Why this matters for FAST: Two-step equations are foundational to algebra and appear frequently on FAST. Students must efficiently combine like terms, apply the distributive property, and use inverse operations to isolate variables.
Students solve 2x + 5 = 13 by dividing first instead of subtracting first. This leads to incorrect answers.
"When solving two-step equations, work BACKWARDS from order of operations. Since we add/subtract AFTER multiplying, we UNDO addition/subtraction FIRST! Think: 'Undo the last operation first.'"
Students write 3(x + 4) = 3x + 4 instead of 3x + 12. They forget to multiply EVERY term inside the parentheses.
"The distributive property means you MULTIPLY the outside number by EVERY term inside. Draw arrows from the outside to each term: 3(x + 4) = 3 times x PLUS 3 times 4 = 3x + 12."
Students incorrectly add 3x + 5 = 8x, treating constants as if they have variables.
"Like terms must have the SAME variable part. 3x and 5x are like terms (both have x). But 3x and 5 are NOT like terms - they cannot be combined! Think of it like adding apples and oranges - you can't combine them into one number."
Review one-step equations: "If x + 5 = 12, what is x?" (x = 7). "If 3x = 15, what is x?" (x = 5). Remind students we use inverse operations to isolate x.
"A two-step equation requires TWO inverse operations to solve. We work BACKWARDS from order of operations. Since multiplication comes before addition in PEMDAS, we UNDO addition/subtraction FIRST, then division/multiplication."
Solving 2x + 5 = 13
Step 1: Subtract 5 from both sides: 2x = 8
Step 2: Divide both sides by 2: x = 4
Check: 2(4) + 5 = 8 + 5 = 13 ✓
Like Terms: Same variable AND same exponent
3x + 5x = 8x (combine the coefficients)
4y + 7 - 2y + 3 = 2y + 10 (combine x's, combine constants)
3x + 5 ≠ 8x (cannot combine - different terms!)
"Think of like terms as 'apples and apples.' You can add 3 apples + 5 apples = 8 apples. But you can't add 3 apples + 5 oranges and get 8 of anything!"
Distributive Property: a(b + c) = ab + ac
3(x + 4) = 3x + 12
-2(y - 5) = -2y + 10 (negative times negative = positive!)
5(2n + 3) = 10n + 15
"Distribution means the number outside MULTIPLIES every term inside the parentheses. Draw arrows to remind yourself - the outside number touches EVERY term inside!"
Work through these together:
"Solve for x: 3x + 8 = 23"
A) x = 5 B) x = 15 C) x = 10.33 D) x = 31
Correct answer: A) x = 5. Subtract 8 from both sides: 3x = 15. Divide by 3: x = 5. Check: 3(5) + 8 = 15 + 8 = 23 ✓
For struggling students: Use algebra tiles or a balance model to visualize equations. Color-code like terms. Start with simpler two-step equations before adding distributive property.
For advanced students: Challenge with multi-step equations that require combining like terms first, or equations with variables on both sides. Introduce real-world problems requiring equation setup.
For home: Send Parent Activity sheet. Families can practice with shopping scenarios: "If 3 items cost $24 total after a $5 discount, what does each item cost?"