CSET Math Glossary

absolute value. A number's distance from zero on the number line. The absolute value of -4 is 4; the absolute value of 4 is 4.

acute. An angle with a measure between zero and 90 degrees. Acute triangles have three acute angles.

adjacent angles. Two angles next to each other, sharing a ray.

algorithm. An organized procedure for performing a given type of calculation or solving a given type of problem. An example is long division.

alternate interior/exterior angles. Angles located inside/outside a set of parallel lines and on opposite sides of the transversal.

angle bisector. A ray that divides an angle into two congruent angles.

area. The number of square units needed to cover a surface.

arithmetic sequence. A sequence of elements such that the difference of successive terms is a constant; for example, the sequence {2, 5, 8, 11, 14, } where the common difference is 3.

box-and-whisker plot. A graphical method for showing the median, quartiles, and extremes of data. A box plot shows where the data are spread out and where they are concentrated.

complementary. Two angles having the sum of 90 degrees.

congruent. Two figures having the same size and shape.

conjecture. An educated guess.

coordinates. A unique ordered pair of numbers identifying a point with the first number defining position with regard to the x-axis and the second number showing position relative to the y-axis.

corresponding angles. Two angles in the same relative position on two parallel lines cut by a transversal.

decimal number. A fraction with a denominator a power of ten and expressed using a decimal point. For example, 0.7 is the decimal equivalent of 7 tenths, 7/10.

degrees. A unit of measurement: circles have 360 degrees, triangles 180 degrees, right angles 90 degrees.

denominator. The number below the fraction bar indicating the number of parts the whole is dividing into.

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.

division. The inverse operation of multiplication.

equation. A mathematical sentence containing an equal sign.

equivalent fractions Different fractions which name the same amount; e.g., ½ and 2/4.

expanded form. The expanded form of an algebraic expression is the equivalent expression without parentheses. For example, the expanded form of ( a + b )2 is a2+ 2ab + b2.

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 102 + 2 x 101 + 3 x 100.

exponent. The power to which a number or variable is raised. 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.

exterior angle. The angle outside a polygon formed by extending one of its sides.

factors. Any two or more numbers or symbols when multiplied together form a product; e.g., 2 is a factor of 6 because it can be multiplied by 3 to give 6; 2 x 3 = 6.

fraction. A rational number of the form a/b with a the numerator and b the denominator separated by the fraction bar.

frequency. The number of items occurring in a given category.

function. A correspondence in which values of one variable determine the values of another.

geometric sequence. A sequence in which there is a common ratio between successive terms. Each successive term of a geometric sequence is found by multiplying the preceding term by the common ratio. For example, in the sequence {1, 3, 9, 27, 81, . . .} the common ratio is 3.

greatest common factor. The largest number that is a common factor of two or more numbers.

histogram. A vertical block graph with no spaces between the blocks. It is used to represent frequency data in statistics.

hypotenuse. The longest side of the triangle that is opposite the right angle.

inequality. A relationship between two quantities indicating that one is strictly less than, greater than, less than or equal, or greater than or equal to the other.

integers. The set consisting of the positive and negative whole numbers and zero; for example, {. . . -2, -1, 0, 1, 2 . . .} and not containing a fraction or decimal.

intercept. The points where a line drawn on a 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 such that the number multiplied by its inverse = 1 (e.g., the reciprocal of 5 is 1/5; the reciprocal of -3/4 is -4/3.

irrational number. A number that cannot be represented as an exact ratio of two integers. For example, the square root of 2 or pi.

isosceles triangle. Triangles with two congruent sides and angles.

least common multiple. LCM of two numbers is the smallest number (not zero) that is a multiple of both.

line segment. A piece of a line with endpoints at both ends.

line symmetry. When a figure is divided by a line and both divisions are mirrors of each other, the figure has line symmetry. The line that divides the figure is the line of symmetry.

linear. An equation or graph is linear if the graph of an equation is a straight line.

mean. In statistics, the average obtained by dividing the sum of two or more quantities by the number of these quantities.

median. In statistics, the quantity designating the middle value in a set of numbers. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two.

mixed numbers. Numbers that have both whole numbers and decimals, such as 4.567, or whole numbers and fractions, such as two and one half 2 ½.

mode. In statistics, the value that occurs most frequently in a given series of numbers.

multiples. The product of multiplying a number by a whole number. For example, multiples of 3 are 6, 9, 12, or any number that can be evenly divided by 3.

multiplication. The operation by which the product of two quantities is calculated. To multiply a number b by c is to add b to itself c times.

natural numbers. One of the counting numbers, i.e. 1, 2, 3, 4... In graphing, numbers to the right of zero.

negative numbers. Numbers less than zero. In graphing, numbers to the left of zero. Negative numbers are represented by placing a minus sign (-) in front of the number.

nonstandard unit. Unit of measurement expressed in terms of objects (such as paper clips, sticks of gum, shoes, etc.).

numerator. The number above the fraction bar that indicates the number of parts of the whole there are in a rational number.

obtuse angle An angle whose measure is greater than 90 degrees.

origin In the Cartesian coordinate plane, the origin is the point at which the horizontal and vertical axes intersect, at zero (0,0).

outlier. A data point (or points) that lie far outside most of the rest of the points in the data set.

parallel. Given distinct lines in the plane that are infinite in both directions, the lines are parallel if they never meet. Two distinct lines in the coordinate plane are parallel if and only if they have the same slope.

percent. A ratio that compares a number to one hundred. The symbol for percent is %.

perimeter. The sum of the lengths of all the sides of a polygon.

perpendicular. Two lines that meet at a right angle are perpendicular. The slopes of perpendicular lines are the negative reciprocal of each other.

permutation A particular ordering of a set of objects. For example, given the set {1, 2, 3}, there are six permutations: {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}.

pi. The designated name for the ratio of the circumference of a circle to its diameter.

pie graph A diagram showing a system of connections or interrelations between two or more things by using a circle divided into segments that look like pieces of pie.

polygon A closed plane figure formed by three or more line segments that do not cross over each other.

prime number A number that has exactly two factors, 1 and the number itself. The first seven primes are 2, 3, 5, 7, 11, 13, 17.

probability The measure of how likely it is for an event to occur. The probability of an event is always a number between zero and 100%.

proportion A relationship between two ratios in which the first ratio is always equal to the second.

protractor An instrument for laying down and measuring angles on paper.

Pythagorean theorem. Used to find side lengths of right triangles, the Pythagorean Theorem states that the square of the hypotenuse is equal to sum of the squares of the two sides, or A2 + B2 = C2, where C is the hypotenuse.

quadratic function. A function given by a polynomial of degree 2.

quadrilateral A polygon that has four sides.

quartile. The medians of the first and second halves of a set of data.

quotient When performing division, the number of times one value can be multiplied to reach the other value represents the quotient. For example, when dividing 6 by 3, 3 can be multiplied twice, making 6, so the quotient is 2.

range. In statistics, the difference between the greatest and smallest values in a data set.

ratio. A comparison expressed as a fraction. For example, there is a ratio of three boys to two girls in a class (3/2, 3:2).

rational numbers. Numbers that can be expressed as the quotient of two integers; for example, 7/3, 5/11, or -5/13, 7 = 7/1.

ray A straight line that begins at a point and continues in one direction.

real numbers. All rational and irrational numbers.

rectangle A parallelogram with four right angles.

reflection. The reflection through a line in the plane or a plane in space is the transformation that takes each point in the plane to its mirror image with respect to the line or its mirror image with respect to the plane in space. It produces a mirror image of a geometric figure.

regular polygon A polygon whose side lengths are all the same and whose interior angle measures are all the same.

rhombus A parallelogram with four congruent sides.

right angle An angle of 90 degrees.

right triangle A triangle containing an angle of 90 degrees.

root extraction. Finding a number that can be used as a factor a given number of times to produce the original number; for example, the square root of 16 = 4 because 4 x 4 = 16).

rotation. To rotate an object means to repeat the object by spinning it on a point a certain angle.

rule of probabilities--multiplication for simultaneous independent events. When finding the probability of two independent events (two things happening where the outcomes are not affected by each other), multiply the probabilities of each event happening to get the probability of both events happening. For example, to find the probability of getting "heads" and then "tails" when flipping a coin twice, multiply the probability of getting heads once by the probability of getting tails once.

scatterplot. A graph of the points representing a collection of data.

scientific notation. A shorthand way of writing very large or very small numbers. A number expressed in scientific notation is expressed as a decimal number between 1 and 10 multiplied by a power of 10 (e.g., 7000 = 7 x 103 or 0.0000019 = 1.9 x 10-6).

similarity. In geometry, two shapes are similar if they are congruent after one of them is expanded or shrunk. The relationship between two objects that have exactly the same shape but not necessarily the same size.

slope of the linear function The slope of the line y = mx + b is the rate at which y is changing per unit of change in x. A measure of the steepness or incline of a straight line obtained by the quotient “rise/run” (vertical change divided by horizontal change) between any two points on that line.

square root. The square roots of n are all the numbers m so that m2 = n. The square roots of 16 are +4 and -4.

symmetry. See line symmetry.

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

translation. A transformation or slide in which the origin of the coordinate system is moved to another position but the direction of each axis remains the same.

transversal. In geometry, given two or more lines in the plane a transversal is another line that intersects each of the given lines in a single point.

vertical angles. The pair of angles that are directly across from each other when two straight lines intersect.

whole numbers. The numbers: 0, 1, 2, 3, 4, 5, ...

POLYA’S 4-STEP PROCESS FOR PROBLEM SOLVING

Step 1. Understand the Problem

• Do you understand all the words?
• Can you restate the problem in your own words?
• Can you identify what information is given?
• Do you know what the goal is?
• Is there enough information? Is there extraneous information?
• Is this problem similar to another problem you have solved?

Step 2. Devise a Plan or determine a strategy/set of strategies.

• Guess and Test
• Look for a pattern
• Make a list
• Use a variable
• Look for a formula
• Solve an equation or inequality
• Draw a picture
• Draw a graph
• Draw a diagram
• Use a model
• Do a simulation

Step 3. Carry Out the Plan

• Implement the strategy or strategies until the problem is solved or a new course of action is indicated.
• Allow a reasonable amount of time to solve the problem.
• If you are not successful, seek hints from others or put the problem aside for a while.
• Do not be afraid to start over. A fresh start and new strategy will often lead to success.

Step 4. Look Back

• Is your solution correct/ your answer satisfy the problem’s statement?
• Can you see an easier solution? extend your solution to a more general case?