – a group of addition/subtraction or multiplication/division facts that uses the same set of numbers in various number sentences.
factor (M) – a number that is multiplied by another number.
fraction (P) – a number showing part of a whole.
n umerator – the top number in a fraction which tells the number of parts selected.
d enominator – the bottom number in a fraction which tells the number of pieces making up a whole.
i mproper fraction – a fraction greater than one whole that is not written as a mixed number.
lowest term/simplest form – a fraction whose numerator and denominator have no common factor greater than 1.
mixed number/mixed fraction – a number written as a whole number and a fraction.
proper – a fraction smaller than one whole.
reduce/simplify – to reduce a fraction to lowest terms.
function (M,H) – gives one output value for each input value.
function table (M) – a table showing the relationship between one number and another.
G
geometry (M) – a strand of mathematics dealing with figures and their parts.
greatest common factor (GCF) (M) – the largest number that will divide evenly into two or more other numbers.
I
inequality (M,H) – not equal in size, amount, or value (usually one of the following symbols is used <, >, ≤, ≥, ≠).
L
least common multiple (LCM) (M) – the smallest common multiple of two or more numbers.
line (M,H) – an infinite set of points forming a straight path extending in two directions.
i ntersecting lines – lines that meet or cross.
p arallel lines – lines that are always the same distance apart.
perpendicular lines – two lines that form a right angle where they intersect.
line segment – a part of a line defined by two endpoints.
M
measurement – the act of measuring or the process of being measured.
(terms, conversions, and tools)
area – the size of the inside of a two-dimensional figure in square units.
c apacity – the maximum amount that a container can hold. Common units of measure: cup, pint, quart, gallon, liter
convert - To express a quantity in alternative units.
l ength – the distance along a line or figure from one point to another.
width – a measure of the distance of an object from side to side.
height – the distance from the base to the top of an object or shape.
Common units of measure: inch, foot, yard, mile, millimeter , centimeter, meter, kilometer,
Common tools: ruler, yardstick, meter stick, tape measure
m ass – the amount of matter in an object. Usually measured by balancing against an object of known mass. Gravity influences weight but not mass.
Common unit of measure: gram
p erimeter – the distance around a figure.
t emperature – amount of heat or cold measured by a thermometer
Common measures: Celsius, Fahrenheit, degree
Common tool: thermometer
time – the way we measure years, days, minutes, etc.
Common units: second, minute, hour, day, year, month, decade, century
Common tools: analog clock, digital clock, stopwatch, calendar
volume – the number of cubic units it takes to fill a 3-dimensional figure.
weight – a measure of the heaviness of an object.
Common units of measure: gram, ounce, pound
Common tool: scale
measures of central tendency – a measure of the “center” of the data. There are three types of these measures: mean, median, and mode. All of these are averages.
mean (M,H) – the number that represents what all of the data items would be if they were leveled out. The mean could also be represented as a point on a number line where the data on either side of the point are balanced.
median (M,H) – the middle value in an ordered data set (if there are two middle values, then it is the mean of those two values).
mode (P,M,H) – the value that occurs most frequently in the data set (there can be one mode {uni-mode}, two modes {bi-modal} or more, or no mode)
maximum value (P) – the value that is the highest in a data set.
minimum value (P) – the value that is the lowest in a data set.
range (P,M,H) – the distance between the highest and lowest data values.
minuend – the number you subtracted from in a subtraction problem.
multiple (M) – the product of any two whole numbers.
multiplicand – the factor in a multiplication problem telling how many groups.
multiplication – the operation of repeated addition.
multiplier – the factor in a multiplication problem telling how many are in each group.
N
negative number (M) – numbers less than zero.
number sentence (P) – an equation (=) or inequality (<,>, ?, ?, ?) with numbers.
number systems – the different subgroups of numbers.
counting/natural numbers – the numbers we naturally count with; 1, 2, 3, 4, 5, . . .
integers – the set of whole numbers and their opposites: . . . ,-2, -1, 0, 1, 2, . . .
real numbers – the combined set of rational and irrational numbers.
whole numbers – the counting numbers plus 0: 0, 1, 2, 3, 4, 5, . . . .
O
odd number (P) – a whole number that can not be divided into 2 equal groups. Odd numbers have 1, 3, 5, 7, or 9 in the ones place.
order of operations (M) - the order in which you compute operations in an expression.
ordered pair – a pair of numbers that gives the coordinates of a point on a grid in this order: (horizontal coordinate, vertical coordinate).
P
pattern (P, M) – a logical sequence of numbers, pictures, shapes, or symbols.
growing (growth)– a type of pattern made by following a certain rule.
repeating – a pattern which has a core (or unit) that happens over and over again indefinitely. The core (or unit) is the shortest string of elements that repeat.