Algebraic expressions

Practice 5 items →

A variable is a number we have not picked yet. Students write expressions from sentences, evaluate them at given values, and combine like terms — terms with the same variable part. The distributive property runs both ways: a(b + c) = ab + ac expands, and ab + ac = a(b + c) factors out a common monomial, which is why GCF comes first in the year. The three standard mistakes: reading 3x at x = 4 as 34, adding 3x + 2x to get 5x², and distributing 2(x + 3) as 2x + 3. Evaluating at negative inputs waits for Math 7.

Specification · for a parent or teacher

Part no.: algebraic-expressions-6
Course: Advanced Math 6 · Unit 8
Realm: Structures
Difficulty: 3 of 4 — Grade 6–7 core. Multi-step, first symbolic work.
Qty: 5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

write expressions from sentences; evaluate at given values; combine like terms; distribute $a(b+c)=ab+ac$ and factor $ab+ac=a(b+c)$ .

Ready when

they simplify $3(2x+4)+x$ to $7x+12$ and evaluate at $x=\frac12$ ( $15.5$ ). Evaluating at negative inputs waits for Math 7, where operations on negatives are taught.

Formulas

Distributive property

a(b+c) = ab + ac

Factoring out a monomial

ab + ac = a(b+c)

Like terms

3x + 2x = 5x

Watch for

$3x+2$ at $x=4$ as 32; $3x+2x=5x^2$ ; $2(x+3)=2x+3$ .

Before · requires

Writing and evaluating expressionsorder-of-operations · Math 5
Whole numbers: primes, GCF, and LCMgcf-lcm-grade6 · Math 6

After · used by

Equations and inequalities (one step)one-step-equations-inequalities · Math 6
Introduction to algebraalgebra-foundations-7 · Math 7

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