# Grade 8 Mathematics Glossary

Absolute value: The distance a number is from \$0\$.

Acute angle: An angle that measures less than 90°.

Algebra: The study of mathematical symbols and the rules for manipulating those symbols.

Algebra grid: A grid used to illustrate values of algebraic expressions.

Angle: The angle \$∠ABC\$ consists of the two rays from \$B\$ that pass through \$A\$ and \$C\$ respectively. The spread between the directions of these rays is measured in degrees (°), and this measure is occasionally written \$m∠ABC\$, or sometimes \$∠ABC\$, or even \$∠B\$. 360° is a complete revolution.

Angle-Angle: A way to tell that two triangles are similar, by comparing two angles in each triangle. Two triangles \$▵ABC\$ and \$▵A'B'C'\$ are similar when the measures of \$∠A\$ and \$∠A'\$ are equal and the measures of \$∠B\$ and \$∠B'\$ are equal.

Angle-Side-Angle: A way to tell that two triangles are congruent, by comparing two angles and the side between them in each triangle. Two triangles \$▵ABC\$ and \$▵A'B'C'\$ are congruent when the measures of \$∠A\$ and \$∠A'\$ are equal, the measures of \$∠B\$ and \$∠B'\$ are equal, and the lengths of \$\ov{AB}\$ and \$\ov{A'B'}\$ are equal.

Area: The size of a region in the plane, measured in unit squares (squares with side length 1).

Association: A relationship or pattern linking the values of two variables.

Associative law of addition: For any three numbers \$a\$, \$b\$, and \$c\$, it is always true that \$(a+b)+c = a+(b+c)\$.

Associative law of multiplication: For any three numbers \$a\$, \$b\$, and \$c\$, it is always true that \$(a(b))(c) = a(b(c))\$.

Base: A number that is raised to a power.

Best fit line: When the points on a grid are not all on a straight line, but seem to have a somewhat linear pattern, you can find a line that is the “best fit” (closest) to the points.

Break even: Have a profit of zero (that is, make exactly as much money as you spend).

Circumference: The distance around an entire figure, such as a circle or a sphere. For a sphere, this means the distance around a circle on the sphere whose center is at the center of the sphere.

Cluster: A group of points in a scatter plot that are near each other.

Coefficient: A constant that a variable or expression is multiplied by.

Combining like terms: Using the distributive law to add any two multiples of an expression such as \$x\$. For example, you can simplify \$4x+5x\$ into \$9x\$.

Commutative law of addition: For any two numbers \$a\$ and \$b\$, \$a + b = b + a\$.

Commutative law of multiplication: For two numbers \$a\$ and \$b\$, \$a(b) = b(a)\$.

Conditional relative frequency: A joint frequency divided by the total of its row or column in a two-way frequency table.

Cone: A solid figure formed by taking a flat circular disk and extending it up to a single point.

Congruence rule: A rule that allows you to tell that two figures are congruent by looking at some of their measurements, such as the Side-Angle-Side (SAS), Angle-Side-Angle (ASA), and Side-Side-Side (SSS) rules for triangles.

Congruent: The same shape and size. Two plane figures are congruent if one can be obtained from the other by a rigid motion (a sequence of translations, rotations, and reflections).

Constant: A single fixed number (unlike a variable, whose value can vary).

Converse to the Pythagorean Theorem: If a triangle has side lengths \$a\$, \$b\$ and \$c\$, and \$a^2+b^2=c^2\$, then the triangle is a right triangle and \$c\$ is the length of the side opposite its right angle.

Coordinates: A point on a 2-dimensional plane is described by a pair \$(x, y)\$. The coordinate \$x\$ is given by the labels below the grid, and the coordinate \$y\$ is given by the labels to the left of the grid.

Coordinate plane: A 2-dimensional flat surface used for plotting points, lines, curves, and regions. It contains an \$x\$ and a \$y\$ axis which intersect at the origin.

Coordinate grid: A grid of lines on a coordinate plane that makes it easy to see \$(x, y)\$ coordinates of locations in that plane.

Corresponding angles: Two angles that are formed by a transversal and each of the two lines that the transversal intersects, if the angles are in the same position relative to those lines. Usually we only talk about corresponding angles if the two lines are parallel, and in that case corresponding angles will have equal measures. Conversely, if any transversal creates two corresponding angles that are equal in measure, then the two lines are parallel.

Cost: In economics, how much money a company spends to produce a product.

Cube: The cube of a number \$x\$ is \$x^3\$, which is the volume of a cube whose edges each have length \$x\$.

Cube root: The cube root of \$a\$, written \$√^3 a\$, is the number whose cube is \$a\$. That is, \$(√^3 a)^3 = a\$.

Cubing: Cubing a number \$x\$ means computing the cube of \$x\$, namely \$x^3\$.

Cylinder: A solid figure formed by taking a flat circular disk and extending it straight up.

Data: A collection of related measurements.

Decimal: A fractional quantity written with a decimal point (like \$0.5\$).

Decreasing function: A function whose output decreases when its input increases.

Denominator: The bottom number or expression in a fraction.

Difference: The distance between two quantities, or the answer to a subtraction problem.

Dilation: A dilation by a positive number \$r\$ about a point \$A\$ is a transformation that moves each other point \$B\$ along the ray from \$A\$ that passes through \$B\$, and multiplies distances from \$A\$ by \$r\$. \$A\$ is called the center of the dilation.

Distance: The distance between two points \$A\$ and \$B\$ is the length of the line segment \$\ov{AB}\$.

Distributive law of multiplication over addition: For any three numbers \$a\$, \$b\$, and \$c\$, \$a(b+c) = a(b)+a(c)\$, and \$(b+c)(a) = b(a)+c(a)\$.

Distributive law of multiplication over subtraction: For any three numbers \$a\$, \$b\$, and \$c\$, \$a(b−c) = a(b)−a(c)\$, and \$(b−c)(a) = b(a)−c(a)\$.

Equation: A mathematical sentence with an equals sign (like \$3x+5=11\$).

Equivalent: Two fractions are equivalent if they have the same numerical value. Two equations are equivalent if they have the same solution set.

Expanding an expression: Using the distributive law to turn expressions which need parentheses (like \$3(x+2)\$) into expressions which do not (like \$3x+6\$).

Exponent: In a power, the number of times the base is multiplied by itself.

Expression: A combination of variables and numbers using arithmetic (like \$6-x\$).

Exterior angles: The angles at each vertex of a polygon that are formed by one side touching that vertex, and the line extending the other side touching that vertex, and that are outside the polygon.

Formula: An expression that is used to compute a value.

Fraction: A numerator divided by a denominator (like \$\$1/2\$\$). Usually we require the numerator and denominator to both be integers.

Frequency: In statistics, the number of times something occurs, or is observed.

Function: A rule that assigns to each input exactly one output. The graph of a function is the collection of points with coordinates \$(x, y)\$, where \$x\$ is an input and \$y\$ is its corresponding output.

Geometry: The mathematics of shape, size, position, and measurement.

Graph: An image formed by plotting the solutions to an equation, or some other collection of pairs of numbers, on a coordinate plane. To graph an expression containing the variable \$x\$, set \$y\$ equal to that expression.

Horizontal: Going from side to side, like the horizon.

Hypotenuse: In a right triangle, the side opposite the right angle.

Increasing function: A function whose output increases when its input increases.

Improper fraction: A fraction in which the numerator is larger than the denominator (like \$\$3/2\$\$).

Infinite: More than any finite (real) number.

Integer: A whole number or the negative of a whole number. For instance, \$37\$ and \$0\$ and \$-5\$ are integers, but \$2.7\$ and \$\$-3/2\$\$ are not.

Interior angles: The angles at each vertex of a polygon that are formed by the two sides meeting at that vertex, and that are inside the polygon.

Irrational number: A number that cannot be written as a fraction \$\$m/n\$\$ where \$m\$ and \$n\$ are integers.

Isolate: Make a variable appear alone on one side of an equation, and not occur in the other side of the equation.

Joint frequency: The number of events that satisfy both of two specified criteria.

Joint relative frequency: A joint frequency divided by the total number of events.

Kilogram: A kilogram, or “kg”, is a mass that weighs about 2.2 pounds in normal Earth gravity.

Laws of exponents: \$\$a^{c + d} = a^c a^d\$\$, \$\$(a b)^d = a^d b^d\$\$, and \$\$(a^c)^d = a^{cd}\$\$. These are always true when \$c\$ and \$d\$ are positive integers. If \$a\$ and \$b\$ are nonzero, then they are true for any integers \$c\$ and \$d\$, as is \$\$a^{c - d} = a^c / a^d\$\$. If \$a\$ and \$b\$ are positive, then all four laws are true for any \$c\$ and \$d\$.

Legs: In a right triangle, the two sides next to the right angle.

Line: An infinite straight collection of points with no gaps, extending in both directions. If \$A\$ and \$B\$ are distinct (different) points, there is exactly one line \$AB\$ that contains them both.

Line segment: The line segment \$\ov{AB}\$ consists of the points \$A\$, \$B\$, and the points on the line \$AB\$ that are between \$A\$ and \$B\$. \$\ov{AB}\$ is the straight path connecting \$A\$ and \$B\$.

Linear: A straight line, or an equation or expression whose graph is a straight line. If \$m\$ and \$b\$ are constants, then \$mx+b\$ is a linear expression, and a function \$f\$ defined by \$f(x)=mx+b\$ is a linear function.

Linear association: Two variables in a scatter plot have a linear association if the points form a pattern which is close to a straight line.

Linear function: A function whose graph is a straight line.

Linear model: An estimate for a variable using a linear expression in another variable.

Meter: A length of about 39.37 inches.

Negate: Take the opposite of a number, by multiplying it by \$-1\$.

Negative association: A negative association between two variables means that when one increases, the other one usually decreases.

Negative number: A value less than zero (like \$-3\$).

Nonlinear association: Two variables in a scatter plot have a nonlinear association if the points form a pattern which is not close to a straight line.

Non-negative number: A value which is not negative (it is either positive or zero).

Numerator: The top number or expression in a fraction.

Obtuse angle: An angle that measures more than 90°.

Origin: The point on a coordinate plane where the \$x\$-axis and \$y\$-axis intersect. It is represented by the coordinates \$(0, 0)\$.

Outlier: A value that “lies outside” (is much smaller or larger than) most of the other values in a collection.

Parallel: Two lines in a plane are parallel if they always have the same distance between them, so they never intersect. If two lines are parallel, they have the same slope.

Perfect square: A whole number which is the square of another whole number.

Perpendicular: Two lines are perpendicular if they create a 90-degree angle. If two lines are perpendicular and the slope of one of them is \$m\$, then the slope of the other line is \$\$-1/m\$\$.

π: (“Pi”, pronounced like “pie.”) The area of a circle with radius 1. A circle with radius \$r\$ has area \$πr^2\$ and circumference \$2πr\$. \$π\$ is approximately 3.1416.

Plane: A two-dimensional infinite flat collection of points, with no gaps or end in any of its directions.

Point: A location. A point in the coordinate plane has coordinates \$(x,y)\$, where \$x\$ is given by the labels below a coordinate grid, and \$y\$ is given by the labels to the left of a coordinate grid.

Point-slope form: If a line contains the point \$(x_1,y_1)\$ and has slope \$m\$, then its equation can be written as \$y−y_1=m(x−x_1)\$. An equation in the form \$y−y_1=m(x−x_1)\$ is said to be in point-slope form.

Polygon: A finite number of line segments in a plane, with each segment starting where the previous one ends, and the first segment starting where the last one ends, with no other intersections between segments. The segments are called “edges” or “sides.”

Positive association: A positive association between two variables means that when one increases, the other one usually increases also.

Positive number: A value greater than zero (like 3).

Power: An expression of the form \$a^d\$. \$a\$ is called the base, \$d\$ is called the exponent, and \$a^d\$ is called “the \$d\$th power of \$a\$”. If \$d\$ is a positive integer, \$a^d\$ means \$a\$ multiplied by itself \$d\$ times.

Product: The answer to a multiplication problem.

Profit: Revenue minus cost.

Proportional sides: A way to tell that two triangles are similar, by comparing all three sides in each triangle. Two triangles \$▵ABC\$ and \$▵A'B'C'\$ are similar when there is a single number \$r\$ such that the length of \$\ov{A'B'}\$ is \$r\$ times the length of \$\ov{AB}\$, the length of \$\ov{A'C'}\$ is \$r\$ times the length of \$\ov{AC}\$, and the length of \$\ov{B'C'}\$ is \$r\$ times the length of \$\ov{BC}\$. Conversely, if two triangles \$▵ABC\$ and \$▵A'B'C'\$ are similar, then there is a positive number \$r\$ with these properties.

Pyramid: A solid figure formed by taking a flat base which is a polygon, and extending it up to a single point.

The Pythagorean Theorem: If a right triangle has side lengths \$a\$, \$b\$, and \$c\$, where \$c\$ is the length of the side opposite the right angle, then \$a^2+b^2=c^2\$.

Quadrant: Each of the four sections of a coordinate plane made by the intersecting \$x\$- and \$y\$-axes. The four quadrants are labeled I, II, III, and IV, counterclockwise from the top right.

Quadrilateral: A polygon with 4 sides.

Quotient: The answer to a division problem.

Radius: The distance from the center of a circle or sphere to any point on the circle or sphere.

Rate of change: The speed at which a variable changes over a period of time. This is given by the change in the variable divided by the change in (amount of) time.

Rational number: A number that can be written as a fraction \$\$m/n\$\$ where \$m\$ and \$n\$ are integers.

Ray: A point \$A\$, together with all points in a single direction from \$A\$.

Reflection: Rigid motion across a fixed line \$AB\$ in a plane, like a mirror image.

Relative frequency: A frequency divided by the total number of events, often expressed as a percentage.

Revenue: How much money a company receives in sales.

Right angle: A 90° angle.

Right prism: A solid figure formed by taking a flat base which is a polygon, and extending it straight up.

Right triangle: A triangle that has a 90° angle.

Rigid motion: A motion that preserves distances and angle measures, with no stretching, shrinking, or bending. A rigid motion in the plane is a sequence of one or more translations, rotations, and/or reflections.

Root-mean-square error: A number that tells you how far away a line or curve is from a collection of points (a smaller number means the line is a better “fit” to the points).

Rotation: Rigid motion around a fixed center \$A\$, with turning but no reflection.

Scatter plot: Dots in the coordinate plane representing pairs of linked measurements, such as heights and weights for a group of people.

Scientific notation: Writing a nonzero number as \$a ⋅ 10^n\$ where \$n\$ is an integer and \$1 ≤ {|a|} < 10\$ (that is, \$a\$ has exactly 1 digit before the decimal point, and that digit is nonzero).

Side-Angle-Side: A way to tell that two triangles are congruent, by comparing two sides and the angle between them in each triangle. Two triangles \$▵ABC\$ and \$▵A'B'C'\$ are congruent when the lengths of \$\ov{AB}\$ and \$\ov{A'B'}\$ are equal, the lengths of \$\ov{AC}\$ and \$\ov{A'C'}\$ are equal, and the measures of \$∠A\$ and \$∠A'\$ are equal.

Side-Side-Side: A way to tell that two triangles are congruent, by comparing all three sides in each triangle. Two triangles \$▵ABC\$ and \$▵A'B'C'\$ are congruent when the lengths of \$\ov{AB}\$ and \$\ov{A'B'}\$ are equal, the lengths of \$\ov{AC}\$ and \$\ov{A'C'}\$ are equal, and the lengths of \$\ov{BC}\$ and \$\ov{B'C'}\$ are equal.

Similar: Two geometric figures are similar if they have the same shape but possibly different sizes, with corresponding lengths differing by a single common scale factor. In other words, two figures are similar if one can be obtained from the other by a similarity transformation. Two triangles are similar if they have the same angles as each other.

Similarity rule: A rule that allows you to tell that two figures are similar by looking at some of their measurements, such as the Angle-Angle (AA) and proportional sides rules for triangles.

Similarity transformation: A rigid motion followed by a dilation. Any combination of rigid motions and dilations has the same effect as some single rigid motion followed by a single dilation, so the entire transformation is a similarity transformation.

Simplify: To rewrite an expression in a way that means the same thing but is simpler (or shorter). You can simplify \$3x - x + 6\$ into \$2x + 6\$.

Slope: A number that measures how steep a line is. It shows the amount of change in the height of the line as you go 1 unit to the right. The slope of the line \$y=mx+b\$ is \$m\$.

Slope-intercept form: The form \$y=mx+b\$ for a linear equation, where \$m\$ and \$b\$ are constants. The numbers \$m\$ and \$b\$ give the slope and \$y\$-intercept of the line that is the graph of that equation.

Solution: In an equation, a number that can be substituted for the variable to make that equation true. If the equation has more than one variable, a solution is a list of numbers that when substituted for the list of variables makes the equation true. For a system of more than one equation, a solution must make all of the equations true.

Solution set: All solutions to an equation or system.

Solve: Find the solutions to an equation or system.

Sphere: The set of points in space that are a given distance from a given center.

Square: The square of a number \$x\$ is \$x^2\$, which is the area of a square whose sides each have length \$x\$.

Square root: A square root of \$a\$ is a number \$b\$ whose square is \$a\$. That is, \$b^2 = a\$. If \$b\$ is a square root of \$a\$, then so is \$- b\$. If \$a ≥ 0\$, “the” square root of \$a\$, written \$√a\$, is the square root of \$a\$ that is positive or zero.

Squaring: Squaring a number \$x\$ means computing the square of \$x\$, namely \$x^2\$.

Standard form: For a linear equation, the form \$Ax+By=C\$ where \$A\$, \$B\$, and \$C\$ are constants.

Statistic: A number used to describe or summarize data.

Statistics: The study of data, and the methods used to describe or summarize data.

Substitution: In an expression or equation, eliminating a variable by replacing it with another expression that it is equal to.

Sum: The answer to an addition problem.

Supplementary angles: Two angles whose total measure is 180°.

System: For equations, two or more equations that are all required to be true.

Term: Element in a sum or difference.

Translation: Rigid motion by a constant distance in a single direction, with no rotation or reflection.

Transversal: A line that intersects two other lines in different points.

Triangle: A polygon with 3 sides.

Two-way frequency table: For events that can be divided into categories two different ways, a table of joint frequencies, using rows of the table to group the events one way, and columns of the table to group the events the other way.

Unit: A standard measurement, such as a meter or an hour.

Value: A number that a variable or expression can equal.

Variable: A letter (like \$x\$) that we can use to mean different numbers at different times.

Vertex: An end of a side of a polygon, or the corner point of an angle.

Vertical: Going up and down.

Vertical angles: Opposite angles formed by the intersection of two lines.

Vertices: The plural of “vertex.”

Volume: The size of a region in space, measured in unit cubes (cubes with edge length 1).

Whole number: One of the numbers 0, 1, 2, 3, ... .

\$x\$-axis: The horizontal line running through the origin on a coordinate plane.

\$x\$-coordinate: The horizontal value in a coordinate pair. It tells how far to the left or right the point is. The \$x\$-coordinate is always written first in the coordinate pair.

\$x\$-intercept: A point where a curve meets the horizontal axis (the \$x\$-axis).

\$y\$-axis: The vertical line running through the origin on a coordinate plane.

\$y\$-coordinate: The vertical value in a coordinate pair. It tells how far up or down the point is. The \$y\$-coordinate is always written last in the coordinate pair.

\$y\$-intercept: A point where a line or curve meets the vertical axis (the \$y\$-axis). The \$y\$-intercept of the line \$y=mx+b\$ is the point \$(0,b)\$.