Maryland Math 8.AT.B.4

8.AT.B.4 is a cluster heading. These are the individual standards under it.

• 8.AT.B.4.a

  Solve inequalities including those requiring the use of the distributive property and combining like terms.

• 8.AT.B.4.b

  Represent the solution set on a number line and describe the set of possible values in the context of the problem.

01

What Students Need to Do

Students solve inequalities with one variable, including ones with parentheses and like terms. They graph the solutions on a number line and explain which values make sense in a word problem.

02

What Mastery Looks Like

A student can solve 3(x - 2) + x < 10 and graph x < 4 with an open circle at 4. They reverse the inequality sign when dividing by a negative number and check a value in the original inequality.

03

Common Misconceptions

Students may forget to distribute a negative sign or try to combine unlike terms. They may leave the inequality sign unchanged when dividing by a negative number, or use a filled circle for a strict inequality.

04

How to Assess It

Exit ticket: A notebook costs $4, plus a $6 delivery fee. You have at most $30. Write and solve an inequality, graph it, and list the possible whole-number notebook counts.

1. 01

   Give pairs number-line strips and markers; have them solve -2(x - 3) + x ≤ 9 and draw the solution ray.

2. 02

   Ask why multiplying 3 < 5 by -2 changes the sign; students plot -6 and -10, then write an explanation.

3. 03

   Play inequality match: students pair cards showing 3(x - 2) + x < 10, its solution, and its number-line graph.

4. 04

   Post a $25 lunch budget with a $5 card fee and $4 meals; students graph and list the possible meal counts.

• 7.AT.C.9.b

  Solve inequalities of these forms and graph the solution set on a number line.