Virginia SOL 7.PFA.4

7.PFA.4 is a Standards of Learning standard. These are the knowledge and skills expectations under it.

• 7.PFA.4.a

  Apply properties of real numbers and the addition, subtraction, multiplication, and division properties of inequality to solve one- and two-step inequalities in...

• 7.PFA.4.b

  Investigate and explain how the solution set of a linear inequality is affected by multiplying or dividing both sides of the inequality statement by a rational ...

• 7.PFA.4.c

  Represent solutions to one- or two-step linear inequalities in one variable algebraically and graphically using a number line.

• 7.PFA.4.d

  Write one- or two-step linear inequalities in one variable to represent a verbal situation, including those in context.

• 7.PFA.4.e

  Create a verbal situation in context given a one or two-step linear inequality in one variable.

• 7.PFA.4.f

  Solve problems in context that require the solution of a one- or two-step inequality.

• 7.PFA.4.g

  Identify a numerical value(s) that is part of the solution set of as given one- or two-step linear inequality in one variable.

• 7.PFA.4.h

  Describe the differences and similarities between solving linear inequalities in one variable and linear equations in one variable.

01

What Students Need to Do

Students translate verbal situations into one- or two-step inequalities and create a matching situation from a given inequality. They solve using inverse operations with rational numbers, reversing the inequality when multiplying or dividing by a negative. They graph solution sets and decide whether specific values belong.

02

What Mastery Looks Like

A student solves accurately, keeps both sides balanced, and explains why the symbol reverses after multiplying or dividing by a negative. They use open or closed points correctly and shade the right direction. They connect the solution to a given context and check proposed values.

03

Common Misconceptions

Students often solve an inequality like an equation and report one value instead of a solution set. They may reverse the symbol during any subtraction, or forget to reverse it when multiplying or dividing by a negative. They also confuse open and closed points, shade the wrong direction, or translate phrases such as "no more than" incorrectly.

04

How to Assess It

Exit ticket: Solve -3x + 5 > 14, graph the solution, and state whether -4 is included. Add one sentence explaining any change to the inequality symbol.

1. 01

   Give pairs inequality cards and yarn number lines; students solve each, place an open or closed clip, and shade the solution set.

2. 02

   Ask: Why does dividing -2x > 8 by -2 reverse the sign? Explain with two test values and a number line.

3. 03

   Play Inequality Match: students pair cards showing an inequality, its solution, its graph, and a value that satisfies it.

4. 04

   Plan a movie trip with a $60 budget, a $12 ticket, and $6 snacks; write and solve for possible snack purchases.

• 6.PFA.3

  The student will write and solve one-step linear equations in one variable, including contextual problems that require the solution of a one-step linear equatio...

• 8.PFA.5

  The student will write and solve multistep linear inequalities in one variable, including problems in context that require the solution of a multistep linear in...

• 7.PFA.3

  The student will write and solve two-step linear equations in one variable, including problems in context, that require the solution of a two-step linear equati...

• 8.PFA.4

  The student will write and solve multistep linear equations in one variable, including problems in context that require the solution of a multistep linear equat...