NY Next Generation Math NY-8.EE.7.b
The Standard
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and combining like terms.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students solve linear equations with rational coefficients, including variables on both sides. They expand expressions with the distributive property, combine like terms, and preserve equivalence through each step.
What Mastery Looks Like
- A student solves three-fourths of (8x - 4) plus 2x = 17 by expanding to 6x - 3 + 2x = 17. The student combines terms and finds x = 2.5, then checks it.
Common Misconceptions
- Students may distribute to only one term, combine unlike terms, or clear fractions on only part of an equation. They may move a term across the equality sign without an equivalent operation.
How to Assess It
- Ask students to solve one-half of (6x + 4) minus x = 10. Require a clear transformation sequence and substitution check.
Lesson moves
Ways to Teach It
Use algebra tiles or area models to expand grouped expressions, then record equivalent equation steps with rational coefficients.
Ask students how applying the same operation to both sides preserves the solution set.
Play equation error analysis with missed distribution, incorrect combining, and unequal operations before solving corrected versions.
Model a rational-rate cost equation and solve for the quantity that produces a stated total.
Free download
Printable NY-8.EE.7.b Worksheet
A ready-to-print activity worksheet aligned to NY-8.EE.7.b, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetKeep exploring
Related Standards
- NY-8.EE.8.c
Solve real-world and mathematical problems involving systems of two linear equations in two variables with integer coefficients.
- NY-7.EE.1
Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations.
- NY-7.NS.3
Solve real-world and mathematical problems involving the four operations with rational numbers
- NY-7.EE.4.a
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. Solve equations of these forms fluentl...
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.
Also for this standard:Make a WorksheetMake a QuizMake a Sub Lesson