Math Tools & Vocabulary
Free middle school math calculators, formulas, and student-friendly vocabulary definitions for Grades 6–8.
Each definition includes links back to the grade-level units where the term appears.
Popular Math Tools
Use these quick calculators to check answers and review common middle school math ideas.
GPA Calculator
Enter grades separated by spaces. Example: A B A C
Rectangle Area
Triangle Area
Circle Area
Pythagorean Theorem
Slope Calculator
Percent of a Number
Mean Calculator
Enter numbers separated by commas.
Middle School Math Vocabulary
These definitions are written in student-friendly language for important Grade 6, Grade 7, and Grade 8 math terms. Many terms appear in more than one grade or unit, so each term is listed once with a clear meaning.
A
Absolute Value
Definition: The distance a number is from 0 on the number line. Absolute value is always zero or positive.
Example: The absolute value of -5 is 5.
Accuracy
Definition: How close a measurement or answer is to the true value.
Example: A measurement of 9.9 cm is accurate if the true length is 10 cm.
Actual
Definition: The real size or real amount, not the scaled or estimated version.
Example: A map uses a scale to represent the actual distance.
Additive Inverse
Definition: A number that adds with another number to make 0.
Example: The additive inverse of 7 is -7.
Adjacent Angles
Definition: Angles that share a vertex and a side.
Example: Two angles next to each other on a straight line are adjacent.
Algebraically
Definition: Using equations, expressions, and symbols to solve or show math.
Example: Solving 2x+3=11 algebraically means using equation steps.
Alternate Interior Angles
Definition: Angles inside two lines and on opposite sides of a transversal.
Example: When lines are parallel, alternate interior angles are equal.
Angle Measure
Definition: The size of an angle, usually measured in degrees.
Example: A right angle has an angle measure of 90 degrees.
Angle Of Rotation
Definition: The amount a figure turns around a center point.
Example: A quarter turn has an angle of rotation of 90 degrees.
Approximate
Definition: To find a value that is close to the exact answer.
Example: 3.14 is an approximate value of pi.
Area
Definition: The amount of space inside a two-dimensional shape.
Example: A 4 by 3 rectangle has an area of 12 square units.
Area Of A Circle
Definition: The space inside a circle. It is found with the formula A = πr².
Example: A circle with radius 3 has area 9π square units.
Assumption
Definition: Something accepted as true while solving a problem.
Example: Assume each box has the same weight.
Attribute
Definition: A characteristic that can be described or measured.
Example: Height and eye color are attributes.
Average
Definition: A value that describes the center of a data set; often means the mean.
Example: The average of 2, 4, and 6 is 4.
Axes
Definition: The horizontal and vertical number lines on a coordinate plane.
Example: The x-axis and y-axis are the axes.
Axis
Definition: One number line on a coordinate plane or graph.
Example: The horizontal axis is usually the x-axis.
B
Balance Point
Definition: The value where data would balance if placed on a number line.
Example: The mean can be thought of as a balance point.
Balanced Hanger
Definition: A diagram showing two equal sides, like an equation.
Example: A balanced hanger helps solve for an unknown weight.
Bar Graph
Definition: A graph that uses bars to show and compare data.
Example: A bar graph can compare favorite sports.
Base
Definition: A chosen side or value used in a formula, expression, or shape.
Example: In a triangle, the base is paired with a height.
Base Of A Cylinder Or Cone
Definition: The circular face used to describe or calculate volume.
Example: The base of a cylinder is a circle.
Base Of An Exponent
Definition: The number being repeatedly multiplied in an exponential expression.
Example: In 5³, the base is 5.
Base Of A Prism Or Pyramid
Definition: The face used to name or describe the solid figure.
Example: A triangular prism has triangular bases.
Base-Ten Diagram
Definition: A drawing that shows place value using blocks, bundles, or units.
Example: Base-ten diagrams can model decimals.
Batch
Definition: One group or amount made from a recipe or process.
Example: A double batch uses twice each ingredient.
Billion
Definition: One thousand million, or 1,000,000,000.
Example: A billion is written as 10⁹.
Bin
Definition: An interval used to group data in a histogram.
Example: A bin might include values from 10 to 19.
Box Plot
Definition: A data display that shows the five-number summary.
Example: A box plot shows median, quartiles, minimum, and maximum.
Bundle
Definition: A group of place-value units combined into a larger unit.
Example: Ten ones can bundle into one ten.
C
Calculation
Definition: A mathematical process used to find a value.
Example: Multiplying 6 by 4 is a calculation.
Categorical Data
Definition: Data sorted into groups or categories.
Example: Favorite colors are categorical data.
Center
Definition: A value or location that represents the middle of data or a figure.
Example: The mean or median can describe the center of data.
Center Of A Circle
Definition: The point that is the same distance from every point on a circle.
Example: The radius goes from the center to the circle.
Center Of A Dilation
Definition: The fixed point from which a figure is enlarged or reduced.
Example: A dilation stretches points away from its center.
Center Of Rotation
Definition: The fixed point around which a figure turns.
Example: A wheel rotates around its center of rotation.
Chance Experiment
Definition: A process with outcomes that are uncertain.
Example: Rolling a number cube is a chance experiment.
Circle
Definition: All points in a plane that are the same distance from a center point.
Example: A circle has a center and radius.
Circumference
Definition: The distance around a circle.
Example: Circumference is like the perimeter of a circle.
Clockwise
Definition: Turning in the same direction as the hands of a clock.
Example: A clockwise turn moves to the right at the top.
Closed Circle
Definition: A filled-in circle on a number line showing the endpoint is included.
Example: Use a closed circle for x ≤ 4.
Cluster
Definition: A group of data points close together on a graph.
Example: A scatterplot may show a cluster of points.
Coefficient
Definition: A number multiplied by a variable.
Example: In 6x, the coefficient is 6.
Combine Like Terms
Definition: To add or subtract terms with the same variable part.
Example: 3x + 2x combines to 5x.
Common Denominator
Definition: A shared denominator used to compare or add fractions.
Example: 12 is a common denominator for 1/3 and 1/4.
Common Factor
Definition: A factor shared by two or more numbers.
Example: 3 is a common factor of 6 and 9.
Common Multiple
Definition: A multiple shared by two or more numbers.
Example: 12 is a common multiple of 3 and 4.
Commutative Property
Definition: A property that says changing the order does not change the result for addition or multiplication.
Example: 3+5=5+3.
Complementary Angles
Definition: Two angles whose measures add to 90 degrees.
Example: 30° and 60° are complementary.
Compose
Definition: To put parts together to make a shape or expression.
Example: Two triangles can compose a rectangle.
Condition
Definition: A requirement that must be true.
Example: A triangle has to meet certain side length conditions.
Cone
Definition: A three-dimensional figure with a circular base and one vertex.
Example: An ice cream cone is shaped like a cone.
Congruent
Definition: Same shape and same size.
Example: Congruent figures match exactly after a rigid transformation.
Constant
Definition: A value that does not change.
Example: In y=3x, the 3 is constant.
Constant Of Proportionality
Definition: The constant multiplier in a proportional relationship.
Example: If y=4x, the constant of proportionality is 4.
Constant Rate
Definition: A rate that stays the same.
Example: A car traveling 60 miles each hour has a constant rate.
Constant Speed
Definition: Speed that does not change.
Example: Walking 3 miles per hour is constant speed.
Constant Term
Definition: A term with no variable.
Example: In 2x+7, the constant term is 7.
Constraint
Definition: A limit or condition in a problem.
Example: A budget is a constraint.
Container
Definition: An object that can hold something.
Example: A box is a container.
Context
Definition: The real-world situation or meaning around a math problem.
Example: Money can be a context for negative numbers.
Coordinate Plane
Definition: A grid formed by two number lines that cross at the origin.
Example: Points can be plotted on a coordinate plane.
Coordinates
Definition: Numbers that tell the location of a point.
Example: The point (3,2) has coordinates 3 and 2.
Correspond
Definition: To match in position or role.
Example: Corresponding sides match between two figures.
Corresponding
Definition: Matching parts of figures that are in the same position.
Example: Corresponding angles match in similar figures.
Counterclockwise
Definition: Turning opposite the direction of clock hands.
Example: A counterclockwise turn moves left at the top.
Cross Section
Definition: The two-dimensional shape made when a three-dimensional figure is sliced.
Example: A slice through a cube can make a square cross section.
Cube
Definition: A rectangular prism with six equal square faces.
Example: A number cube is shaped like a cube.
Cube Root
Definition: A number that is multiplied by itself three times to make another number.
Example: The cube root of 27 is 3.
Cubed
Definition: Multiplied by itself two more times.
Example: 3 cubed is 3×3×3=27.
Cubic Centimeter
Definition: A unit for volume equal to the space inside a 1 cm by 1 cm by 1 cm cube.
Example: Volume may be measured in cubic centimeters.
D
Data Display
Definition: A visual way to show data.
Example: A scatterplot is a data display.
Decimal Approximation
Definition: A decimal that is close to the exact value.
Example: 1.414 is a decimal approximation for √2.
Decimal Point
Definition: The dot that separates whole numbers from decimal parts.
Example: In 3.75, the decimal point is between 3 and 7.
Decimal Representation
Definition: A way to write a number using decimals.
Example: 1/2 has decimal representation 0.5.
Decompose
Definition: To break something into smaller parts.
Example: A polygon can be decomposed into triangles.
Degrees Celsius
Definition: A temperature scale used in many countries and in science.
Example: Water freezes at 0°C.
Degrees Fahrenheit
Definition: A temperature scale commonly used in the United States.
Example: Water freezes at 32°F.
Denominator
Definition: The bottom number in a fraction that tells how many equal parts are in the whole.
Example: In 3/5, the denominator is 5.
Dependent Variable
Definition: A quantity that depends on another quantity.
Example: Distance may depend on time.
Deposit
Definition: Money added to an account.
Example: A $20 deposit increases the balance.
Description
Definition: Words that explain what something is like or what is happening.
Example: A graph description explains the pattern.
Diagonal
Definition: A line segment connecting non-adjacent vertices.
Example: A rectangle has two diagonals.
Diameter
Definition: A segment across a circle through the center.
Example: The diameter is twice the radius.
Difference
Definition: The result of subtraction.
Example: The difference between 9 and 4 is 5.
Different Triangle
Definition: A triangle that is not identical to another triangle.
Example: Changing a side length can make a different triangle.
Digits
Definition: Symbols used to write numbers: 0 through 9.
Example: The digits in 407 are 4, 0, and 7.
Dilate
Definition: To enlarge or reduce a figure using a scale factor.
Example: A dilation with scale factor 2 doubles distances from the center.
Dilation
Definition: A transformation that makes a figure larger or smaller.
Example: A dilation creates a scaled copy.
Dimension
Definition: A measurement such as length, width, height, or radius.
Example: The dimensions of a box describe its size.
Direction
Definition: The way something moves, turns, or points.
Example: A translation has a distance and direction.
Discount
Definition: A decrease from the original price.
Example: A $5 discount lowers the price by $5.
Distance
Definition: How far apart two points or numbers are.
Example: The distance from -3 to 0 is 3.
Distance From Zero
Definition: How far a number is from 0 on a number line.
Example: -8 has distance 8 from zero.
Distribution
Definition: The pattern or shape of a data set.
Example: A distribution shows how data values are spread out.
Distributive Property
Definition: A property that connects multiplication and addition.
Example: 3(4+5)=3×4+3×5.
Dividend
Definition: The number being divided.
Example: In 12÷3, 12 is the dividend.
Divisor
Definition: The number you divide by.
Example: In 12÷3, 3 is the divisor.
Dot Plot
Definition: A data display using dots above a number line.
Example: A dot plot can show class test scores.
E
Edge
Definition: A line segment where two faces meet on a 3D figure.
Example: A cube has 12 edges.
Edge Length
Definition: The length of an edge on a 3D figure.
Example: A cube with edge length 4 has volume 64 cubic units.
Elevation
Definition: Height above or below sea level.
Example: A mountain has positive elevation.
Equal-Sized
Definition: Having the same size.
Example: Equal-sized groups have the same number in each group.
Equally Likely As Not
Definition: Having a probability of 1/2.
Example: A fair coin landing heads is equally likely as not.
Equation
Definition: A statement that two expressions are equal.
Example: x+3=8 is an equation.
Equation Of A Line
Definition: An equation whose solutions form a line on a graph.
Example: y=2x+1 is an equation of a line.
Equivalent Expressions
Definition: Expressions that have the same value for all allowed variable values.
Example: 2(x+3) and 2x+6 are equivalent expressions.
Equivalent Ratios
Definition: Ratios that describe the same relationship.
Example: 2:3 and 4:6 are equivalent ratios.
Equivalent Scales
Definition: Scales that represent the same relationship between drawing and actual size.
Example: 1 inch to 4 feet and 2 inches to 8 feet are equivalent scales.
Estimate
Definition: A reasonable answer close to the exact value.
Example: Estimating helps check if an answer makes sense.
Evaluate
Definition: To find the value of an expression.
Example: Evaluate 3+4 to get 7.
Event
Definition: An outcome or group of outcomes in a chance experiment.
Example: Rolling an even number is an event.
Expanded
Definition: Written out as repeated multiplication or in a longer form.
Example: 5³ expanded is 5×5×5.
Expand An Expression
Definition: To use multiplication or distribution to rewrite an expression.
Example: 3(x+2) expands to 3x+6.
Exponent
Definition: A number that tells how many times the base is used as a factor.
Example: In 2⁵, the exponent is 5.
Expression
Definition: A mathematical phrase with numbers, variables, and operations.
Example: 4x+7 is an expression.
F
Face
Definition: A flat surface of a three-dimensional figure.
Example: A cube has 6 faces.
Factor
Definition: A number or expression multiplied by another.
Example: 3 and 4 are factors of 12.
Factor An Expression
Definition: To rewrite an expression as a product.
Example: 6x+9 can factor to 3(2x+3).
Fair Share
Definition: An equal amount each person or group would get.
Example: The mean can represent a fair share.
False Equation
Definition: An equation that is not true.
Example: 3+4=9 is a false equation.
Figure
Definition: A shape or object in geometry.
Example: A triangle is a figure.
Final Amount
Definition: The amount after a change such as increase or decrease.
Example: The final amount after a discount is the sale price.
Fitted Line
Definition: A line used to model the trend in data.
Example: A fitted line helps make predictions from a scatterplot.
Five-Number Summary
Definition: Minimum, first quartile, median, third quartile, and maximum.
Example: A box plot shows the five-number summary.
Floorplan
Definition: A scale drawing of a room or building from above.
Example: A floorplan shows room dimensions.
Formula
Definition: A rule written with symbols for calculating a value.
Example: A=lw is the formula for rectangle area.
Fraction Of
Definition: A part of a whole or amount.
Example: 1/3 of 12 is 4.
Functional Relationship
Definition: A relationship where each input has exactly one output.
Example: A table can show a functional relationship.
Function
Definition: A rule or relationship where each input has exactly one output.
Example: If x=2 always gives y=5, that can be part of a function.
G
Gallon
Definition: A unit of liquid volume.
Example: Milk is often sold by the gallon.
Gap
Definition: An empty space between shapes or parts.
Example: Tiles should cover a floor without gaps.
Good Deal
Definition: An option that gives more value for the cost.
Example: The lower unit price is usually the better deal.
Greater Than
Definition: A comparison showing one value is larger than another.
Example: 8 is greater than 5.
Greater Than Or Equal To
Definition: A comparison meaning larger than or the same as.
Example: x ≥ 3 means x is at least 3.
Greatest Common Factor
Definition: The greatest factor shared by two or more numbers.
Example: The GCF of 12 and 18 is 6.
H
Height
Definition: The perpendicular distance from a base to the opposite side or vertex.
Example: Triangle area uses base and height.
Hemisphere
Definition: Half of a sphere.
Example: Half a ball is a hemisphere.
Histogram
Definition: A graph that uses bars to show numerical data grouped in intervals.
Example: A histogram can show ages grouped by range.
Horizontal
Definition: Going left to right.
Example: The x-axis is horizontal.
Horizontal Axis
Definition: The left-right axis on a graph.
Example: The horizontal axis is often the x-axis.
Horizontal Intercept
Definition: The point where a graph crosses the horizontal axis.
Example: The horizontal intercept is also called the x-intercept.
Horizontal Line
Definition: A line that goes left and right and has slope 0.
Example: y=4 is a horizontal line.
Hypotenuse
Definition: The longest side of a right triangle, across from the right angle.
Example: The Pythagorean Theorem uses the hypotenuse.
I
Identical Copy
Definition: A figure that matches another exactly in size and shape.
Example: Two identical triangles can form a parallelogram.
Image
Definition: The new figure after a transformation.
Example: After a reflection, the reflected figure is the image.
Impossible
Definition: An event with probability 0.
Example: Rolling a 7 on a standard number cube is impossible.
Independent Variable
Definition: A quantity that can be chosen or changed.
Example: Time is often the independent variable.
Inequality
Definition: A statement comparing values using symbols like <, >, ≤, or ≥.
Example: x<5 is an inequality.
Infinite Decimal Expansion
Definition: A decimal that continues forever.
Example: 1/3 has an infinite repeating decimal expansion.
Infinitely Many Solutions
Definition: A situation where every value in a set works.
Example: The equation x+1=x+1 has infinitely many solutions.
Initial Amount
Definition: The starting amount before a change.
Example: The original price is the initial amount before tax.
Initial Value
Definition: The starting value when the input is 0.
Example: In y=3x+2, the initial value is 2.
Input
Definition: The value put into a function.
Example: If f(3)=7, the input is 3.
Integer
Definition: A whole number, its opposite, or zero.
Example: -2, 0, and 5 are integers.
Interquartile Range
Definition: The difference between the third quartile and first quartile.
Example: IQR measures the spread of the middle half of data.
Intersect
Definition: To cross or meet.
Example: Two lines intersect at a point.
Intersection Point
Definition: The point where graphs or lines meet.
Example: The solution to a system is an intersection point.
Interpretation
Definition: The meaning of a number, equation, or result in context.
Example: In 12÷3, one interpretation is how many groups of 3.
Irrational Number
Definition: A number that cannot be written as a ratio of two integers.
Example: √2 is irrational.
L
Label
Definition: A word or number used to identify part of a graph, diagram, or measurement.
Example: Axis labels tell what quantities are shown.
Least Common Multiple
Definition: The smallest multiple shared by two or more numbers.
Example: The LCM of 4 and 6 is 12.
Legs
Definition: The two sides that form the right angle in a right triangle.
Example: The legs are used in the Pythagorean Theorem.
Less Than
Definition: A comparison showing one value is smaller than another.
Example: 3 is less than 8.
Less Than Or Equal To
Definition: A comparison meaning smaller than or the same as.
Example: x ≤ 10 means x is at most 10.
Like Terms
Definition: Terms with the same variable part.
Example: 3x and 5x are like terms.
Line Of Reflection
Definition: The line a figure is reflected across.
Example: A mirror line is a line of reflection.
Line Segment
Definition: A part of a line with two endpoints.
Example: A side of a triangle is a line segment.
Linear Association
Definition: A pattern in data that is close to a line.
Example: A scatterplot with points near a line has linear association.
Linear Equation
Definition: An equation whose graph is a line.
Example: y=2x+5 is a linear equation.
Linear Function
Definition: A function with a constant rate of change.
Example: A linear function graphs as a line.
Linear Model
Definition: A line used to represent or predict a trend in data.
Example: A linear model can estimate future values.
Linear Relationship
Definition: A relationship with a constant rate of change.
Example: A linear relationship makes a straight-line graph.
Location
Definition: A position on a number line, plane, or map.
Example: The point (2,3) gives a location.
Long Division
Definition: A written method for dividing numbers.
Example: Long division can be used to divide decimals.
M
Markdown
Definition: A decrease from a price.
Example: A $10 markdown lowers the price.
Markup
Definition: An increase added to a cost.
Example: A store adds markup to make a selling price.
Mathematical Model
Definition: A math representation of a real situation.
Example: An equation can be a mathematical model.
Maximum
Definition: The greatest value in a set or allowed situation.
Example: The maximum of 3, 8, and 5 is 8.
Mean
Definition: The sum of data values divided by the number of values.
Example: The mean of 2, 4, and 6 is 4.
Mean Absolute Deviation
Definition: The average distance of data values from the mean.
Example: MAD describes variability in a data set.
Meaningful Difference
Definition: A difference large enough to matter in context.
Example: A 1-minute difference may or may not be meaningful.
Measure
Definition: To find the size or amount of something.
Example: Use a ruler to measure length.
Measure Of Center
Definition: A value that describes the middle of a data set.
Example: Mean and median are measures of center.
Measure Of Spread
Definition: A value that describes how spread out data is.
Example: Range and MAD are measures of spread.
Measure Of Variability
Definition: A value that describes how much data values vary.
Example: IQR is a measure of variability.
Measurement
Definition: A number with a unit that describes size or amount.
Example: 5 inches is a measurement.
Measurement Error
Definition: The difference between a measured value and the actual value.
Example: A ruler reading may have measurement error.
Median
Definition: The middle value when data are ordered.
Example: The median of 2, 5, 9 is 5.
Meters Per Second
Definition: A unit of speed.
Example: A runner may move at 5 meters per second.
Midpoint
Definition: The point halfway between two endpoints.
Example: The midpoint splits a segment into two equal parts.
Minimum
Definition: The least value in a set or allowed situation.
Example: The minimum of 3, 8, and 5 is 3.
Mode
Definition: The value that appears most often in a data set.
Example: In 2, 3, 3, 5, the mode is 3.
Multiple
Definition: A product of a number and a whole number.
Example: 12 is a multiple of 3.
Multiplicative Inverse
Definition: A number that multiplies with another number to make 1.
Example: The multiplicative inverse of 3 is 1/3.
N
Negative Association
Definition: A relationship where one quantity tends to decrease as the other increases.
Example: As speed increases, travel time may decrease.
Negative Exponent
Definition: An exponent that represents repeated division by the base.
Example: 10⁻² = 1/100.
Negative Number
Definition: A number less than zero.
Example: -4 is a negative number.
Net
Definition: A two-dimensional pattern that can fold into a three-dimensional figure.
Example: A cube net folds into a cube.
New Amount
Definition: The amount after a change.
Example: After a price increase, the result is the new amount.
No Association
Definition: No clear relationship between two quantities in data.
Example: A scatterplot with no pattern may show no association.
No Solution
Definition: A situation where no value makes an equation or system true.
Example: x+1=x+2 has no solution.
Nonlinear Association
Definition: A relationship in data that does not follow a straight-line pattern.
Example: A curved pattern is nonlinear.
Number Line
Definition: A line used to show numbers in order.
Example: Negative numbers are left of 0 on a number line.
Numerator
Definition: The top number in a fraction.
Example: In 3/5, the numerator is 3.
Numerical Data
Definition: Data made of numbers or measurements.
Example: Heights are numerical data.
O
Observation
Definition: Something noticed from data, a diagram, or a situation.
Example: An observation may describe a pattern.
One-Dimensional
Definition: Having length only.
Example: A line segment is one-dimensional.
One Solution
Definition: A situation where exactly one value works.
Example: x+2=5 has one solution.
Open Circle
Definition: An unfilled circle on a number line showing the endpoint is not included.
Example: Use an open circle for x<4.
Operation
Definition: A math action such as addition, subtraction, multiplication, or division.
Example: Multiplication is an operation.
Opposite
Definition: Across from or in the reverse direction.
Example: The opposite of 6 is -6.
Opposite Angles
Definition: Angles across from each other in a figure.
Example: Opposite angles in a parallelogram are equal.
Opposite Numbers
Definition: Numbers the same distance from zero but on opposite sides.
Example: 5 and -5 are opposite numbers.
Opposite Sides
Definition: Sides across from each other in a polygon.
Example: A rectangle has two pairs of opposite sides.
Opposite Vertex
Definition: A vertex across from a chosen side or base.
Example: The height of a triangle may go from a base to the opposite vertex.
Order
Definition: To arrange values by size or position.
Example: Order numbers from least to greatest.
Ordered Pair
Definition: Two numbers that give a point’s location on a coordinate plane.
Example: (4,2) is an ordered pair.
Origin
Definition: The point (0,0) on the coordinate plane.
Example: The axes meet at the origin.
Original
Definition: The starting figure before a transformation or scaling.
Example: A scaled copy is made from an original.
Original Amount
Definition: The starting amount before a change.
Example: A discount is based on the original amount.
Outcome
Definition: A possible result of a chance experiment.
Example: Rolling a 4 is an outcome.
Outlier
Definition: A data point far from most other data points.
Example: A very high score may be an outlier.
Output
Definition: The value produced by a function.
Example: If f(3)=7, the output is 7.
Overlap
Definition: When parts cover the same space or data sets share values.
Example: Two distributions may overlap.
Overpredict
Definition: To predict a value higher than the actual value.
Example: If the actual is 10 and the prediction is 12, you overpredict.
P
Parallel
Definition: Lines that stay the same distance apart and never meet.
Example: Opposite sides of a rectangle are parallel.
Parallelogram
Definition: A quadrilateral with two pairs of parallel sides.
Example: A rectangle is a parallelogram.
Partial Products
Definition: Products found by breaking a multiplication problem into parts.
Example: 23×4 can use partial products 20×4 and 3×4.
Partial Quotients
Definition: A division method that subtracts parts of the quotient.
Example: Partial quotients can help divide 156 by 6.
Parts
Definition: Pieces or quantities that make up a whole.
Example: A ratio can compare parts.
Pace
Definition: A rate that describes time per distance.
Example: Minutes per mile is a pace.
Percent Error
Definition: A comparison of measurement error to the actual value, written as a percent.
Example: Percent error helps describe accuracy.
Percentage Decrease
Definition: A decrease described as a percent of the original amount.
Example: A price dropping from $50 to $40 is a 20% decrease.
Percentage Increase
Definition: An increase described as a percent of the original amount.
Example: A price rising from $50 to $60 is a 20% increase.
Per
Definition: For each or for every.
Example: Miles per hour means miles for each hour.
Perimeter
Definition: The distance around a polygon.
Example: Add all side lengths to find perimeter.
Perpendicular
Definition: Lines or segments that meet at a right angle.
Example: The height of a triangle is perpendicular to the base.
Pi
Definition: The constant ratio of a circle’s circumference to its diameter, about 3.14.
Example: C=πd uses pi.
Piecewise Linear Function
Definition: A function made of line segments with different rules or rates.
Example: A graph with several straight pieces may be piecewise linear.
Plane
Definition: A flat surface that extends forever in all directions.
Example: A coordinate plane is a flat grid.
Plot
Definition: To place a point on a graph or coordinate plane.
Example: Plot (2,5) on the coordinate plane.
Polygon
Definition: A closed two-dimensional shape made of straight line segments.
Example: A triangle is a polygon.
Polyhedron
Definition: A three-dimensional figure made of flat polygon faces.
Example: A rectangular prism is a polyhedron.
Population
Definition: The entire group being studied in statistics.
Example: All students in a school can be a population.
Positive Association
Definition: A relationship where one quantity tends to increase as the other increases.
Example: Height and arm span may have positive association.
Positive Exponent
Definition: An exponent greater than zero.
Example: 3² has a positive exponent.
Positive Number
Definition: A number greater than zero.
Example: 7 is a positive number.
Power
Definition: An expression with a base and exponent.
Example: 2⁵ is a power.
Powers Of 10
Definition: Numbers like 10, 100, 1,000, or 1/10 written using exponents.
Example: 10³ = 1,000.
Powers Of Powers
Definition: An expression where a power is raised to another power.
Example: (2³)² is a power of a power.
Precision
Definition: How detailed or exact a measurement is.
Example: Measuring to the nearest millimeter is more precise than to the nearest centimeter.
Predict
Definition: To estimate a value based on data or a model.
Example: Use a fitted line to predict a value.
Prism
Definition: A three-dimensional figure with two matching parallel bases.
Example: A rectangular prism is a prism.
Probability
Definition: A number from 0 to 1 that describes how likely an event is.
Example: A probability of 1 means certain.
Product
Definition: The result of multiplication.
Example: The product of 6 and 4 is 24.
Proportion
Definition: A statement that two ratios are equivalent.
Example: 2/3 = 4/6 is a proportion.
Proportional Relationship
Definition: A relationship where one quantity is a constant multiple of the other.
Example: If y=3x, y is proportional to x.
Pyramid
Definition: A three-dimensional figure with one base and triangular faces meeting at a vertex.
Example: A square pyramid has a square base.
Pythagorean Theorem
Definition: A rule for right triangles: a² + b² = c², where c is the hypotenuse.
Example: If legs are 3 and 4, the hypotenuse is 5.
Q
Quadrant
Definition: One of the four regions of a coordinate plane.
Example: Quadrant I has positive x and positive y values.
Quadrilateral
Definition: A polygon with four sides.
Example: A rectangle is a quadrilateral.
Quantity
Definition: An amount that can be measured or counted.
Example: Time and distance are quantities.
Quartile
Definition: A value that divides ordered data into four parts.
Example: The median is the second quartile.
Quotient
Definition: The result of division.
Example: The quotient of 12÷3 is 4.
R
Random
Definition: Chosen by chance in a way that is not predictable.
Example: A random sample gives each member a fair chance.
Random Sample
Definition: A sample chosen by chance from a population.
Example: A random sample can help represent a population.
Range
Definition: The difference between the maximum and minimum values.
Example: The range of 2, 5, 9 is 7.
Rate Per 1
Definition: A rate written for one unit.
Example: $3 per pound is a rate per 1 pound.
Rate Of Change
Definition: How one quantity changes compared to another.
Example: Slope is a rate of change.
Ratio
Definition: A comparison of two quantities.
Example: The ratio of 2 boys to 3 girls is 2:3.
Rational Number
Definition: A number that can be written as a fraction of two integers.
Example: 0.75 and -2 are rational numbers.
Reasonable
Definition: Making sense in the situation.
Example: An answer of 500 miles for a short walk is not reasonable.
Rearrange
Definition: To move parts into a different order or shape.
Example: Rearrange pieces of a parallelogram into a rectangle.
Recipe
Definition: A set of amounts used to make something.
Example: A recipe can show ratios of ingredients.
Reciprocal
Definition: One of two numbers whose product is 1.
Example: The reciprocal of 4 is 1/4.
Rectangular Prism
Definition: A prism with rectangular faces.
Example: A cereal box is a rectangular prism.
Reflection
Definition: A transformation that flips a figure across a line.
Example: A reflection makes a mirror image.
Region
Definition: A part of a plane or the inside area of a figure.
Example: The shaded region is the part being measured.
Regular Price
Definition: The original price before a discount or sale.
Example: The regular price was $40 before the sale.
Relate
Definition: To show how two quantities are connected.
Example: An equation can relate distance and time.
Relationship
Definition: A connection between quantities.
Example: A graph can show a relationship.
Relative Frequency
Definition: A fraction or percent showing how often something occurs compared to the total.
Example: If 6 out of 20 chose blue, the relative frequency is 30%.
Remainder
Definition: The amount left after division.
Example: 17÷5 has a remainder of 2.
Repeating Decimal
Definition: A decimal with a digit or group of digits that repeats forever.
Example: 1/3 = 0.333... is repeating.
Represent
Definition: To show something with numbers, words, symbols, diagrams, tables, or graphs.
Example: A table can represent a relationship.
Representative Sample
Definition: A sample that reflects the population fairly well.
Example: A representative sample should not be biased.
Result
Definition: The answer or outcome of a calculation or process.
Example: The result of 8+5 is 13.
Right Angle
Definition: An angle that measures 90 degrees.
Example: The corner of a square is a right angle.
Right Triangle
Definition: A triangle with one right angle.
Example: The Pythagorean Theorem applies to right triangles.
Rigid Transformation
Definition: A transformation that preserves distance and angle measures.
Example: Translations, rotations, and reflections are rigid transformations.
Rotate
Definition: To turn a figure around a point.
Example: Rotate a square 90 degrees.
Rotation
Definition: A transformation that turns a figure around a center point.
Example: A wheel makes a rotation.
Row
Definition: A horizontal set of entries in a table.
Example: A row goes left to right.
S
Sale Price
Definition: The price after a discount.
Example: A $30 item with $5 off has a sale price of $25.
Sales Tax
Definition: An extra amount added to a purchase, usually a percent of the price.
Example: Sales tax increases the final price.
Sample
Definition: A smaller group chosen from a population.
Example: Surveying 50 students is using a sample.
Sample Space
Definition: The list of all possible outcomes.
Example: For a coin toss, the sample space is heads and tails.
Scale
Definition: A relationship between a drawing or model and the actual object.
Example: A map scale might be 1 inch to 10 miles.
Scale Drawing
Definition: A drawing that represents an object using a scale.
Example: A floor plan is a scale drawing.
Scale Factor
Definition: A number used to multiply lengths to make a scaled copy.
Example: A scale factor of 2 doubles side lengths.
Scale Without Units
Definition: A scale written as a ratio without measurement units.
Example: A scale of 1 to 100 means each length is 100 times as large.
Scaled Copy
Definition: A copy of a figure where all lengths are multiplied by the same scale factor.
Example: A photo enlargement is a scaled copy.
Scaling
Definition: Changing the size of a figure by multiplying lengths by a scale factor.
Example: Scaling by 3 triples lengths.
Scatterplot
Definition: A graph of paired numerical data shown as points.
Example: A scatterplot can show height and shoe size.
Scientific Notation
Definition: A way to write very large or very small numbers using powers of 10.
Example: 3.2×10⁵ is scientific notation.
Sea Level
Definition: The average level of the ocean, used as a reference for elevation.
Example: A location below sea level has negative elevation.
Segment
Definition: A part of a line with two endpoints.
Example: A side of a polygon is a segment.
Segmented Bar Graph
Definition: A bar graph divided into parts to show categories or relative frequencies.
Example: A segmented bar graph can compare survey results.
Sequence Of Transformations
Definition: A series of transformations performed one after another.
Example: Reflect, then translate is a sequence.
Shaded
Definition: Colored or filled in to show a region.
Example: Find the area of the shaded region.
Side Length
Definition: The length of one side of a figure.
Example: A square with side length 5 has area 25.
Sign
Definition: A symbol showing whether a number is positive or negative.
Example: The sign of -6 is negative.
Similar
Definition: Having the same shape but possibly different size.
Example: Similar triangles have equal angles and proportional sides.
Similarity
Definition: A relationship between figures with the same shape.
Example: Similarity can be shown using dilations and rigid transformations.
Simulation
Definition: A model of a chance experiment.
Example: Flipping coins can simulate a yes/no event.
Slide
Definition: An informal word for a translation.
Example: Slide the triangle right 3 units.
Slope
Definition: A number that describes the steepness and direction of a line.
Example: Slope is change in y divided by change in x.
Slope Triangle
Definition: A right triangle used to show vertical and horizontal change on a line.
Example: A slope triangle helps calculate slope.
Solution Of A System Of Equations
Definition: An ordered pair that makes all equations in the system true.
Example: The intersection point is often the solution.
Solution Of An Equation
Definition: A value that makes an equation true.
Example: x=5 is a solution of x+2=7.
Solution To An Inequality
Definition: A value that makes an inequality true.
Example: x=3 is a solution to x<5.
Sphere
Definition: A perfectly round three-dimensional figure.
Example: A ball is shaped like a sphere.
Spread
Definition: How far apart data values are.
Example: Range and IQR describe spread.
Square Of A Number
Definition: A number multiplied by itself.
Example: The square of 6 is 36.
Square Root
Definition: A number that can be multiplied by itself to make another number.
Example: The square root of 49 is 7.
Square Root Symbol
Definition: The symbol √ used to show a square root.
Example: √25 = 5.
Squared
Definition: Multiplied by itself.
Example: 7 squared is 49.
Statistical Question
Definition: A question that expects variability in the answers.
Example: How many minutes do students read each day?
Steady
Definition: Not changing; staying constant.
Example: A steady speed is a constant speed.
Straight Angle
Definition: An angle that measures 180 degrees.
Example: A straight line forms a straight angle.
Strategy
Definition: A plan or method for solving a problem.
Example: Drawing a diagram is a strategy.
Substitute
Definition: To replace a variable with a value or expression.
Example: Substitute x=3 into 2x+1.
Substitution
Definition: A method of solving by replacing one expression with an equivalent one.
Example: Use substitution to solve a system.
Supplementary Angles
Definition: Two angles whose measures add to 180 degrees.
Example: 110° and 70° are supplementary.
Surface Area
Definition: The total area covering the outside of a three-dimensional figure.
Example: Wrapping paper covers the surface area of a box.
Survey
Definition: A way to collect information by asking questions.
Example: A survey can collect favorite lunch choices.
Symmetric
Definition: Balanced or matching on both sides.
Example: A symmetric distribution has similar left and right sides.
Symmetry
Definition: A property where parts of a figure match after a flip, turn, or slide.
Example: A butterfly has line symmetry.
System Of Equations
Definition: Two or more equations considered together.
Example: A system can be solved by finding where lines intersect.
T
Table
Definition: An arrangement of information in rows and columns.
Example: A table can show x and y values.
Tape Diagram
Definition: A drawing using bars to represent quantities and relationships.
Example: Tape diagrams can solve ratio problems.
Tax Rate
Definition: The percent used to calculate sales tax.
Example: A 7% tax rate means 7 cents per dollar.
Term
Definition: A part of an expression separated by addition or subtraction.
Example: In 3x+4, the terms are 3x and 4.
Three-Dimensional
Definition: Having length, width, and height.
Example: A cube is three-dimensional.
Tick Marks
Definition: Marks on a number line or diagram showing equal intervals.
Example: Tick marks help read a double number line.
Tip
Definition: Extra money paid for service, usually a percent of the bill.
Example: A 20% tip on $30 is $6.
To The Power
Definition: A phrase used to describe an exponent.
Example: 2 to the power of 3 means 2³.
Translate
Definition: To slide a figure without turning or flipping it.
Example: Translate the point 4 units right.
Translation
Definition: A transformation that slides every point the same distance and direction.
Example: A translation moves a figure without changing its size.
Transversal
Definition: A line that crosses two or more other lines.
Example: A transversal creates angle pairs with parallel lines.
Travel
Definition: To move from one place to another.
Example: Distance and time can describe travel.
Tree Diagram
Definition: A diagram that shows possible outcomes in stages.
Example: A tree diagram can show coin toss outcomes.
Triangle
Definition: A polygon with three sides.
Example: A triangle has 3 sides and 3 angles.
Trillion
Definition: One thousand billion, or 1,000,000,000,000.
Example: A trillion is 10¹².
True Equation
Definition: An equation that is correct.
Example: 3+4=7 is a true equation.
Turn
Definition: An informal word for rotation.
Example: A quarter turn is 90 degrees.
Two-Dimensional
Definition: Having length and width but no depth.
Example: A rectangle is two-dimensional.
Two-Way Frequency Table
Definition: A table that shows counts for two categories at once.
Example: A two-way table can compare grade level and favorite sport.
U
Undefined Slope
Definition: The slope of a vertical line, where the change in x is 0.
Example: A vertical line has undefined slope.
Underpredict
Definition: To predict a value lower than the actual value.
Example: If the actual is 20 and the prediction is 17, you underpredict.
Unit Price
Definition: The cost for one unit.
Example: $3 per pound is a unit price.
Unit Rate
Definition: A rate written for one unit of the second quantity.
Example: 60 miles per hour is a unit rate.
Unique Triangle
Definition: Only one triangle can be made from the given information.
Example: Some side and angle conditions determine a unique triangle.
Unknown
Definition: A value that is not known yet.
Example: In x+5=12, x is unknown.
Unknown Amount
Definition: A quantity we do not know yet.
Example: A variable can represent an unknown amount.
V
Value
Definition: The amount or number something has.
Example: The value of x is 4.
Value Of A Variable
Definition: The number assigned to a variable.
Example: If x=6, the value of the variable x is 6.
Value Of An Expression
Definition: The result after evaluating an expression.
Example: The value of 3+5 is 8.
Variable
Definition: A letter or symbol that represents a number.
Example: x is a variable in x+2.
Variability
Definition: How much data values differ from each other.
Example: More spread means more variability.
Vertex
Definition: A point where sides, edges, or rays meet.
Example: A triangle has 3 vertices.
Vertex Of An Angle
Definition: The point where the two rays of an angle meet.
Example: The corner of an angle is its vertex.
Vertex Of A Pyramid
Definition: The point where the triangular faces meet.
Example: The top point of a pyramid is a vertex.
Vertical Angles
Definition: Opposite angles formed when two lines intersect.
Example: Vertical angles have equal measures.
Vertical Axis
Definition: The up-down axis on a graph.
Example: The vertical axis is often the y-axis.
Vertical Intercept
Definition: The point where a graph crosses the vertical axis.
Example: The vertical intercept is also called the y-intercept.
Vertical Line
Definition: A line that goes up and down and has undefined slope.
Example: x=3 is a vertical line.
Volume
Definition: The amount of space inside a three-dimensional figure.
Example: Volume is measured in cubic units.
Y
X-Axis
Definition: The horizontal axis on the coordinate plane.
Example: The x-axis goes left and right.
X-Coordinate
Definition: The first number in an ordered pair.
Example: In (4,7), the x-coordinate is 4.
X-Intercept
Definition: The point where a graph crosses the x-axis.
Example: At the x-intercept, y=0.
Y-Axis
Definition: The vertical axis on the coordinate plane.
Example: The y-axis goes up and down.
Y-Coordinate
Definition: The second number in an ordered pair.
Example: In (4,7), the y-coordinate is 7.
Y-Intercept
Definition: The point where a graph crosses the y-axis.
Example: In y=2x+3, the y-intercept is 3.
Zero Exponent
Definition: An exponent of 0. Any nonzero base to the zero power equals 1.
Example: 5⁰ = 1.
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