Variable
A letter that represents a number.
Examplex + 4 = 10
Notice: Here, x represents 6.
Learning supports
Algebra Visual Dictionary
See the word, study the picture, and connect it to a real math example.
Helpful habit:When you meet a new math word, point to the part of the example that matches its meaning.
Download Printable PDFWhy should I care?
Math Words Tell You What to Do
If a direction says “evaluate the expression,” understanding those two words helps you know the first step before you calculate anything.
Word group 1
Parts of an Expression
Learn the pieces before putting them together.
Coefficient
The number multiplying a variable.
Example5x + 2
Notice: 5 is multiplying x.
Constant
A number that stands alone.
Example3x + 8
Notice: 8 has no variable beside it.
Term
One part separated by a plus or minus sign.
Example4x + 3 - 2y
Notice: This expression has 3 terms.
Factor
A number or variable being multiplied.
Example3x
Notice: 3 and x are factors.
Exponent
A small raised number that tells how many times to use the base as a factor.
Examplex² = x · x
Notice: The exponent is 2.
Word group 2
Math Statements
These words describe what kind of math you are looking at.
Expression
Numbers, variables, and operations with no equal sign.
Example2y - 7
Notice: An expression does not make a claim.
Equation
A statement that two amounts are equal.
Examplex + 4 = 10
Notice: An equation always has an equal sign.
Inequality
A statement comparing amounts that may not be equal.
Examplex ≤ 9
Notice: It uses <, >, ≤, or ≥.
Solution
A value that makes an equation or inequality true.
Example6 + 4 = 10
Notice: 6 is the solution to x + 4 = 10.
Evaluate
Replace a variable with a number and calculate.
Example2x + 1 when x = 5
Notice: Substitute 5 for x, then solve.
Simplify
Rewrite something in an easier form without changing its value.
Example4 + 3 → 7
Notice: The value stays the same.
Word group 3
Relationships and Patterns
Algebra helps us describe how values connect and change.
Like Terms
Terms with the same variable and the same exponent.
Example3x + 8x = 11x
Notice: x and x² are not like terms.
Ordered Pair
Two numbers that locate a point.
Example(2, 5)
Notice: Move to x first, then y.
Input
The value that goes into a rule or function.
Examplef(2) = 7
Notice: The input is 2.
Output
The value produced by a rule or function.
Examplef(2) = 7
Notice: The output is 7.
Function
A rule that gives exactly one output for each input.
Exampley = 2x + 1
Notice: One input cannot point to two outputs.
Slope
How steep a line is and which direction it moves.
Examplem = 2/3
Notice: Rise 2, then run 3.
Word group 4
Coordinate Plane
These words help you read and describe a graph.
x-axis
The horizontal number line on a coordinate plane.
Exampleleft ↔ right
Notice: Horizontal means side to side.
y-axis
The vertical number line on a coordinate plane.
Exampleup ↕ down
Notice: Vertical means up and down.
Origin
The point where the x-axis and y-axis meet.
Examplex = 0 and y = 0
Notice: The origin is the center starting point.
Quadrant
One of the four sections of a coordinate plane.
ExampleQuadrant I: (+, +)
Notice: Quadrants are numbered counterclockwise.
x-intercept
The point where a graph crosses the x-axis.
Example(4, 0)
Notice: The y-value is always 0.
y-intercept
The point where a graph crosses the y-axis.
Example(0, 3)
Notice: The x-value is always 0.
Compare carefully
Words That Are Easy to Confuse
Place the ideas side by side and look for the difference.
ExpressionversusEquation
Look for the equal sign
3x + 5 is an expression. 3x + 5 = 20 is an equation.
CoefficientversusConstant
Beside a variable or alone?
In 4x + 7, 4 is the coefficient and 7 is the constant.
TermversusFactor
Added parts or multiplied parts?
In 3x + 5, 3x is a term. Inside 3x, 3 and x are factors.
InputversusOutput
What goes in and what comes out?
In f(2) = 7, 2 is the input and 7 is the output.
Watch out
Common Mistakes
- Thinking every number in an expression is a coefficient.
- Combining terms that have different variables or exponents.
- Calling an expression an equation even though it has no equal sign.
Quick strategy
Point, Name, Explain
Point to one part of a math example, name it, and explain why it has that name. Example: “The 5 in 5x is the coefficient because it multiplies x.”
Your turn
10-Question Algebra Vocabulary Practice
Choose the correct word or answer. Use the examples above whenever you need help.
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