NY Next Generation Math NY-8.EE.7

NY-8.EE.7 is a cluster heading. These are the individual standards under it.

• NY-8.EE.7.a

  Recognize when linear equations in one variable have one solution, infinitely many solutions, or no solutions. Give examples and show which of these possibiliti...

• NY-8.EE.7.b

  Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and ...

01

What Students Need to Do

Students solve one-variable linear equations with rational coefficients, including equations with variables on both sides. They simplify expressions and determine whether an equation has one, no, or infinitely many solutions.

02

What Mastery Looks Like

The student distributes, combines like terms, and isolates the variable while preserving equality. The student recognizes a final true statement as infinitely many solutions and a false statement as no solution.

03

Common Misconceptions

Students may change a term's sign without applying the same operation to both sides. They may report zero as the solution when variables cancel and a true or false statement remains.

04

How to Assess It

Ask students to solve 3(x - 2) = x + 8 and 2(x + 4) = 2x + 8. Require a solution classification for each.

1. 01

   Use balance mats and algebra tiles to model equations before recording matching symbolic steps.

2. 02

   Ask students to explain what remains when variables cancel and how that statement determines the number of solutions.

3. 03

   Run an equation sort into one solution, no solution, and infinitely many solutions, with written justifications.

4. 04

   Write and solve a break-even equation comparing two plans with different fixed fees and per-use charges.

• NY-8.EE.8.c

  Solve real-world and mathematical problems involving systems of two linear equations in two variables with integer coefficients.

• NY-8.EE.8.b

  Solve systems of two linear equations in two variables with integer coefficients: graphically, numerically using a table, and algebraically. Solve simple cases ...