Algorithm.An established step-by-step procedure used to achieve a desired result. For example, the 55 addition algorithm for the sum of two two-digit+ 27numbers where carrying is required: 82

**Arbitrary unit (of measure).** A unit that is not part of
the standardized metric or US Customary systems. For example,
using one¿s own shoe size to measure the length of a door
opening or saying that the area of an exhibition hall floor is
¿about the size of two football fields.¿

**Associative property.** When adding or multiplying three
numbers, it doesn¿t matter if the first two or the last two
numbers are added or multiplied first. For example,

3 + 9 + 7 = (3 + 9) + 7 = 3 + (9 + 7) 12 + 7 = 3 + 16 19 = 19 3 x 9 x 7 = (3 x 9) x 7 = 3 x (9 x 7) 27 x 7 = 3 x 63 189 = 189

**Attribute (measurable).** An identifiable property of an
object, set, or event that is subject to being measured. For example,
some of the measurable attributes of a box are its length, weight,
and capacity (how much it holds).

**Box plot.**
A graphic method that shows
the distribution of a
set of data by using the
median, quartiles, and
the extremes of the data set.
The box shows the middle
50% of the data; the longer the box,
the greater the spread of the data.
spread of the data.

**Central tendencies.** A number which in some way conveys
the ¿center¿ or ¿middle¿ of a set of data.
The most frequently used measures are the mean and the median.

**Combinations.** Subsets chosen from a larger set of objects
in which the order of the items in the subset does not matter.
For example, determining how many different committees of four
persons could be chosen from a set of nine persons. (See also,
Permutations)

**Commutative property.** Numbers can be added or multiplied
in either order.

For example, 15 + 9 = 9 + 15; 3 x 8 = 8 x 3.

**Congruence.** The relationship between two objects that have
exactly the same size and shape.

**Correlation.** The amount of positive or negative relationship
existing between two measures. For example, if the height and
weight of a set of individuals were measured, it could be said
that there is a positive correlation between height and weight
if the data showed that larger weights tended to be paired with
larger heights and smaller weights tended to be paired with smaller
heights. The stronger those tendencies, the larger the measure
of correlation.

**Deciles.** The 10th, 20th, 30th, ...90th percentile points
(See definition for Percentile.)

**Direct measurement.** A process of obtaining the measurement
of some entity by reading a measuring tool, such as a ruler for
length, a scale for weight, or a protractor for angle size.

**Dispersion. **The scattering of the values of a frequency
distribution (of data) from an average.

**Distributive property.** Property indicating a special way
in which multiplication is applied to addition of two (or more)
numbers. For example,

5 x 23 = 5 x (20 + 3) = 5 x 20 + 5 x 3 = 100 + 15 = 115.

**Expanded notation.** Showing place value by multiplying each
digit in a number by the appropriate power of 10. For example,
523 = 5 x 100 + 2 x 10 + 3 x 1 or 5 x 10^{2} + 2 x 10^{1} + 3 x 10^{0}.

**Exponential function.** A function that can be represented
by an equation of the form

y = ab^{x} + c, where a, b, and c are arbitrary, but fixed, numbers
and 0 and b > 0 and b≠1.

**Exponential notation (exponent).** A symbolic way of showing
how many times a number or variable is used as a factor. In the
notation 5 ^{3}, the exponent 3 shows that 5 is a factor used three times; that is 5 ^{3} = 5 x 5 x 5 =125.

**Frequency distribution.** An organized display of a set of
data that shows how often each different piece of data occurs.

**Function.** A relationship between two sets of numbers or
other mathematical objects where each member of the first set
is paired with only one member of the second set. Functions can
be used to understand how one quantity varies in relation to (is
a function of) changes in the second quantity. For example, there
is a functional relationship between the price per pound of a
particular type of meat and the total amount paid for ten pounds
of that type of meat.

**Identity.** For addition: The number 0; that is N + 0 = N
for any number N. For multiplication: The number 1; that is, N
x 1 = N for any number N.

**Indirect measurement.** A process where the measurement of
some entity is not obtained by the direct reading of a measuring
tool, or by counting of units superimposed alongside or on that
entity. For example if the length and width of a rectangle are
multiplied to find the area of that rectangle, then the area is
an indirect measurement.

**Integers.** The set of numbers: {..., -6, -5, -4, -3, -2,
-1, 0, 1, 2, 3, 4, 5, 6,...}

**Intercept.** The points where a line drawn on a rectangular-coordinate-system
graph intersect the vertical and horizontal axes.

**Inverse.** For addition: For any number N, its inverse (also
called opposite) is a number -N so that N + (-N) = 0 (e.g., the
opposite of 5 is -5, the opposite of -3/4 is 3/4).

For multiplication: For any number N, its inverse (also called reciprocal) is a number N* so that N x (N*) = 1 (e.g., the reciprocal of 5 is 1/5; the reciprocal of -3/4 is -4/3.

**Line of best fit.**
A straight line used as a
best approximation of a summary of all the
points in a scatter-plot* (See definition
below). The position and slope of the line
are determined by the amount of correlation*
(See definition above) between the two paired
variables involved in generating the
scatter-plot. This line can be used to make
predictions about the value of one of the
paired variables if only the other value in
the pair is known.

**Line plot.**
A graphical display of a set of
data where each separate piece of data is
shown as a dot or mark above a number line.

**Linear equation.** An equation of the form y = ax + b, where
a and b can be any real number. When the ordered pairs (x, y)
that make the equation true for specific assigned values of a
and b are graphed, the result is a straight line.

**Matrix (pl.: matrices).** A rectangular array of numbers,
letters, or other entities arranged in rows and columns.

**Maximum/minimum (of a graph).** The highest/lowest point
on a graph. A relative maximum/minimum is higher/lower than any
other point in its immediate vicinity.

**Mean.** The arithmetic average of a set of numerical data.

**Median.** The middle value of an ordered set of numerical
data. For example, the median value of the set {5, 8, 9, 10, 11,
11,13} is 10.

**Mode.** The most frequently occurring value in a set of data.
For example, the mode of the set {13, 5, 9, 11, 11, 8, 10} is
11.

**Model (mathematical).** A [verb] and a noun. [Generate] a
mathematical representation (e.g., number, graph, matrix, equation(s),
geometric figure) for real world or mathematical objects, properties,
actions, or relationships.

**(Non)-Linear functional relationship. **(See definition of
Function above.) Many functions can be represented by pairs of
numbers. When the graph of those pairs results in points lying
on a straight line, a function is said to be linear. When not
on a line, the function is nonlinear.

**Outlier.** For a set of numerical data, any value that is
markedly smaller or larger than other values. For example, in
the data set {3, 5, 4, 4, 6, 2, 25, 5, 6, 2} the value of 25 is
an outlier.

**Patterns.** Recognizable regularities in situations such
as in nature, shapes, events, sets of numbers. For example, spirals
on a pineapple, snowflakes, geometric designs on quilts or wallpaper,
the number sequence {0, 4, 8, 12, 16,...}.

**Percentile.** A value on a scale that indicates the percent
of a distribution that is equal to it or below it. For example,
a score at the 95th percentile is equal to or better than 95 percent
of the scores.

**Permutations.** Possible arrangements of a set of objects
in which the order of the arrangement makes a difference. For
example, determining all the different ways five books can be
arranged in order on a shelf.

**Prime number.** A whole number greater than 1 that can be
divided exactly (i.e., with no remainder) only by itself and 1.
The first few primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
37.

**Pythagorean theorem (relationship).** In a right triangle,
c^{2} = a^{2} + b^{2} , where c represents the length of the hypotenuse
(the longest side of the triangle which is opposite the right (angle), and a and b represent the lengths of the other two, shorter sides of the triangle.

**Quadratic function.** A function that can be represented
by an equation of the form y = ax^{2} (or ax^2) + bx + c, where a, b, and c
are arbitrary, but fixed, numbers and a 0. The graph of this
function is a parabola.

**Quartiles.** The 25th, 50th and 75th percentile points. (See
definition of Percentile.)

**Range (of a set of data).** The numerical difference between
the largest and smallest values in a set of data.

**Rational number.** A number that can be expressed as the
ratio, or quotient, of two integers, a/b, provided b
Ͱ0. Rational
numbers can be expressed as common fractions or decimals, such
as 3/5 or 0.6. Finite decimals, repeating decimals, mixed numbers
and whole numbers are all rational numbers. Nonrepeating decimals
cannot be expressed in this way, and are said to be irrational.

**Real numbers.** All the numbers which can be expressed as
decimals.

**Real-world problems.** Quantitative and spatial problems
that arise from a wide variety of human experiences, applications
to careers. These do not have to be highly complex ones and can
include such things as making change, figuring sale prices, or
comparing payment plans.

**Rectangular coordinate system.** This system uses two (for
a plane) or three (for space) mutually perpendicular lines (called
coordinate axes) and their point of intersection (called the origin)
as the frame of reference. Specific locations are described by
ordered pairs or triples (called coordinates) that indicate distance
from the origin along lines that are parallel to the coordinate
axes.

**Scaling (Scale drawing).** The process of drawing a figure
either enlarged or reduced in size from its original size. Usually
the scale is given, as on a map 1 inch equals 10 miles.

**Scatter plot.**
Also known as scattergram or scatter diagram.
A two dimensional graph representing a set of bi-variate
data. That is, for each element being graphed, there are
two separate pieces of data. For example, the height and
weight of a group of 10 teenagers would result in a scatter
plot of 10 separate points on the graph.

**Scientific notation.** A short-hand way of writing very large
or very small numbers. The notation consists of a decimal number
between 1 and 10 multiplied by an integral power of 10. For example,
47,300 = 4.73 x ^{4}; 0.000000021 = 2.1 x 10 ^{-8}

**Similarity.** The relationship between two objects that have
exactly the same shape but not necessarily the same size.

**Simulation.** Carrying out extensive data collection with
a simple, safe, inexpensive, easy-to-duplicate event that has
essentially the same characteristics as another event which is
of actual interest to an investigator. For example, suppose one
wanted to gather data about the actual order of birth of boys
and girls in families with five children. (e.g., BBGBG is one
possibility) Rather than wait for five children to be born to
a single family, or identifying families that already have five
children, one could simulate births by repeatedly tossing a coin
five times. Heads vs. tails has about the same chance of happening
as a boy vs. a girl being born.

**Slope.** A measure of the steepness or incline of a straight
line drawn on a rectangular-coordinate-system graph. The measure
is obtained by the quotient ¿rise/run¿ (vertical change
divided by horizontal change) between any two points on that line.

Stem-and-leaf plot.A way of 1|3699 showing the distribution of a set 2|268 of data along a vertical axis. The 3|344 plot at right shows the data 13, 19, 33, 26, 19, 22, 34, 16, 28, Key: 1|5 means 15 34. The ten¿s digits of these data are the stems and the one¿s digits are the leaves.

**Summary statistics.** A single number representation of the
characteristics of a set of data. Usually given by measures of
central tendency and measures of dispersion (spread).

**Symmetry.** A figure has symmetry if it has parts that correspond
with each other in terms of size, form, and arrangement. For example,
a figure with line (or mirror) symmetry has two halves which match
each other perfectly if the figure is folded along its line of
symmetry.

**Transformation.** A change in the size, shape, location or
orientation of a figure.

**Transitive property.** For equality: If a=b and b=c, then
a=c;

For inequality: If a»b and b»c, then a»c; or If a«b
and b«c, then a«c.

**Tree diagram.** A schematic way of
showing the number of ways a
compound event may occur. For
example, the tree diagram at the
right shows the eight possible ways
the tossing of three coins could
happen.

**Unit fraction.** A fraction with a numerator of 1, such as
1/4 or 1/7.

**Variable.** A quantity that may assume any one of a set of
values. Usually represented in algebraic notation by the use of
a letter. In the equation

y = 2x + 7, both x and y are variables.

**Variance.** The value of the standard deviation squared.

**Vertical angles.** The pair of angles that are
directly across from each other when two straight
lines intersect. Angles a and b at the right are
an example of vertical angles.

**Whole numbers.** The numbers: 0, 1, 2, 3, 4, 5, ...

*For questions about this information, contact Diana Kasbaum (608) 266-7712*