7th Grade Mathematics - Important Vocabulary Words
The mathematical vocabulary terms below can be found in the Mathworks Math Explorations textbooks.
- The absolute value of a number is its distance from zero.
- For any x, |x| is defined as follows: | x |= x, if x > 0, and | x |= −x, if x < 0
An angle whose measure is greater than 0 degrees and less than 90 degrees.
A triangle in which all three angles are acute angles.
Addition Property of Equality
If a= b, then a + c= b + c.
For any number x, there exists a number −x, such that x + −x= 0.
Two angles that share a common vertex and a common side.
Altitude of a Triangle
A segment drawn from a vertex of the triangle perpendicular to the opposite side of the triangle, called the base, (or perpendicular to an extension of the base).
An angle is formed when two rays share a common vertex.
The surface area of a two-dimensional figure.
A mathematical model based on the area of a rectangle, used to represent multiplication or to represent fractional parts of a whole.
A sequence a1, a2, a3, a4,... is an arithmetic sequence if there is a number c such that for each n, an + 1= an + c, that is an + 1 – an = c.
Associative Property of Addition
For any numbers x, y , and z: (x + y) + z= x + (y + z).
A distinguishing characteristic of an object such as angles or sides of a triangle.
A number line in a plane. Plural form is axes. Also see: Coordinate Plane.
- If any number x is raised to the nth power, written as x^n, x is called the base of the expression;
- Any side of a triangle;
- Either of the parallel sides of a trapezoid;
- Either of the parallel sides of a parallelogram.
Box and Whisker Plot
For data ordered smallest to largest the median, lower quartile and upper quartile are found and displayed in a box along a number line. Whiskers are added to the right and left and extended to the least and greatest values of the data.
Center of a Circle
A point in the interior of the circle that is equidistant from all points of the circle.
A segment whose endpoints are points on a circle.
The set of points in a plane equidistant from a point in the plane.
See: Pie graph.
The distance around a circle. Its length is the product of the diameter of the circle and pi.
In the product of a constant and a variable the constant is the numerical coefficient of the variable and is frequently referred to simply as the coefficient.
Combining Like Terms
nk + nm= n(k + m). Also commonly called factoring.
A common multiple of the denominators of two or more fractions. Also see: Least Common Denominator
A factor that two or more integers have in common. Also see: Greatest Common Factor.
See: Least Common Multiple.
Commutative Property of Addition
For any numbers x and y: x + y = y + x.
Commutative Property of Multiplication
For any numbers a and b: ab= ba.
The complement of a set is a set of all the elements of the universal set that are not in the given set.
Two angles are complementary if the sum of their measures totals 90º.
A prime number is an integer p greater than 1 with exactly two positive factors: 1 and p. A composite number is an integer greater than 1 that has more than two positive factors. The number 1 is neither a prime nor a composite number.
Interest added to the principal of an account, so that the added interest also earns interest going forward.
A three-dimensional figure with a circular base joined to a point called the apex.
Used to refer to angles or sides having the same measure and to polygons that have the same shape and size.
An assumption that is thought to be true based on observations.
A fixed value.
Constant of Proportionality
If a function has a rule in the form y= Kx, then for any input x≠0, the quotient of y/x will always have the value K. The number K is called constant of proportionality.
Constant Rate Of Change
y= mx + b, here m is the constant rate of change.
Constant Rate Of Proportionality
Another term for scale factor.
A number assigned to each point on the number line which shows its position or location on the line. In a coordinate plane that ordered pair, (x,y), assigned to each point of the plane showing its position in relation to the x-axis and y-axis.
A plane that consists of a horizontal and vertical number line, intersecting at right angles at their origins. The number lines, called axes, divide the plane into four quadrants. The quadrants are numbered I, II, III, and IV beginning in the upper right quadrant and moving counterclockwise.
- If two lines are cut by a transversal the angles on the same side of the transversal and on the same side of the two lines are corresponding angles. If the lines are parallel the pairs of angles will have equal measure.
- If two polygons are similar the angles that are in the same relative position in the figures are corresponding angles and have equal measures.
If two polygons are similar the sides of the polygons in the same relative positions are corresponding sides and the ratio of the lengths of each pair is the same.
A circular movement opposite to the direction of the movement of the hands of a clock.
The counting numbers are the numbers in the following never-ending sequence: 1, 2, 3, 4, 5, 6, 7... We can also write this as +1, +2, +3, +4, +5, +6, +7,... These numbers are also called the positive integers or natural numbers.
A percentage discount or a fixed amount of money taken off the sale price of an item.
- A three-dimensional shape having six congruent square faces.
- The third power of a number.
A three-dimensional figure with parallel circular bases of equal size joined by a lateral surface whose net is a rectangle.
The process of making sense of collected data.
- The circumference of a circle is divided into 360 equal parts or arcs. Radii drawn to both ends of the arc form an angle of 1 degree.
- The degree of a term is the sum of the exponents of the variables. The degree of a polynomial is the highest degree of any of its terms.
The denominator of a fraction indicates into how many equal parts the whole is divided. The denominator appears beneath the fraction bar.
The output values for a function.
A segment with endpoints on the circle that passes through its center.
n(k + m)= nk + nm.
For any two numbers x and y, the distance between x and y is the absolute value of their difference; that is, Distance= |x – y|.
The quantity that is to be divided.
Suppose that n and d are integers, and that d is not 0. The number n is divisible by d if there is an integer q such that n= dq. Equivalently, d is a factor of n or n is a multiple of d.
Given two positive integers a and b, we can always find unique integers q and r such that a= bq + r and 0 ≤ r < b. We call a the dividend, b the divisor, q the quotient, and r the remainder.
The quantity by which the dividend is divided.
The set of input values in a function.
Members of a set.
Probability determined by real data collected from real experiments.
Also called a Null Set. A set that has no elements.
A math sentence using the equal sign to state that two expressions represent the same number.
An equilateral triangle is a triangle with three congruent sides. An equilateral triangle also has three congruent angles, which we can also call equiangular triangle.
- A term used to describe equations or inequalities that have the same solution.
- A term used to describe fractions or ratios that are equal.
- A term used to describe fractions, decimals, and percents that are equal.
An event is any subset of the sample space. A simple event is a subset of the sample space containing only one possible outcome of an experiment. A compound event is a subset of the sample space containing two or more outcomes.
A repeatable action with a set of outcomes.
See: Empirical Probability.
Mathematical phrases used to describe quantities.
Suppose that n is a whole number. Then, for any number x, the nth power of x, or x to the nth power, is the product of n factors of the number x. This number is usually written x^n. The number x is usually called the base of the expression x^n, and n is called the exponent.
A notation that expresses a number in terms of a base and an exponent.
An integer that divides evenly into a dividend. Use interchangeably with divisor except in the Division Algorithm.
The factorial of a non-negative number n is written n! and is the product of all positive integers less than or equal to n. By definition 0!= 1!= 1.
Numbers of the form m/n, where n is not zero.
The number of times a data point appears in a data set.
A function is a rule which assigns to each member of a set of inputs, called the domain, a member of a set of outputs, called the range.
Greater than, Less Than
Suppose that x and y are integers. We say that x is less than y, x < y, if x is to the left of y on the number line. We say that x is greater than y, x > y, if x is to the right of y on the number line.
Greatest Common Factor, GCF
Suppose m and n are positive integers. An integer d is a common factor of m and n if d is a factor of both m and n. The greatest common factor, or GCF, of m and n is the greatest positive integer that is a factor of both m and n. We write the GCF of m and n as GCF (m,n).
See: Coordinate Plane.
The side opposite the right angle in a right triangle.
If the outcome of the first event does not affect the outcome of the second event.
The input values for a function.
A statement that one expression is less than or greater than another.
The values of the domain of a function.
The collection of integers is composed of the counting numbers, their negatives, and zero; ... −4, −3, −2, −1, 0, 1, 2, 3, 4...
Intersection of Sets
A set whose elements are all the elements that the given sets have in common, written A ∩ B.
A polygon that is not a regular polygon.
A triangle with at least two sides of equal length is called an isosceles triangle.
A point of the coordinate plane, (x,y), in which both x and y are integers.
Law Of Large Numbers
As the number of trials in an experiment are increased, the average of the experimental probability approaches the theoretical probability.
Least Common Denominator
The least common denominator of the fractions p/n and k/m is LCM(n, m).
Least Common Multiple, LCM
The integers a and b are positive. An integer m is a common multiple of a and b if m is a multiple of both a and b. The least common multiple, or LCM, of a and b is the smallest integer that is a common multiple of a and b. We write the LCM of a and b as LCM (a,b).
- The two sides of a right triangle that form the right angle.
- The equal sides of an isosceles triangle or the non-parallel sides of a trapezoid.
See: Greater Than.
A graph used to display data that occurs in a sequence. Consecutive points are connected by segments.
A graph that shows frequency of data along a number line.
Line of Symmetry
Half of the figure is the mirror image of the other half.
Line of Reflection
The line across which a figure is reflected.
Linear Model for Multiplication
Skip counting on a number line.
The average of a set of data; sum of the data divided by the number of items. Also called the arithmetic mean or average.
Measures of Central Tendency
Generally measured by the mean, median, or mode of the data set
The middle value of a set of data arranged in increasing or decreasing order. If the set has an even number of items the median is the average of the middle two items.
Missing Factor Model
A model for division in which the quotient of an indicated division is viewed as a missing factor of a related multiplication.
The sum of an integer and a proper fraction.
The value of the element that appears most frequently in a data set.
The number x is called the multiplicative inverse or reciprocal of the positive integer n if x · n= 1.
The number of times a factor appears in a factorization.
Total number of yards gained or lost at the end of a series of plays in a sports game.
Integers less than zero.
One way to see the surface area of a three dimensional figure by cutting along its edges to produce a two-dimensional figure.
A technical system of symbols used to convey mathematical information.
Number Line Model
A pictorial representation of numbers on a straight line.
See: Empty Set.
The expression written above the fraction bar in a common fraction to indicate the number of parts counted.
A triangle that has one obtuse angle.
The angle that is opposite to a given side of a plane figure.
Order Of Operations
The order of mathematical operations, with computations inside parentheses to be done first, and addition and subtraction from left to right done last.
A pair of numbers that represent the coordinates of a point in the coordinate plane with the first number measured along the horizontal scale and the second along the vertical scale.
The point with coordinate 0 on a number line; the point with coordinates (0,0) in the coordinate plane.
The set of possible results of an experiment.
A term referring to a value that is drastically different from most of the other data values.
The set of results obtained by applying a function rule to a set of input values.
A parallelogram is a four-sided figure with opposite sides parallel.
A way of expressing a number as parts out of 100; the numerator of a ratio with a denominator of 100.
An integer n that can be written in the form n= k³, where k is an integer.
An integer n that can be written in the form n= k², where k is an integer.
The perimeter of a polygon is the sum of the lengths of its sides.
Two lines or segments are perpendicular if they intersect to form a right angle.
The ratio of the circumference to the diameter of any circle, represented either by the symbol π, or the approximation 22/7 or 3.1415926...
A graph using sectors of a circle that are proportional to the percent of the data represented.
A polygon is a simple, closed, plane figure formed by three or more line segments.
A three-dimensional figure with four or more faces, all of which are polygons.
See: Counting Numbers.
See: Composite Number.
The process of finding the prime factors of an integer. The term is also used to refer to the result of the process.
A type of polyhedron that has two bases that are both congruent and parallel, and lateral faces which are parallelograms.
In an experiment in which each outcome is equally likely, the probability P(A) of an event A is m/n where m is the number of outcomes in the subset A and n is the total number of outcomes in the sample space S.
A reasoning to help establish a fact.
A fraction whose value is greater than 0 and less than 1.
An equation of ratios in the form a/b = c/d, where b and d are not equal to zero.
An instrument used to measure angles in degrees.
A type of polyhedron that has one face, called a base, and triangular lateral faces that meet at a point called the apex.
The formula that states that if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then a² + b² = c².
A plane figure with four straight edges and four angles.
The result obtained by doing division. See the Division Algorithm for a different use of quotient.
The distance from the center of a circle a point of the circle. Plural form is radii.
The difference between the largest and smallest values of a data set. See Function for another meaning of range.
A rate is a division comparison between two quantities with different units. Also see Unit Rate.
A division comparison of two quantities with or without the same units. If the units are different they must be expressed to make the ratio meaningful.
A number that can be written as a/b where a is an integer and b is a natural number.
Part of a line that has a starting point and continues forever in only one direction.
Money that the customer receives, typically from the manufacturer, after making a purchase.
See: Multiplicative Inverse.
A solid 3D object that has six faces, each face being a rectangle.
The transformation that moves points or shapes by “flipping” them across a line or axis; a mirror image of the original set of points. If B is the reflection of A in line L, then L is the perpendicular bisector of segment AB.
A polygon with equal length sides and equal angle measures.
Two integers m and n are relatively prime if the GCF of m and n is 1.
See: Division Algorithm.
A decimal in which a cycle of one or more digits is repeated infinitely.
An angle formed by the intersection of perpendicular lines; an angle with a measure of 90º.
A triangle that has a right angle.
The nodes in a tree diagram to represent events.
The set of all possible outcomes of an experiment.
A method of division in which partial quotients are computed, stacked, and then combined.
If polygons A and B are similar and s is a positive number so that for each side of A with length k there is a corresponding side of B with length sk, then s is the scale factor of A to B.
A triangle with all three sides of different lengths is called a scalene triangle.
- A process by which a shape is reduced or expanded proportionally.
- Choosing the unit of measure to be used on a number line.
A mathematical shorthand to represent large numbers.
A region of a circle bounded by two radii and an arc of the circle which joins their endpoints.
A list of terms ordered by the natural numbers. The outputs of a function whose domain is the natural numbers or whole numbers.
A collection of objects or elements.
A representation of groups of objects.
Two polygons whose corresponding angles have equal measures and whose corresponding side lengths form equal ratios.
Interest (money) that one earns by investing money in an account.
Simplest Form of a Fraction
A form in which the greatest common factor of the numerator and denominator is 1.
The process of finding equivalent fractions to obtain the simplest form.
An uneven representation of a set of data.
An altitude of a face of a pyramid or a cone.
The value of the variable that makes the equation true.
For non-negative numbers x and y, y= x , read “y is equal to the square root of x,” means y² = x.
Mathematical notation that is commonly used.
Stem and Leaf Plot
A method of showing the frequency of a certain data by sorting and ordering the values.
An angle with a measure of 180 degrees formed by opposite rays.
Set B is a subset of set A if every element of set B is also an element of set A.
Subtraction Property of Equality
If a= b, then a – c= b – c.
Two angles are supplementary if the sum of their measures totals 180º.
The total area of all the faces of a polyhedron. The total of the lateral area and base area of a cone. The total of the lateral area and the two bases of a cylinder.
- Each member of a sequence.
- Each expression in a polynomial separated by addition and subtraction signs.
If a and b are natural numbers with b ≠ 0 and a ÷ b yields a finite quotient, the decimal formed is a terminating decimal.
Tiling of a plane with some shape.
Probability based on mathematical law rather than a collection of data.
A transformation that moves a figure along a line in a plane but does not alter its size or shape.
Any line that intersects two or more lines at different points.
A four sided plane figure with exactly one set of parallel sides.
- A process used to find the prime factors on an integer.
- A method to organize the sample space of compound events.
A plane figure with three straight edges and three angles.
Triangle Sum Theorem
The sum of the measures of the interior angles of any triangle is 180 degrees.
A property stating that exactly one of these statements is true for each real number: it is positive, negative, or zero.
Union of Two Sets
A set that contains all of the elements that appear in either of the given sets, written A ∪ B.
A ratio of two unlike quantities that has a denominator of 1 unit.
A set containing all of the elements under consideration.
A diagram involving two or more overlapping circles that aids in organizing data.
- The common endpoint of two rays forming an angle.
- A point of a polygon or polyhedron where edges meet.
If two straight lines intersect at a point, then each line is divided into two rays. The angles formed by using opposite rays from each line are called vertical angles.
Vertical Angle Theorem
If two lines intersect at a point P, then the vertical angles formed will always have the same measure.
See: Coordinate Plane.
A measure of space; the number of unit cubes needed to fill a three-dimensional shape.
The first number provided in an ordered pair (a, b).
The second number provided in an ordered pair (a, b).