Variables & Expressions
Grades 6–8 Algebra Number sense
A variable is a letter that holds a place for a number.
When you see x, don't think "mystery" — think "empty box
waiting for a value." In 3x + 2, the box holds whatever
number we decide; the expression's value changes with it.
Evaluating an expression
Swap the variable for a number, then follow order of operations:
3x + 2 when x = 5
= 3·(5) + 2 ← swap x for 5
= 15 + 2
= 17
Words into algebra
Most of algebra is translation. Learn the phrases:
- "three more than n" →
n + 3 - "five times y" →
5y(we drop the × sign) - "seven less than w" →
w − 7— careful, order flips! - "half of t" →
t/2
Watch out
"Five less than x" is
x − 5, not 5 − x. The
number doing the subtracting comes second. Read it as "take 5 away
from x."
Terms and coefficients
In
4x + 7: 4x and 7 are
terms. The 4 is the
coefficient — how many x's you have. A term with no
variable (7) is a constant.
Practice — evaluate & translate
Evaluate 3x + 2 when x = 5.
Evaluate 4y − 2 when y = 6.
"Eight less than m" means:
Write "six times n" in algebra form.
Next: one-step equations · Back: order of operations