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Writing and Evaluating Expressions

5 min readGrade 8 · Algebra & Patterning

An expression is a mathematical phrase — a recipe written in symbols. In 0.5n − 3n + 25, n is the variable, 0.5 and −3 are coefficients, and 25 is the constant. Students translate words into expressions, substitute to evaluate, and simplify by collecting like terms.

What students explore

Students write expressions from words and contexts, name the parts of an expression, evaluate by substitution, and simplify by collecting like terms — the foundation for solving equations.

Key ideas

An expression has variables, coefficients, constants, and terms but no equals sign. To evaluate, replace the variable with its value and follow the order of operations. To simplify, combine like terms (terms with the same variable).

Worked example

Evaluate 0.5n − 3n + 25 when n = 14: 0.5(14) − 3(14) + 25 = 7 − 42 + 25 = −10. Simplify first: 0.5n − 3n = −2.5n, so −2.5(14) + 25 = −35 + 25 = −10.

KEY VOCABULARY

Variable — A letter that represents an unknown or changing quantity.

Coefficient — The number multiplying a variable, such as the 3 in 3x.

Constant — A fixed number in an expression, with no variable attached.

Like terms — Terms with the same variable raised to the same power, which can be combined.