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.
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. However, capacity usually refers to
fluids, whereas volume usually refers to solids.
Circumference
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.
Composite
A whole number
that has no more than two factors.
Concrete Representations
of Numbers
Having a definite form or relating to an actual thing.
Congruent
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.
Coordinates
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).
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 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).
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 = 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)).
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 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.
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, 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
1/2.
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.
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 is 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. 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.
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, 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.
Odds
The ratio of an event occurring to it not occurring.
Operation
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.
Pattern
(Relationship)
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).
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 (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.
Plane
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.
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 by
the equation a^2+b^2=c^2.
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 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.
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 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.
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 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
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 mathematical 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 drawing 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 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.
Sequence
An ordered list with either a constant difference (arithmetic) or a
constant ratio (geometric).
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 corresponding 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 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).
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 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).
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 (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.
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. 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. |