Congruent 
Having
the same shape and the same size. 


Conjecture 
A
statement believed to be true but not proved. 


Coordinate system 
A
method of locating points in the plane or in space by means of numbers. A point in the
plane is located by its distances from both a horizontal and a vertical line called the
axes. The horizontal line is called the xaxis. The vertical line is called the yaxis.
The pairs of numbers are called ordered pairs. The first number, called the x coordinate,
designates the distance along the horizontal axis. The second number, called the
ycoordinate, designates the distance along the vertical axis. The point at which the two
axes intersect has the coordinates (0,0) and is called the origin. 


Correlation 
A
measure of the mutual relationship between two variables. 


Customary system 
A
system of weights and measures frequently used in the United States. The basic unit of
weight is the pound; the basic unit of capacity is the quart. 


Deductive reasoning 
The
process of reasoning from statements accepted as true to reach a conclusion. 


Direct variation 
When
two variables are so related that their ratio remains constant, one of them is said to
vary directly as the other. 


Domain 
The
set of all possible replacements for the placeholder in an open sentence. 


Equation 
A
statement of equality between two mathematical expressions. (e.g., X + 5 = Y 2). 


Equivalent forms 
Different
forms of numbers that name the same number; e.g., fraction, decimal, percent as 1/2, .5,
50%. 


Exponential function 
A
function whose general equation is y = a x b^{x} or
y = a x bk^{x}, where a, b, and k stand for constants. 


Exponent 
A
numeral used to tell how many times a number or variable is used as a factor. (e.g., a^{2},
2^{n}, y^{x}). 


Expression 
A
mathematical phrase that can include operations, numerals, and variables. In algebraic
terms: 2l + 3x; in numeric terms: 13.4  4.7. 


Factor 
The
numbers or variables multiplied in a multiplication expression. 


Factorial 
The
expression n! (n factorial) is the product of all the numbers from 1 to n for any positive
integer n. 


Function 
A
relation in which each value of an independent variable takes on a unique value of the
dependent value. 


Geoboard 
A
board with pegs aligned in grid fashion which permits rubber bands to be wrapped around
pegs to form geometric figures. 


Graphing calculator 
A
calculator that will store and draw the graph of several functions at once. 


Independent events 
Events
such that the outcome of the first event has no effect on the probabilities of the outcome
of the second event. (e.g., two tosses of the same coin are independent events). 


Inductive reasoning 
Forming
generalizations from particular observations in a common occurrence. 


Inequality 
A
mathematical sentence that contains a symbol; such as, >, <, >, <, or = and in
which the terms on either side of the symbol are unequal. (e.g., x < y, 7 >3, n >
4). 


Infinite 
Has
no end or goes on forever. 


Integer 
A
number that is a positive whole number, a negative whole number, or zero. 


Inverse 
A
new conditional formed by negating both the antecedent and the consequent of a conditional 


Inverse operations 
Operations
that undo each other. (e.g., addition and subtraction are inverse operations,
multiplication and division are inverse operations). 


Inverse variation 
When
the ratio of one variable to the reciprocal of the other is constant, one of them is said
to vary inversely as the other. 


Irrational number 
A
number that cannot be written as a simple fraction. It is an infinite and nonrepeating
decimal. 


Limit 
A
number to which the terms of a sequence get closer so that beyond a certain term all terms
are as close as desired to that number. 


Line of best fit 
The
line that fits a set of data points with the smallest value for the sum of the squares of
the errors (vertical distances) from the data points to the line. Also called the
regression line. 


Linear function 
A
function whose general equation is y = mx + b, where m and b stand for constants, and m =
0. 


Linear measurement 
Measurement
in a straight line. 


Logarithm 
The
exponent indicating the power to which a fixed number, the base, must be raised to produce
a given number. For example, if n^{x} = a, the logarithm of a, with n as the base,
is x; symbolically, log_{n}a = x. If the base is 10, the log of 100 is 2 or 10^{2}. 


Manipulatives 
Materials
that allow students to explore mathematics concepts in a concrete mode. 


Mathematical induction 
A
formal method of proving that a statement about a positive integer n is true for all
positive integers n, by: 1) proving that the statement is hue for the first integer, then
, 2) proving that if the statement is true for n, it must be true for (n1). 


Mathematical mode 
A
representation in the mathematical world of some phenomenon in the real world. It
frequently consists of a function or relation specifying how two variables are related. 


Matrix 
A
rectangular array of numbers representing such things as the coefficients in a system of
equations arranged in rows and columns. 


Maximum 
The
greatest number in a set of data. 


Mean 
The
mean of a set of numbers is the sum of the set of numbers divided by n, the number of
numbers in the set. 


Median 
The
number that lies in the middle when a set of numbers is arranged in order. If there are
two middle values, the median is the mean of these values. 


Metric system 
A
system of measurement used throughout the world based on factors of 10. It includes
measures of length, weight, and capacity. 


Minimum 
The
least number in a set of data. 


Missing addend 
A
member of an addition number sentence in which that term is missing. (e.g., 5 + _ = 8). 


Mode 
The
number(s) which occurs most often in a set of numbers. (e.g., in the set 1, 2, 3, 3, 5, 8;
the mode is 3). 


Multiple 
A
number which is the product of a given integer and another integer. (e.g., 6 and 9 are
multiples of 3). 


Normal curve 
A
graph describing the normal distribution in which more scores are found in the center and
fewer scores are found at the extremes. 


Onetoone
Correspondence 
When
one and only one element of a second set is assigned to an element of a first set, all
elements of thc second set are assigned, and every element of the first set has an
assignment, the mapping is called onetoone. (e.g., in the set Bill Clinton, George Bush,
Ronald Reagan, Jimmy Carter, Hillary Clinton, Barbara Bush, Nancy Reagan, and Rosalynn
Carter, there is a onetoone correspondence between the pairs.) 


Open sentence 
A
statement that contains at least one unknown. It becomes true or false when a quantity is
substituted for the unknown. (e.g.,x + 5 = 9, y  2 = 7). 


Order of operations 
Rules
for evaluating an expression: work first within parentheses: then calculate all powers,
from left to right; then do multiplications or divisions, from left to right; then do
additions and subtractions, from left to right. 


Patterns 
Regularities
in situations such as those in nature, events, shapes, designs and sets of numbers (for
example, spirals on pineapples, geometric designs in quilts, the number sequence 3, 6, 9,
12,...). 


Permutation 
An
arrangement of a given number of objects from a given set. 


Perpendicular lines 
Two
lines which intersect to form right angles. 

(e.g.) 


Plotting points 
Locating
points by means of coordinates, or a curve by plotted points, and to represent an equation
by means of a curve so constructed. 


Polygon 
A
union of segments connected end to end, such that each segment intersects exactly two
others at its endpoints. 




Powers 
A
number expressed using an exponent. The number 53 is read five to the third power or five
cubed. 


Prime 
An
integer greater than one whose only positive factors are 1 and itself. (2, 3, 5, 7, 11,
13, 17, and 19 are prime numbers.) 


Probability 
A
number from 0 to 1 that indicates how likely something is to happen. 


Problem solving 
Finding
ways to reach a goal when no routine path is apparent. 


Proof by contradiction 
A
proof in which, if s is to be proven, one reasons from not s until a contradiction is
deduced; from this it is concluded that not s is false, which means that s is true. 


Proportion 
An
equation of the form a/b = c/d which states that the two ratios are equivalent. 


Quadrilateral 
A
foursided polygon. 


Quartiles 
The
three values that divide an ordered set into four subsets of approximately equal size. The
second quartile is the median. 


Radian 
A
unit of angular measure equal to 1/(2) of
a complete revolution. 


Range (1) 
The
difference between the greatest number and the least number in a set of data. 


Range (2) 
The
set of output values for a function 


Rate of change 
The
limit of the ratio of an increment of the function value at the point to that of the
independent variable as the increment of the variable approaches zero. 


Ratio 
A
comparison of two numbers by division. 


Rational numbers 
Any
number that can be written in the form a/b where a is any integer and b is any integer
except zero. 


Real numbers 
The
set consisting of all rational numbers and all irrational numbers. 


Reasonableness 
Quality
of a solution such that it is not extreme or excessive. 


Reciprocal 
The
fractional number that results from dividing one by the number. 


Rectangular prism 
A
threedimensional figure whose sides are all rectangles, a box. 


Reflection 
A
transformation that produces the mirror image of a geometric figure 


Regression 
The
line that represents the least deviation from the points in a scatter plot of data. 


Regular polygon 
A
polygon in which all sides have the same measure and all angles have the same measure. 


Relation 
A
set of ordered pairs. 


Reliability 
The
extent to which a measuring procedure yields the same results on repeated trials. 


Repeated addition 
A
model for multiplication. (e.g., 2 + 2 + 2 = 3 x 2). 


Rotation 
A
transformation that maps every point in the plane to its image by rotating the plane
around a fixed point. 


Scientific calculator 
A
calculator which represents very large or very small numbers in scientific notation and
with the powering, factorial, square root, negative, and reciprocal keys. 


Scientific notation 
A
way of writing a number of terms of an integer power of 10 multiplied by a number greater
than or equal to 1 and less than 10. 


Sequence 
A
set of ordered quantities. (e.g., positive integers). 


Series 
The
indicated sum of the terms of a sequence. 


Similarity 
Having
the same shape but not necessarily the same size. 


Simple event 
An
event whose probability can be obtained from consideration of a single occurrence. (e.g.,
the tossing of a coin is a simple event). 


Simulation 
Modeling
a real event without actually observing the event. 


Slope 
The
slope of a line is the ratio of the change in y to the corresponding change in x. The
constant m in the linear function equation. Rise/run. 


Standard deviation 
The
square root of the variance. 


Stemandleaf plot 
A
frequency distribution made by arranging data. (e.g., student scores on a test were 98,
96, 85, 93, 83, 87, 85, 87, 93, 75, 77, and 83. This data is displayed in a stemandleaf
plot below. 

9
 8, 6, 3, 3 

8
 7, 5, 5, 3, 3 

7
 7, 5 


Systems of equations 
Two
or n lore equations that are conditions imposed simultaneously on all the variables, but
may or may not have common solutions. (e.g., x + y = 2, and 3x + 2y = 5). 


Symmetry 
A
line of symmetry separates a figure into two congruent halves, each of which is a
reflection of the other. (e.g., 0, the line through the center of the circle divides it
into congruent halves). 


ttest 
A
statistical test done to test the difference of means of two samples. 


Tessellations 
A
repetitive pattern of polygons that covers an area with no holes and no overlaps, like
floor tiles. 


Transformations 
An
operation on a geometric figure by which each point gives rise to a unique image. 


Translations 
A
transformation that moves a geometric figure by sliding each of the points the same
distance in the same direction. 


Tree diagram 
A
diagram used to show the total number of possible outcomes in a probability experiment. 


Trigonometric functions 
A
function (sine, cosine, tangent, cotangent, secant, cosecant) whose independent variable
is an angle measure, usually in degrees or radians. 


Valid argument 
An
argument with the property no matter what statements are substituted in the premises, the
truth value of the form is true. If the premises are true, then the conclusion is true. 


Variable 
A
symbol used to stand for any one of a given set of numbers or other objects. (e.g., in the
equation y = x + 5, y and x are variables). 


Variance 
In
a data set, the sum of the squared deviations divided by one less than the number of
elements in the set (sample variance s^{2}) or by the number of elements in the
set (population variance). 


Vector 
A
quantity that has both magnitude and direction. (e.g., physical quantities such as
velocity and force). 


Venn diagram 
A
display that pictures unions and intersections of sets. 




Volume 
The
amount of space enclosed in a space (3dimensional) figure, measured in cubic units. 


Yintercept 
The
yintercept of a line is the ycoordinate of the point at which the graph of an equation
crosses the yaxis. 



pi,
the ratio of the circumference of a circle to its diameter: about 3.1415926535.
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