GLOSSARY OF TERMS

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, c²= a²+ b², 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 = ax² (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≠ 0. 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.

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-toduplicate 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 rectangularcoordinate- system graph. The measure is obtained by the quotient “rise/run” (vertical change divided by horizontal change) between any two points on that line.

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.