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th
8
Grade
FoR
Math
UNIT ONE
Alternate Exterior Angles
When two lines are crossed by another line
{the transversal}, the pairs of angles on opposite sides
of the transversal, but outside the two lines.
Alternate Interior Angles
Two lines are crossed by another line {the
transversal}, the pairs of angles on opposite sides
of the transversal but inside the two lines.
Angle of Rotation
The amount of rotation about a
fixed point
Congruent Figures
Figures that have the same size and
shape
Corresponding sides
Sides that have the same relative
positions in geometric figures
Corresponding Angles
Angles that have the same relative
positions in geometric figures
Dilation
To resize something. In math it
means to make it larger or smaller.
Linear Pair
Adjacent, supplementary angles.
Excluding their common side, a linear pair
forms a straight line
Reflection
A transformation that "flips" a
figure over a line of reflection
Reflection Line
A line that is the perpendicular bisector of the
segment with endpoints at a pre-image point
and the image of that point after a reflection
Rotation
A transformation that turns a figure about a
fixed point through a given angle and a given
direction
Same-Side Interior Angles
Pairs of angles formed when a third line {a
transversal} crosses two other lines. These angles are
on the same side of the transversal and are between
the other two lines
Same-Side exterior Angles
Pairs of angles formed when a third line {a
transversal} crosses two other lines. These angles are
on the same side of the transversal and are outside
the other two lines
Scale Factor
The ratio of any two corresponding
lengths of the sides of two similar figures
Similar Figures
Figures that have the same shape
but not necessarily the same size
Transformation
The mapping, or movement, of all the points of
a figure in a plane according to a common
operation
Translation
A transformation that "slides" each point of a
figure the same distance in the same direction
Transversal
A line that crosses two or more lines
UNIT TWO
Addition Property of Equality
For real numbers a, b, and c, if a = b,
then a + c = b + c.
Additive Inverses
Two numbers whose sum is 0 are additive
inverses of one another.
Example: 3/4 and – 3/4 are additive inverses of one another
because 3/4 + (-3/4) = 0
Algebraic Expression
A mathematical phrase involving at least one
variable. Expressions can contain numbers and
operation symbols
Addition Property of Equality
For real numbers a, b, and c, if a=b
then a + c = b + c.
Cube Root
A special value that, when used in a
multiplication three times, gives that number
Decimal Expansion
The decimal expansion of a number is its
representation in base10.
2
Example: The decimal expansion of 25 is 625.
Equation
A mathematical sentence that
contains an equals sign
Evaluate the Algebraic Expression
To perform operations to obtain
a single number or value
Exponent
The number of times a base is used as a
factor of repeated multiplication
Exponential Notation
A representation of real numbers as the product of a
number between 1 and 10 and a power of 10, used
primarily for very large or very small numbers
Inverse Operation
Pairs of operations that undo each other, for example,
addition and subtraction are inverse operations and
multiplication and division are inverse operations
Irrational
A real number whose decimal form is nonterminating and non-repeating that cannot be
written as the ratio of two integers
Like Terms
Monomials that have the same variable raised
to the same power. Only the coefficients of
like terms can be different
Linear Equation in One Variable
An equation that can be written in the
form ax + b = c where a, b, and c are
real numbers and a ≠ 0.
Multiplication Property of Equality
For real numbers a, b, and c (c ≠ 0),
if a=b, then ac=bc.
Multiplicative Inverses
Two numbers whose product is 1 are
multiplicative inverses of one another.
Example: 3/4 and 4/3 are multiplicative inverses because 3/4 x 4/3 = 1
Perfect Square
A number that has a rational
number as its square root
Radical
A symbol √ that is used to
indicate square roots
Rational
A number that can be written as the ratio of
two integers with a nonzero denominator
Scientific Notation
A representation of real numbers as the product of a
number between 1 and 10 and a power of 10, used
primarily for very large or very small numbers
.
Significant
Digits
A way of describing how precisely a
number is written
Solution
The value or values of a variable that
make an equation a true statement
Solve
Identify the value that when substituted for
the variable makes the equation a true
statement
Square Root
One of two equal factors of a nonnegative
number.
Example: 5 is a square root of 25 because 5•5 = 25
Variable
A letter or symbol used to
represent a number
UNIT THREE
Altitude of a Triangle
The perpendicular distance between a vertex
of a triangle and the side opposite that vertex.
Sometimes called the height of a triangle
Base {of a polygon}
For two-dimensional figures, any side can be a
base. Typically, however, the bottom side, on
which the polygon ‘sits,’ is called the base
Coordinate Plane
A two-dimensional surface on which
points are plotted and located by their x
and y coordinates.
Coordinate Point
A pair of numbers defining the position
of a point on a two-dimensional plane
Cone
A three dimensional figure with a circular
or elliptical base and one vertex
Converse
of Pythagorean Theorem
If the square of the length of the longest side
of a triangle is equal to the sum of the squares
of the lengths of the other two sides, the
triangle is a right triangle
Cylinder
A 3D object with two parallel,
congruent, circular bases
Deductive Reasoning
The process by which one makes conclusions
using known facts, definitions, rules, or
properties
Diameter
The distance across a circle through its
center. The line segment that includes the
center and whose endpoints lie on the circle.
Distance Formula
An application of the Pythagorean Theorem
based on the distance between two points
Geometric
Solid
The collective term of all bounded
three dimensional geometric figures
Heights of Solids
The vertical height (or altitude) which is the
perpendicular distance from the top down to
the base
Hypotenuse
The side of a right triangle that is
directly across from the right angle
Irrational
A real number whose decimal form is nonterminating and non-repeating that cannot
be written as the ratio of two integers
Leg of a Triangle
Either of the two shorter sides of a right
triangle. These two sides together form
the right angle in the right triangle
Literal Equation
An equation with more than one variable.
Formulas are literal equations.
Perfect
Squares
The product of a rational number
multiplied by itself.
Perfect CUbes
In arithmetic and algebra, the cube of a number
n is its third power. It is the result of the
number multiplying by itself three time
Pythagorean Theorem
A theorem that states that in a right triangle, the
square of the length of the hypotenuse equals the
sum of the squares of the lengths of the legs
Pythagorean Triples
A set of positive integers, a, b, and c that
2
2
2
fit the rule a + b = c
Sphere
The set of all points in space that are
equidistant from a fixed point, called the center
Square Root
The square root of a number is a special value
that, when multiplied by itself, gives the
number.
Radius
The distance from the center of a circle to any point on
the circle. Also, the line segment that has the center of
the circle as one endpoint and a point on the circle as
the other endpoint.
Rational Number
A number expressible in the form a/b or
–a/b for some fraction a/b. The rational
numbers include the integers
Right
Triangle
A triangle with exactly one
right angle
Volume
The amount of space occupied by
an object.
UNIT FOUR
Domain
Domain of a relation is the set of all
X-coordinates of the ordered pairs of
that relation
Function
A rule of matching elements of two sets of
numbers in which an input value from the first
set has only one output value in the second set
Graph of a Function
The set of all the points on a coordinate
plane whose coordinates makes the rule
of function true
Range of a Function
The set of all output values or the y-values of
a function or a relation is called the range of
the function or the relation
UNIT FIVE
Intersecting Lines
Two lines that cross each other.
Origin
The point of intersection of the vertical and
horizontal axes of a Cartesian plane. The
coordinates of the origin are (0, 0)
Proportional Relationship
A relationship between two equal
ratios
Slope
How steep a straight line is.
Unit Rate
A comparison of two measurements in
which the second term has a value of 1.
UNIT SIX
Model
A mathematical representation of a
process, device, or concept by means of
a number of variables
Interpret
To establish or explain the
meaning or significance of something
Initial Value
y-intercept
Qualitative Variables
A variable whose values are not numerical.
Example: gender (male, female)
Linear
A relationship or function that can
be represented by a straight line
Non-Linear
A relationship which does not create
a straight line
Rate of Change
The ratio of the change in the
output value and change in the input
value of a function
Bivariate Data
Two different response variables
that are from the same population.
Quantitative
Variables
A variable whose values are
numerical.
Example: grades, height, temperature
Scatter Plot
The graph of a collection of ordered pairs that allows
an exploration of the relationship between the points
Line of Best Fit
A straight line drawn through the center of a
group of data points plotted on a scatter plot.
Clustering
The partitioning of a data set into subsets (clusters), so that the
data in each subset (ideally) share some common trait -often
similarity or proximity for some defined distance measure
Outlier
An element of a data set that distinctly
stands out from the rest of the data
UNIT SEVEN
System of Linear Equations
Two or more equations that together
define a relationship between variables.
Simultaneous Equations
Another name for a system of
Linear Equations