Absolute value

A number's distance from zero (0) on a number line. The absolute value of both 4, written |4|, and negative 4, written |-4|, equals 4.

Acute Angle

An angle with a measure of less than 90 degrees.

Additive identity

The number (0), that is, adding 0 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 (0) (e.g., in the equation 3 + -3 = 0, 3 and -3 are additive inverses of each other).

Algebraic equation

A mathematical sequence in which two expressions are connected by an equality symbol.

Algebraic expression

A mathematical sentence in which two expressions are connected by an equality symbol.

Algebraic order of operations

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.

Algebraic rule

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

Angle

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

Area

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).

Axes

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

Base

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

Break

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.

Capacity

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

Circumference

The perimeter of a circle is called its circumference.

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.

Composite

A whole number that has no more than two factors.

Concrete representations of numbers

Having a definite for or relating to an actual thing.

Congruent

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

Coordinate grid or system

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

Coordinates

Numbers that correspond to points on a 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., five-tenths is written 0.5).

Diameter

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, x(a + b) = 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).

Enlargement

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

Equation

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 = (a +b)x].

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 = (a + b)x].

Estimation

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 the variables 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, 2³ is the exponential form of 2 x 2 x 2. The numeral two (2) is called the base, and the numeral three (3) is called the exponent.

Expression

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

Extrapolate

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

Face

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

Factor

A number or expression that divides exactly another number (e.g., 1, 2, 3, 4, 5, 10, and 20 are factors of 20).

Finite graph

A graph having definable limits.

Flip

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

Fraction

Any part of a whole is called a fraction (e.g., one-half written in fractional form is ½. )

Function

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. See Pattern

Function table

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

Grid

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

Height

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.

Hypothesis

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.

Inequality

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

Integers

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

Intercept

The value of a variable when all other variables in the equation equal zero (0). On a graph, the values where a function crosses the axes.

Intersection

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.

 
Length

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

Likelihood

The chance that something is likely to happen. See Probability.

Line

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).

Mean

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

Median

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.

Mode

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

Multiples

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 (1), 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 (1) (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.

Odds

The ratio of one event occuring to it not occuring.

Operation

Any mathmatical 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. See Data displays.

Parallel lines

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

Pattern (relationship)

A predictable or prescribed sequence of numbers, objects, etc. Patterns and relationships may be described or presented using munipulatives, tables, graphics (pictures or drwings), or algebraic rules (functions). Also called a Relation.

Percent

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).

Perimeter

The length of the boundary around a figure.

Perpendicular

Forming a right angle.

Pi

The symbol designating the ratio of the circumference of a circle to its diameter, represented as either 3.17 or 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.

Plane

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

Plane figure

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

Point

A location in space that has no length or width.

Polygon

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.).

Prism

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

Probability

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.

Proof

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 in the equation c²=a²+b².

Quadrant

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.

Radicand

A number that appears with a radical sign.

Radius

A line segment exrtending 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; sometimes calculated as H - L + 1.

Rate/distance

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

Ratio

The compression of two quantities (e.g., the ratio of a and 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.

Ray

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

Real numbers

All rational and irrational numbers.

Reciprocal

see Multiplicative inverse.

Reflection

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 quilateral and quiangular.

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 theorem.

Rise

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

Rotation

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.

Rule

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

Run

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

Scale model

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

Scales

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 (1) and less than 10 (e.g., 7.59 x 10⁵ = 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 10²⁷ instead of 1 x 10²⁷.

Sequence

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

Side

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 coorisponding sides that are proportional in length.

Similarity

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

Slide

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

Slope

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 figure

Three-dimensional figures that completely enclose a portion of space (e.g., a reatangularsolid, cube, sphere, right circular cylindar, right ciscular 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 =12).

Squiggle

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 mathmatical 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).

Symmetry

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.

Tessellation

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

Transformation

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.

Translation

see Slide.

Tree diagram

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

Turn

see Rotation.

Unorganized data

Data that are presented in a random manner.

Variable

Any symbol that could represent a number.

Vertex

The common endpoint from which two rays begin (i.e., 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 oppisite angles formed when two lines intersect.

Volume

The amount of space occupied in 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.

Weight

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 (0). 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 (0). The y-axis is the vertical number line on a rectangular coordinate system.