Wyoming Math 8.EE.7

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

• 8.EE.7a

  Solve linear equations and inequalities with rational number coefficients that include the use of the Distributive Property, combining like terms, and variable ...

• 8.EE.7b

  Recognize the three types of solutions to linear equations: one solution, infinitely many solutions, or no solutions.

01

What Students Need to Do

Students solve multi-step equations and inequalities with fractions or decimals. They distribute, combine like terms, and work with variables on both sides. They identify equations with one solution, no solution, or infinitely many solutions.

02

What Mastery Looks Like

A student solves 1/2(x + 4) = x - 1 and checks that x = 6 works. They graph the solution x ≤ -3 for -2(x - 1) ≥ 8. They can explain what it means when the variables cancel and leave a true or false statement.

03

Common Misconceptions

Students may multiply x by 1/2 but forget to multiply the 4 inside the parentheses. They may forget to reverse an inequality sign when dividing by a negative number. When variables cancel, they may write x = 0 instead of checking the statement that remains.

04

How to Assess It

Exit ticket: Solve 1/2(x + 4) = x - 1 and -2(x - 1) ≥ 8, then graph the inequality solution. Classify 2(x + 1) = 2x + 3 as having one solution, no solution, or infinitely many solutions.

1. 01

   Use a balance mat and paper tiles labeled x, x/2, and 1 to solve x/2 + 2 = x - 1.

2. 02

   Ask why dividing -2x < 6 by -2 reverses the sign, then have students test x = -4 and x = 0.

3. 03

   Sort cards showing x + 2 = x + 2, 2x + 1 = 2x + 3, and 3x - 1 = x + 5 by solution type.

4. 04

   Compare ride fares of $4 plus $2 per mile and $10 plus $1 per mile; find when the first costs less.

• 7.EE.4

  Apply the concepts of linear equations and inequalities in one variable to real-world and mathematical situations.

• 7.EE.4d

  Identify and justify the steps for solving multi-step linear equations and two-step linear inequalities.

• 8.F.4

  Apply the concepts of linear functions to real-world and mathematical situations.

• 6.EE.7

  Write and solve real-world and mathematical problems in the form of one-step, linear equations involving non negative rational numbers.