Mathematics Vocabulary6th, 7th,8th, Algebra, and Geometry

Percent

"Out of 100" A percent is a special decimal fraction in which the denominator is 100. When we write 68%, we mean 68 out of 100. When we write the percent sign (%) after a number to indicate percent.

Rate

A comparison of quantities measured in two different units is called a rate. A rate can be thought of aa a direct comparison of two sets (20 cookies for 5 children) or as an average amount (4cookies per child) a rate such as 5.5 miles per hour can be written as 5.5miles/1 hour or 5.5 miles :1 hour

Vertex

A corner of a polygon. For example G,H,I,J and K are all vertices in the pentagon below. All angles have vertices.

Repeating Decimals

A decimal with a pattern of digits that repeats over and over, such as 0.33333333333... and 0.73737373737373... Repeating decimals are rational numbers

Terminating Decimals

A decimal with a representation that ends, or terminates, such as 0.5 or 0.125. Terminating decimals are rational numbers

Reciprocal

A factor by which you multiply a given number so that their prodict is 1. For example 3/5 is the reciprocal of 5/3 and 5/3 is the reciprocal of 3/5.

Pentomino

A figure made of five congruent squares joined edge to edge

Improper Fraction

A fraction in which the numerator is larger than the denominator. An improper fraction is a fraction that is greater than 1. The fraction 5/2 is an improper fraction. The fraction 5/2 means 5 halves and is equivalent to 2.5 which is greater than 1.

Coordinate Graph

A graphical representation in which points are used to denote pairs of related numerical values. For each point, the two coordinates of the point give the assoiciated numerical values in the appropriate order.

Bar Graph

A graphical representation of a table of data in which the height or length of each bar indicates its frequency. The bars are seperated from each other to highlight that the data are discrete or counted data. In a vertical bar graph, the horizontal axis shows the values or categories, and the vertical axis shows the the frequency or talley for each of the values or categories on the horizontal axis. In a horizontal bar graph, the vertical axis shoes the values or categories and the horizontal axis shows the frequencies

Coordinate Graph

A graphical representation of pairs of related numerical values that shows the relationship between two variables. It relates the independent variable (shown on the x-axis) and the dependent variable (shown on the y-axis)

Scale

A labeling scheme used on each of the axes on a coordinate plane. The distance between two consecutive tick marks on the x and y axes of a coordinate grid. When graphing, an appropriate scale must be selected so that the resulting graph will be clearly shown, For example, when graphing the equation y=60x, a scale of 1 for the x axis and a scale of 15 or 30 for the y-axis would be reasonable.

Transversal

A line that intersects two or more lines.

Table

A list of values for two or more variables that shows the relationship between them. Tables oftern represent data made from observations, from experiments, or from a series of arithmetic operations. A table may show a pattern of change between two variable that can be used to predict values not in the table.

Simulation

A model of an experiment used to find the likelihood of an event. For example, suppose you want to find the likelihood you will win a contest with ten contestants. Since it is difficult to gather information about the contestants you can simulate the contest. Wrtie the numbers 1-10 on cards and select a card at random. The number 1 represents a win and the numbers 2-10 represent a loss

Positive Numbers

A number greater than 0. On a number line, positive numbers are located to the right of 0. On a vertical line, positive numbers are located above 0.

Negative Numbers

A number less than 0. On a number line, negative numbers are located to the left of 0. On a vertical line, negative numbers are located below 0.

Rational Number

A number that can be written as a quotient of two positive or negative numbers. You are familiar with positive rational numbers like 3/4, 107/5, and 3. Some examples of the negative rational numbers you will see in the future are -3, and -20. Both positive and negative rational numbers can be used to represent real life situations. For example, temperature or yardage during a football game can be positive, negative, or zero. There are other numbers such as pi that are not rational numbers

Mixed Number

A number that is written with both a whole number and a fraction. A mixed number is the sum of the whole number and the fraction. The number 2 and 1/2 represents two wholes and one half can be thought of as 2 + 1/2/

Probability

A number with a value from 0 to 1 that describes the likelihood that an event will occur. For example, if a bag contains a red marble, a white marble and a blue marble then the probability of selecting a red marble is 1/3.

Regular Polygons

A polygon that has all of its sides equal and all of its angles equal.

Irregular Polygons

A polygon which has at least two sides with different lengths or two angles with different measures

Quadrilateral

A polygon with four sides

Outcomes

A possible result of an action. For example, when one number cube is rolled, the possible outcomes are 1,2,3,4,5,and 6

Experimental Probability

A probability found as a result of an experiment. Experimental probabilities are used to predict behavior over the long run. For example, you could find the experimental probability of getting heads when you toss a coin by tossing the coin several times and keeping track of the outcomes. Ther experimental prbability would be the relative frequency of heads, that is the ratio of the number of heads to total number of trials

Theoretical Probability

A probability found by analyzing a situation. If all the outcomes are equally likely, you can find a theoretical probability of an event by first listing all the possible outcomes and then finding the ratio of the number of outcomes you are interested in to the total number of outcomes. For example, there are 36 possible equally likely outcomes when two number cubes are rolled. Of these outcomes 6, have a sum of 7, so the probability of rolling a sum of 7 is 6/36 or 1/6

Parallelogram

A quadrilateral with opposite sides parallel. Both pairs of opposite angles are also equal. In the definition of parallel lines, figure D. rectangle C and square E. are all parallelograms

Variable

A quantity that can change. Letters are often used as symbols to represent variables in rules or equations that describe patterns.

Line Plot

A quick simple way to organize data along a number line where the X above a number represents how often each value is mentioned

Stem & Leaf

A quick way to picture the shape of a distribution while including the actual numerical values in the graph.

Ratio

A ratio is a comparison of two quantitites It is sometimes expressed as a fraction. For example, suppose the length of side AB is 2 inches and the length of CD is 3 inches. The ration of the length of side AB to the length of side CD is 2 to 3 or 2/3. The ratio of the length of side CD is the length of side AB is 3 to 2 or 3/2

Benchmarks

A reference number that can be used to estimate the size of other numbers. For work with fractions, 0,1/2 and 1 are good benchmarks. We often estimate fractions or decimals with benchmarks because it is easier to do arithmetic with them and estimates often give enough accuracy for the situation.

Equation

A rule containing variables that represents a mathematical relationship. An example is the formula for finding the area of a circle: A=πr²

Radius

A segment from the center of a circle to a point on the circle. The length of this segment is also called the radius. The radius is half of the diameter. The plural of radius is radii. All of the radii of a circl have the same length.

Diameter

A segment that goes from one point on a circle through the center of the circle to another point on the circle. Also, diameter is used to indicate the length of this segment.

Algorithm

A set of rules for perfoming a procedure. Mathematicians invent algoritms that are useful in many kinds of situations . Some examples of algorithms are the rules for long division or the rules for adding two fractions.

Polygon

A shape formed by line segments, called sides, so that each of the segments meets exactly to other segments and all f the points where the segments meet are endpoints of the segments

Rule

A summary of a predictable relationship that tells how to find the value of a variable. A rule may be given in words or as an equation. For example, this rule relates time, rate and distance: distance is equal to rate times time. Or d=rt.

Tree Diagram

A systematic way to find tall the possible outcomes in a probability situation

Unit Rate

A unit rate is a rate in which the second number (usually written as the denominator) is 1 or 1 of a quantity. For example 1.9 children per family, 32 miles per gallon and 3 flavors of ice cream per bannana split are unit rates. Unit rate are often founf by scaling other rates.

Outliers

A value that lies far from the center of a distribution, Outlier is a relative term, but it indicates a data point that is much higher or much lower than the values that could be normally expected for the distribution

Relationship

An association between two or more variables. If one of the variables changes, the other variable may also change, and the change may be predictable.

Proportion

An equation stating that two ratios are equal. Ie 2/7=10/35

Coordinate Pair

An ordered pair of numbers used to locate a point on a coordinate grid. The first number in a coordinate pair is the value for the x-coordinate. And the second number is the value for the y-coordinate.

Corresponding Angles

Corresponding angles have the same relative position in similar figures.

Categorical

Data that are words that represent possible responses within a given category. Frequency counts can be made of the entries for a given category. The table below shows examples of categories and their possible entries

Equivalent Fractions

Fractions that are equal in value, but may have different numerators and denominators . For example 2/3 and 14/21 are equivelent fractions.

Linear Dimensions

Linear measurements, such as length, width, base and height, which describe the size of figures. You need to be flexible when you encounter these tems, so you are able to determine their meanings from the context of the situation

Rational Numbers

Number that can be expressed as a quotient of two integers where the divisor is not zero

Independent Variable

One of the two variables in a relationship. Its value depends upon or is determined by the other variable called the dependent variable. For example, if you organize a bike tour the number of people who register to go (independent variable) determines the cost for renting bikes (dependent variable)

Dependent Variable

One of the two variables in a relationship. Its value depends upon or is determined by the other variable called the independent variable. For example, the coast of a long-distance phone call (dependent variable) depends on how long you talk (independent variable.)

Equivalent Ratio

Ratios whose fraction representations are equivalent are called equivalent ratios. For instance the ratios 3 to 4 and 6 to 8 are equvalent because 3/4=6/8

Scaling Down

Scale is the number to multiply both parts of a ratio to produce an equal but possivle more informative ratio.

Scaling up

Scale is the number to multiply both parts of a ratio to produce an equal but possivle more informative ratio.

Similar

Similar figures have corresponding angles of equal measure and the ratios of each pair of corresponding sides are equivalent.

Mode

The category or numerical value that occurs most often. It is possible for a set of data to have more than one mode

Range

The difference between the least value and the greatest value in a distribution.

Circumference

The distance around (orperimeter of) a circle. It takes slightly more than three diameters to match the circumference of a circle. More formally, the circumference of a circle is pi times the diameter of the circle

Image

The figure that results from some transformation of a figure. It is often of interest to consider what is the same and what is different about a figure and its image

X-axis

The horizontal number line used to make a graoh

PI

The mathematical name for the ratio of a circle's circumference to its diameter. This ratio is the same for every circle, and is appoximately equal to 3.1416

Area

The measure of the amount of surface enclosed by the boundry of a figure. To find the area of a figure you can count how many unit squares it taks to cover the figure, You can find the are of a rectangle by multiplying the length by the width. This is a shortcut method for finding the number of unit squares it takes to cover the rectangle. If a figure has curved or irregular sides you can estimate the area. Cover the the surface with a grid and count whole grid squares and parts of grid squares. When you find the area of a shape, write the units, such as square centimeters(cm2), to indicate the unit square that was used to find the area

Width

The measurement or extent of something from side to side.

Perimeter

The meaure of the distance around a figure. Perimeter is a measure of length. To find the perimeter of a figure, you count the number of unit lengths it takes to surround the figure. When you find the perimeter of a shape, write the units (such as centimeters, feet, or yards) to indicate the unit that was used to find the perimeter.

X-axis

The number line that is horizontal on a coordinate grid. "X stands on his own two feet"

Y-axis

The number line that is vertical on a coordinate grid. "Y reaches for the sky"

Median

The number that marks the middle of an ordered set of data. At least half of the values lie at or above the median, and at least half lie at or below the median.

Scale Factor

The number used to multiply the lengths of a figure to stretch or shrink it to a simular image. If we use a scale factor of 3, all lengths in the image are 3 times as long as the corresponding lengths in the original. When you are given two similar figures , the scale factor is the ratio of the image side length to the coorisponding original side length.

Numerator

The number written above the line in a fraction. In the fraction 5/8., 5 is the numerator. When you interpret the fraction 5/8 as a part of a whole, the numerator represents 5 of 8 equal parts

Denominator

The number written below the line in a fraction. In the fraction 3/4, 4 is the denominator. In the part-whole interpretation of fractions, the denominator shows the numver of equal-size parts into which the whole has been split.

Angle Sum

The sum of all the measures of the interior angles of a polygon

Y-coordinate

The value on the Y-axis used to locate a point on the coordinate graph. It is the second value in an ordered pair

X-coordinate

The value on the x-axis used to locate a point on the coordinate graph. It is the first value in an ordered pair

Mean

The value you would get if all the data are combined and then redistributed evenly. The mean of a set of data is the sum of the values divided by then number of values in the set

Y-Axis

The vertical number line used to make a graph

Integers

The whole numbers and their opposites. 0 is an integer. But is neither positive nor negative.

Nested Triangles

Triangles that share a common angle are sometimes called nested.

Perpendicular

Two lines that intersect to form right angles

Equally Likely

Two or more events that have the same chance of happening. For example, when you toss a fair coin, heads and tails are equally likely. Each has a 50% chance of happening. When you toss a tack, it is not equally likely to land on its side and on its head. It is more likely to land on its side.

Numerical Data

Values that are number such as counts, measurements, and ratings. Here are some examples... number of children in families, pulse rates, height, amount of time people spend reading in one day.

Square Root

a number that when multiplied by itself equals a given number

Square

a plane rectangle with four equal sides and four right angles

Sum

a quantity obtained by addition

Product

a quantity obtained by multiplication

Underestimating

an estimate that is too low

Height

distance from the base of something to the top

Overestimating

estimate as being greater than it actually is

Symmetry

exact correspondence of form on opposite sides of a dividing line or plane

Average

relating to or constituting the middle value of an ordered set of values (or the average of the middle two in an even-numbered set) adjectiveEx. "the median value of 17, 20, and 36 is 20"; "the median income for the year was $15,000"

Corresponding Side

sides that have the same relative position in similar shapes

Distribution

the act of distributing or spreading or apportioning

Base

the bottom side of a geometric figure from which the altitude can be constructed

Length

the longest horizontal dimension of something that is fixed in place

Measure of Center

the mean, median, and mode used to describe data

Quotient

the number obtained by division

Difference

the number that remains after subtraction

Opposites

two numbers whose sum is 0. For example -3 and 3 are opposites. On a number line, opposites are the same distance from 0 but in different directions. The number 0 is its own opposite