CCSS.Math.Content.8.EE.C.7b
The standard
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Common Core State Standards for Mathematics
What this standard means
Students need to solve one-variable linear equations that include fractions, decimals, parentheses, and like terms on one or both sides. They should know when to distribute, combine like terms, clear fractions, and use inverse operations to isolate the variable.
Mastery looks like clean, logical work with each step justified by keeping both sides balanced. Students can handle equations like 3(x - 4) + 1.5x = 9 without guessing. Common trouble spots are sign errors when distributing negatives, forgetting to apply a multiplier to every term, and combining unlike terms.
Ways to teach it
- Hands-on activity: Give pairs algebra tiles or paper tiles to model 2(x + 3) = 14, then match each move to a written equation step.
- Discussion or writing prompt: Ask students, “Which step would you do first and why?” for an equation with parentheses, fractions, and terms on both sides.
- Quick assessment: Put three worked solutions on the board, one correct and two with common errors, and have students identify and fix the mistakes.
- Real-world connection: Use a phone plan equation with an activation fee and monthly charge, then have students solve when two total costs are equal.
Plan a lesson for CCSS.Math.Content.8.EE.C.7b
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- CCSS.Math.Content.HSA-REI.A.2
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
- CCSS.Math.Content.HSA-CED.A.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rati...
- CCSS.Math.Content.HSA-REI.B.3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.