Grade 7 Unit 6 Mathematics Glossary

A complete set of vocabulary flashcards covering algebraic and geometric terminology from the Grade 7 Unit 6 curriculum.

Boundary point

The point on a number line or graph that separates solutions of an inequality from non-solutions. If it is a solution (e.g., $\ge$ or $\le$), it is a closed circle; if not (e.g., $>$ or $<$), it is an open circle. Example: The boundary point of $x > 3$ is $3$.

Coefficient

A number that is multiplied by a variable. In the expression $5x + 8$, $5$ is the coefficient of $x$.

Distributive property

The property stating that $a(b + c) = ab + ac$. Multiplying a number by the sum of two or more terms is equal to multiplying the number by each term separately before adding the products. Example: $3(2x + 5) = 3 \times 2x + 3 \times 5 = 6x + 15$.

Equivalent expressions

Expressions that are equal for every value of a variable. For example, $6x + 2x$ is equivalent to $5x + 3x$.

Expand

To use the distributive property to multiply the factors in an expression and rewrite the expression as a sum (e.g., rewriting $3(x + 5)$ as $3x + 15$).

Factor

To use the distributive property to rewrite an expression as the product of two or more factors (e.g., rewriting $3x + 15$ as $3(x + 5)$).

Greater-than-or-equal-to ($\ge$)

A symbol meaning the value of a variable is either exactly the number or any value greater than that number. Example: $x ≥ 3$.

Inverse operations

Two operations that undo each other. Adding and subtracting are inverse operations, as are multiplying and dividing.

Less-than-or-equal-to ($\le$)

A symbol meaning the value of a variable is either exactly the number or any value less than that number. Example: $x ≤ 9$.

Like terms

Terms with variables and exponents that are the same. For example, $8x$ and $12x$ are like terms, but $3x$ and $3x^2$ are not.

Scaled copy

A copy of an image that may change in size but maintains the same shape and angle measurements as the original. Each length is multiplied by the same number.

Scale factor

The number that every length of the original shape is multiplied by to produce a scaled copy. For example, the scale factor from $ABCD$ to $A'B'C'D'$ is $2$.

Solution to an equation

A value of a variable that makes the equation true. For example, $5$ is a solution to $3x = 15$ because $3(5) = 15$.

Solution to an inequality

All of the values of a variable that make the inequality true. For example, $x < 5$ represents the solutions to $3x < 15$.

Tape diagram

A way to represent relationships between quantities as lengths of a tape. The entire diagram represents the whole and is divided to represent the parts, such as representing the equation $3y + 2.25 = 6$.

Term

A part of an expression that can be a single number, a variable, or a number and variable multiplied together. In the expression $5x + 8$, the terms are $5x$ and $8$.