Absolute Value
A number's distance from zero on a number line. The absolute value of 4, written |4|, and the absolute value of -4, written |-4|, are both equal to 4.


Acute Angle
An angle with a measure of less than 90 degrees.


Additive Identity
Adding the number zero does not change a number's vale (e.g. 5 + 0 = 5).


Additive Inverse Property
A number and its additive inverse have a sum of zero (e.g. in the equation 3 + -3 = 0 both the number 3 and -3 are additive inverses).


Algebraic Equation
A mathematical sequence in which two expressions are connected by an equality symbol (e.g. x^2 = 8x + 9).


Algebraic Expression
An expression containing numbers and variables (e.g. 7x) and operations that involve numbers and variables (e.g. 2x + y or 3a - 4). Algebraic expressions do not contain equality or inequality symbols (e.g. = < >).


Algebraic Order of Operations
The order in which to complete algebraic operations within an expression.  Begin with anything inside grouping symbols (e.g. parenthesis), and anything above and below fraction bars.  Compute from left to right in the following order:  FIRST exponents (e.g. x^2), SECOND multiplication and division (e.g. 3 x 4 or 7 ÷ 8), THIRD addition and subtraction (e.g. 1 + 2 or 3 - 4).


Algebraic Rule
A mathematical expression that contains variables and describes a pattern or relationship.


The shape made by two rays extending from a common end point, the vertex. Measures of angles are described using the degree system.


The inside region of a two-dimensional figure measured in square units (e.g. a rectangle with sides of 4 units by 6 units contains 24 square units or has an area 24 square units).


Associative Property
The way in which three or more numbers are grouped for addition or multiplication does not change their sum or product (e.g. 2 + 3 = 3 + 2 or 4 x 7 = 7 x 4).


The horizontal and vertical number lines used in a rectangular graph or coordinate grid system.


The line or plane upon which a figure is thought of as a resting.


A zigzag on the line of the x- or y-axis in a line or a bar graph indicating that the data being displayed does not include all of the values that exist on the number line being used. Also called a Squiggle.


The amount of space that can be filled. Both capacity and volume are used to measure three-dimensional spaces.  However, capacity usually refers to fluids, whereas volume usually refers to solids.


The perimeter of a circle is called its circumference.  Equal to twice the radius of the circle multiplied by Pi, or C = 2 π r.


Closed Figure
A two-dimensional figure whose beginning and ending points meet, such that the plane in which the figure lies is divided into two parts -- the part inside the figure and the part outside the figure (e.g. circles, squares, rectangles).


Commutative Property
The order in which two numbers are added or multiplied does not change their sum or product (e.g. 2 + 3 = 3 + 2 or 4 x 7 = 7 x 4).


Complementary Angles
Two angles, the sum of which is exactly 90 degrees.


A whole number that has no more than two factors.


Concrete Representations of Numbers
Having a definite form or relating to an actual thing.


Figures or objects that are the same shape and the same size.


Coordinate System (Grid)
A network of evenly spaced, parallel horizontal and vertical lines especially designed for locating points, displaying data, or drawing maps.


Numbers that correspond to points on a coordinate system or graph in the form (x , y).


Customary Units
The units of measure developed and used in the United States. Customary units for length are inches, feet, yards and miles. Customary units for volume are cubic inches, cubic feet, and cubic yards. Customary units for capacity or fluid ounces, cups, pints, quarts, and gallons.


Data Displays
Different ways of displaying data in tables, charts, or graphs, including pictographs, circle graphs, single, double, or triple bar and line graphs, histograms, stem-and-leaf plots, and scatter plots.


Decimal Number
Any number written with a decimal point in the number. A decimal number falls between two whole numbers (e.g. 1.5 falls between 1 and 2). Decimal numbers smaller than 1 are sometimes called decimal fractions (e.g. three-tenths is written 0.3).


A line segment from any point on the circle passing through the center to another point on the circle.


Direct Measure
Obtaining the measure of an object by using measuring devices, either standard devices of the customary or metric systems, or nonstandard devices such as a paper clip or pencil.


Distributive Property
For any real numbers a, b, and x the expression x(a + b) can be written as ax + bx.


Effects of Operations
The results of applying an operation to given numbers (e.g. adding two whole numbers results in a number greater than or equal to the original numbers).


An increase in size in all directions by a uniform amount.


A mathematical sentence (e.g. 2x = 10) that equates one expression 2x to another expression 10.


Equivalent Expressions
Expressions that have the same value but are represented in a different format using the properties of numbers (e.g. ax + bx = x(a +b)).


Equivalent Forms of a Number
Expressions that have the same value but are represented in a different format using the properties of numbers (e.g., ax + bx = x(a + b)).


The use of rounding and/or other strategies to determine a reasonably accurate approximation, without calculating an exact answer.


Evaluate an Expression
Substitute numbers for variables in the expression and follow the operation symbols to find the numerical value of the expression.


Explain in Words
Directions requesting a written description of the procedures for finding the solution to the problem presented.


Exponent (Exponential Form)
The number of times the base occurs as a factor. For example, 2^3 is the exponential form of 2 x 2 x 2. The numeral two is called the base, and the numeral three is called the exponent.


A collection of numbers, symbols, and/or operation signs that stands for a number.


To estimate or infer a value or quantity beyond the known range.


One of the plane surfaces bounding a three-dimensional figure (a side).


A number or expression that divides exactly another number (e.g. 1, 2, 4, 5, 10 and 20 are factors of 20).


Finite Graph
A graph having definable limits.


A transformation that produces the mirror image of a geometric figure. Also called a reflection.


Any part of a whole is called a fraction (e.g. one-half written in fractional form is 1/2.


The relationship between two sets (e.g. sets of numbers) in which each element of one set has one assigned element in the other set.


Function table
A table of x- and y-values (ordered pairs) that represents the function, pattern, relationship, or sequence between the two variables.



A network of evenly spaced, parallel horizontal and vertical lines.


A line segment extending from the vertex or apex of a figure to its base and forming a right angle with the base or basal plane.


A proposition or supposition developed to provide a basis for further investigation or research.


Indirect Measure
Obtaining the measurement of an object through the known measure of another object.


A sentence that states one expression is greater than or equal to, less than, less than or equal to another expression (e.g., A is not = 5 or x < 7 ).


The numbers in the set {...,-4, -3, -2, -1, 0, 1, 2, 3, 4,...}.


The value of a variable when all other variables in the equation equal zero. On a graph, the values where a function crosses the axes.

The point at which two lines meet.


Inverse Operation
An action that cancels a previously applied action. For example, subtraction is the inverse operation of addition.


Irrational Number
A real number that can not be expressed as a ratio of two numbers (e.g. 20 = 2(w+4) + 2w and y = 3x + 4).


Labels (for a Graph)
The titles given to a graph, the axes of a graph, or to the scales on the axes of a graph.


A one-dimensional measure that is the measurable property of line segments.


The chance that something is likely to happen.

A straight line that is endless in length.


Line Segment
A portion of a line that has a defined beginning and end (e.g. the line segment AB is between point A and point B).


Linear Equation
An algebraic equation in which the variable quantify or quantities are in the first power and the graph is a straight line (e.g. 20 = 2(w + 4) + 2w and y = 3x + 4).


The arithmetic average of a set of ordered numbers where half of the numbers are above the median and half are below it.


The middle point of a set of ordered numbers where half are below it.


Metric Units
The units of measure developed in Europe and used in most of the world. Like the decimal system, the metric system uses the base 10. Metric units for length are millimeters, centimeters, meters, kilometers. Metric units for weight are milligrams, grams, and kilograms. Metric units for volume are cubic millimeters, cubic centimeters, and cubic meters. Metric units for capacity are milliliters, centiliters, liters, and kiloliters.


Midpoint of a Line Segment
The point on a line segment that divides it into two equal parts.


The score or data point found most often in a set of numbers.


The numbers that result from multiplying a given number by the set of whole numbers (e.g. the multiples of 15 are 0, 15, 30, 45, 60, 75, etc . . .).


Multiplicative Identity
The number one, that is, multiplying by 1 does not change a number's value          (e.g. 5 x 1= 5).


Multiplicative Inverse (Reciprocal)
Any two numbers with a product of 1. (e.g. 4 and 1/4).


Natural Numbers (Counting Numbers)
The numbers in the set {1, 2, 3, 4, 5, ...}.


Negative Exponent
Used in scientific notation to designate a number smaller than one (e.g. 3.45 x 10^-2 equals 0.0345).


Nonstandard Units of Measure
Units such as blocks, paper clips, crayons, or pencils that can be used to obtain a measure.


Number Line
A line on which numbers can be written or visualized.


Obtuse Angle
An angle with a measure of more than 90 degrees but less than 180 degrees.


The ratio of an event occurring to it not occurring.


Any mathematical process, such as addition, subtraction, multiplication, division, exponents, or square roots.

Operational Shortcut

A method having fewer arithmetic calculations.


Ordered Pair
The location of a single point on a rectangular coordinate system where the digits represent the position relative to the x-axis and y-axis [e.g. (x,y) or (3,4)]


Organize Data
To arrange data in a display that is meaningful and that assists in the interpretation of the data.


Parallel Lines

Two lines in the same plane that never meet. Also, lines with equal slopes.


A predictable or prescribed sequence of numbers, objects, etc. Patterns and relationships may be described or presented using manipulatives, tables, graphics (pictures or drawings), or algebraic rules (functions).


A special-case ratio in which the second term is always 100. The ratio is written as a whole number followed by a percent sign (e.g. 25% means the ratio of 25 to 100).


The length of the boundary around a figure.


Forming a right angle.


Pi (π)
The symbol designating the ratio of the circumference of a circle to its diameter, represented approximately as either the decimal 3.1415 or the fraction 22/7.


Place Value
The position of a single digit in a whole number or decimal number containing one or more digits.


Planar Cross Section
The intersection of a plane and a three-dimensional figure.

An undefined, two-dimensional (no depth) geometric surface that has no boundaries specified. A plane is determined by defining points or lines existing on the plane.


Plane Figure
A two-dimensional figure that lies entirely within a single plane.


A location in space that has no length or width.


A closed plane figure whose sides are straight lines and do not cross.


Prime Number
Any whole number with only two factors, 1 and itself (e.g. 2, 3, 5, 7, 11, etc . . .).


A three-dimensional figure (polyhedron) with congruent polygonal bases and lateral faces that are all parallelograms.


The likelihood of an event happening. An impossible event has a probability of zero. An event that will occur with absolute certainty is assigned a probability of one. Every event that is neither certain nor impossible has a probability that is between zero and one, and is obtained by dividing the number of favorable outcomes of an event by the total number of possible outcomes.


Probability, Empirical
The likelihood of an event happening that is based on experience and observation rather than on theory.


Probability, Theoretical
The likelihood of an event happening that is based on theory rather than on experience and observation.


A set of steps that demonstrates the truth of a given statement. Each step can be justified with a reason, such as a given, a definition, an axiom, or a previously proven property.


Pythagorean Theorem
The square of the hypotenuse (c) of a right triangle is equal to the sum of the square of the legs (a and b), as shown by the equation a^2+b^2=c^2.


Any of the four regions formed by the axes in a rectangular coordinate system.


Radical Sign
The symbol used before a number to show that the number is radicand.


A number that appears with a radical sign.


A line segment extending from the center of a circle or sphere to a point on the circle or sphere.


Range of a Set of Numbers
The difference between the highest (H) and the lowest (L) value in a set of data.  Also, the values that a function takes when evaluated over a domain.



Calculations involving rates, distances, and time intervals, based on the distance, rate, time formula D = r t.


The compression of two quantities (e.g. the ratio of a to b is a/b, where b doesn't equal zero).


Rational Number
A real number that can be expressed as a ratio of two integers.


A portion of a line that begins at a point and goes on forever in one direction.


Real Numbers
All rational and irrational numbers.


see Multiplicative Inverse


see Flip

Reflexive Axiom of Equality
A number or expression is equal to itself (e.g. ab = ab).


Regular Polygon
A polygon that is both equilateral and equi-angular.


Relation (Relationship)
see Pattern


Relative Size
The size of one number in comparison to the size of another number or numbers.


Right Angle
An angle whose measure is exactly 90 degrees.


Right Circular Cylinder
A cylinder in which the bases are parallel circles perpendicular to the side of the cylinder.


Right Triangle Geometry
Finding the measures of missing sides or angles of a right triangle when given the measures of other sides or angles. See Pythagorean Theory


The change in y going from one point of y to another (the horizontal change on the graph).


A transformation of a figure by turning it about a center point or axis. The amount of rotation is usually expressed in the number of degrees (e.g. a 90 degree rotation). Also called a Turn.


A mathematical expression that describes a pattern or relationship, or a written description of the pattern or relationship.


The change in x going from one point of y to another (the horizontal change on the graph).


Scale Model
A model or drawing based on a ratio of the dimensions for the model and the actual object it represents (e.g. a map).


The numeric values assigned to the axes of a graph.


Scatter Plot
A graph of data points, usually from an experiment, that is used to observe the relationship between two variables.


Scientific Notation
A shorthand method of writing very large or very small numbers using exponents in which a number is expressed as the product of a power of 10 and a number that is greater than or equal to one and less than 10 (e.g. 7.59 x 10^5=759,000). It is based on the idea that is easier to read exponents than it is to count zeros. If a number is already a power of 10, it is simply written 10^27 instead of 1 x 10^27.


An ordered list with either a constant difference (arithmetic) or a constant ratio (geometric).


The edge of a geometric figure (e.g. a triangle has three sides).


Similar Figures
Two figures that are the same shape, have corresponding, congruent angles, and having corresponding sides that are proportional in length.


Figures that are the same shape are similar; they are not necessarily the same size or in the same position.


To move along in constant contract with the surface in a vertical, horizontal, or diagonal direction. Also called a Translation


The incline of a line, defined by the ratio of the change in units on the vertical axis to the change in one unit on the horizontal axis.


Solid Figures
Three-dimensional figures that completely enclose a portion of space (e.g. a rectangular solid, cube, sphere, right circular cylinder, right circular cone, and regular square pyramid).


Spatial Relationships
Relationships of figures existing or happening in space.


Square Root
A positive real number that can be multiplied by itself to produce a given number (e.g., the square root of 144 is 12 or √144 = 12).


see Break

Standard Units of Measure
The measurement of an object by using accepted measuring devices and units of the customary or metric system.


Straight Angle
An angle whose measure is exactly 180 degrees.


Supplementary Angles
Two angles, the sum of which is exactly 180 degrees.


Surface Area of a Geometric Solid
The sum of the area of the faces of the figure that create the geometric solid.


Symbolic Expression
A symbol or set of symbols expressing a mathematical quantity or operation (e.g. 2x is equal to two times x).


Symbolic Representations of Numbers
Being expressed by symbols (e.g. circles shaded to represent 1/4, or variables used to represent quantities).


When a line can be drawn through the center of a figure such that the two halves are congruent.


Systems of Equations
A group of two or more equations that share variables. The solution to a system of equations is an ordered number set that makes all of the equations true.


A covering of a plane with congruent copies of the same pattern with no holes and no overlaps, like floor tiles.


An operation on a geometric figure by which another image is created. Common transformations include flips, slides, and turns.


Transitive Property
When the first element has a particular relationship to a third element that in turn has the same relationship to a third element, the first has this same relationship to the third element (e.g. if a = b and b = c, then a = c). Identity and equality are transitive relationships.


see Slide


Tree Diagram
A diagram in which all the possible outcomes of a given event are displayed.


see Rotation


Unorganized Data
Data that are presented in a random manner.


Any symbol that could represent a number.


The common endpoint from which two rays begin (e.g. the vertex of an angle) or the point where two lines intersect; the point on a triangle or pyramid opposite to and farthest from the base.


Vertical Angles
The opposite angles formed when two lines intersect.


The amount of space occupiedin three dimensions and expressed in cubic units. Both capacity and volume are used to measure empty spaces; however, capacity usually refers to fluids, whereas volume usually refers to solids.


Measures that represent the force that attracts an object to the center of Earth. In the customary system, the basic unit of weight is the pound.


Whole Numbers
The numbers in the set {0, 1, 2, 3, 4,...}.


X Intercept
The value of x on a graph when y is zero. The x-axis is the horizontal number line on a rectangular coordinate system.


Y Intercept
The value of y on a graph when x is zero. The y-axis is the vertical number line on a rectangular coordinate system.