Vocabulary

Students need to use and apply the vocabulary of mathematics in their written responses on the Pennsylvania Mathematics Assessment. Students demonstrate competency by using the correct vocabulary, i.e., the term "subtraction" instead of "take-away." When the student response is correct in every other way, the use of appropriate vocabulary will enable the student to receive a level 5 score of "Advanced Understanding." In order for students to be comfortable in using math vocabulary, they need daily exposure to it by teachers who model its use in instruction. An extensive glossary of math terms is available in the Mathematics Standards. Although many of the terms listed will not be necessary for written responses, this listing provides a classroom resource for teachers and can be copied.

Absolute Value

A number's distance from zero on a number line. The absolute value of 2 is equal to the absolute value of -2.

Algorithm

A method of performing an arithmetic operation.

Analog time

Time displayed on a timepiece having hour and minute hands.

Array

Arrangement of a series of items according to the values of the items, e.g., largest to smallest.

Box-and-whisker plot

A graphic method for showing a summary of data using median, quartiles and extremes of data.

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Capacity

The volume of a container given in units of liquid measure.

Combination

A subset of the elements in a given set, without regard to the order in which those elements are arranged.

Composite number

Any positive integer exactly divisible by one or more positive integers other than itself and 1.

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 x-axis. The vertical line is called the y-axis. 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 y-coordinate, 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 bx or
y = a x bkx, 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., a2, 2n, yx).

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 non-repeating 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 nx = a, the logarithm of a, with n as the base, is x; symbolically, logna = x. If the base is 10, the log of 100 is 2 or 102.

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 (n-1).

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.

One-to-one
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 one-to-one. (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 one-to-one 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.wpe2.jpg (932 bytes))

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.

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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 four-sided 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/(2pi.gif (58 bytes)) 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 three-dimensional 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.

Stem-and-leaf 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 stem-and-leaf 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).

t-test

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 s2) 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.

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Volume

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

Y-intercept

The y-intercept of a line is the y-coordinate of the point at which the graph of an equation crosses the y-axis.

pi.gif (58 bytes)

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

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