Glossary of Alaska Mathematics Standards
addition and subtraction within 5, 10, 20, 100, or 1000
Addition or subtraction of two whole numbers with whole number answers, and with sum or minuend in the range 0-5, 0-10, 0-20, or 0-100, respectively. Example: 8 + 2 = 10 is an addition within 10, 14 – 5 = 9 is a subtraction within 20, and 55 – 18 = 37 is a subtraction within 100.
additive inverses
Two numbers whose sum is 0 are additive inverses of one another. Example: 3/4 and – 3/4 are additive inverses of one another because 3/4 + (– 3/4) = (– 3/4) + 3/4 = 0.
associative property of addition
See Table 3 in this Glossary.
associative property of multiplication
See Table 3 in this Glossary.
bivariate data
Pairs of linked numerical observations. Example: a list of heights and weights for each player on a football team. Box plot. A method of visually displaying a distribution of data values by using the median, quartiles, and extremes of the data set. A box shows the middle 50% of the data.
cardinality
Cardinal numbers, known as the “counting numbers,” indicate quantity.
commutative property
See Table 3 in this Glossary.
complex fraction
A fraction A/B where A and/or B are fractions (B nonzero).
computation algorithm
A set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly. See also: computation strategy.
computation strategy
Purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another. See also: computation algorithm.
congruent
Two plane or solid figures are congruent if one can be obtained from the other by rigid motion (a sequence of rotations, reflections, and translations).
counting on
A strategy for finding the number of objects in a group without having to count every member of the group. For example, if a stack of books is known to have 8 books and 3 more books are added to the top, it is not necessary to count the stack all over again. One can find the total by counting on—pointing to the top book and saying “eight,” following this with “nine, ten, eleven. There are eleven books now.”
dot plot
See: line plot
dilation
A transformation that moves each point along the ray through the point emanating from a fixed center, and multiplies distances from the center by a common scale factor.
expanded form
A multi-digit number is expressed in expanded form when it is written as a sum of single-digit multiples of powers of ten. For example, 643 = 600 + 40 + 3.
expected value
For a random variable, the weighted average of its possible values, with weights given by their respective probabilities.
first quartile
For a data set with median M, the first quartile is the median of the data values less than M. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the first quartile is 6. See also: median, third quartile, interquartile range.
fraction
A number expressible in the form a/b where a is a whole number and b is a positive whole number. (The word fraction in these standards always refers to a non-negative number.) See also: rational number.
identity property of 0
See Table 3 in this Glossary.
independently combined probability models
Two probability models are said to be combined independently if the probability of each ordered pair in the combined model equals the product of the original probabilities of the two individual outcomes in the ordered pair.
integer
A number expressible in the form a or –a for some whole number a.
interquartile range
A measure of variation in a set of numerical data, the interquartile range is the distance between the first and third quartiles of the data set. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the interquartile range is 15 – 6 = 9. See also: first quartile, third quartile.
line plot
A method of visually displaying a distribution of data values where each data value is shown as a dot or mark above a number line. Also known as a dot plot.
mean
A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list. Example: For the data set {1, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean is 21.
mean absolute deviation
A measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing by the number of data values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the mean absolute deviation is 20.
median
A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list—or the mean of the two central values, if the list contains an even number of values. Example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 90}, the median is 11.
midline
In the graph of a trigonometric function, the horizontal line halfway between its maximum and minimum values. Multiplication and division within 100. Multiplication or division of two whole numbers with whole number answers, and with product or dividend in the range 0-100. Example: 72 ÷ 8 = 9.
multiplicative inverses
Two numbers whose product is 1 are multiplicative inverses of one another. Example: 3/4 and 4/3 are multiplicative inverses of one another because 3/4 × 4/3 = 4/3 × 3/4 = 1.
number line diagram.
A diagram of the number line used to represent numbers and support reasoning about them. In a number line diagram for measurement quantities, the interval from 0 to 1 on the diagram represents the unit of measure for the quantity.
ordinality
Ordinal numbers indicate the order or rank of things in a set (e.g., sixth in line; fourth place).
percent rate of change
A rate of change expressed as a percent. Example: if a population grows from 50 to 55 in a year, it grows by 5/50 = 10% per year.
probability distribution
The set of possible values of a random variable with a probability assigned to each.
probability
A number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, tossing a ball at a target, or testing for a medical condition).
probability model
A probability model is used to assign probabilities to outcomes of a chance process by examining the nature of the process. The set of all outcomes is called the sample space, and their probabilities sum to 1. See also: uniform probability model.
properties of equality
See Table 4 in this Glossary.
properties of inequality
See Table 5 in this Glossary.
properties of operation
See Table 3 in this Glossary.
random variable
An assignment of a numerical value to each outcome in a sample space. Rational expression. A quotient of two polynomials with a non-zero denominator.
rational expression
A quotient of two polynomials with a non-zero denominator.
rational number
A number expressible in the form a/b or – a/b for some fraction a/b. The rational numbers include the integers.
rectilinear figure
A polygon all angles of which are right angles.
rigid motion
A transformation of points in space consisting of a sequence of one or more translations, reflections, and/or rotations. Rigid motions are here assumed to preserve distances and angle measures.
repeating decimal
The decimal form of a rational number. See also: terminating decimal.
sample space
In a probability model for a random process, a list of the individual outcomes that are to be considered.
scatter plot
A graph in the coordinate plane representing a set of bivariate data. For example, the heights and weights of a group of people could be displayed on a scatter plot.
similarity transformation
A rigid motion followed by a dilation.
tape diagram
A drawing that looks like a segment of tape, used to illustrate number relationships. Also known as a strip diagram, bar model, fraction strip, or length model.
terminating decimal
A decimal is called terminating if its repeating digit is 0.
third quartile
For a data set with median M, the third quartile is the median of the data values greater than M. For example: For the data set {2, 3, 6, 7, 10, 12, 14, 15, 22, 120}, the third quartile is 15. See also: median, first quartile, interquartile range.
transitivity principle for indirect measurement
If the length of object A is greater than the length of object B, and the length of object B is greater than the length of object C, then the length of object A is greater than the length of object C. This principle applies to measurement of other quantities as well.
uniform probability model
A probability model which assigns equal probability to all outcomes. See also: probability model.
vector
A quantity with magnitude and direction in the plane or in space, defined by an ordered pair or triple of real numbers.
visual fraction model
A tape diagram, number line diagram, or area model.
whole numbers
The numbers 0, 1, 2, 3,...
Table 4: The Properties of Equality
Here a, b and c stand for arbitrary numbers in the rational, real, or complex number systems.
Here a, b and c stand for arbitrary numbers in the rational or real number systems.