Maryland Math 7.AT.C.9.b

Math7th GradeAlgebraic Thinking

The Standard

7.AT.C.9: Use variables to represent quantities and write and solve inequalities to model and reason about constraints and conditions in context.

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

Maryland College and Career Ready Standards for Mathematics (2025) · MODEL WITH AND SOLVE EQUATIONS AND INEQUALITIES.

Teacher's field guide

What Students Need to Do: Students solve inequalities with rational numbers, including negative coefficients. They graph every solution on a number line with the correct endpoint and shading.
What Mastery Looks Like: For −2x + 3 < 11, a student gets x > −4. They draw an open circle at −4, shade right, and explain why dividing by −2 reverses the sign.
Common Misconceptions: Students may forget to reverse the sign when dividing by a negative number. They may fill in the circle for < or >, shade the wrong side, or mark only one answer.
How to Assess It: Exit ticket: Solve −2x + 3 < 11, graph the solution on a number line, and check whether x = 0 works.

Lesson moves

Give pairs a paper number line, an open-circle cutout, and an arrow; have them model the solution to 3x + 2 < 14.
Ask students to explain in writing why dividing −2x < 8 by −2 reverses the sign.
Run a card match with 2x − 1 > 5, x > 3, and a number line shaded right from an open circle at 3.
Give a $5 entry fee and $3 per game with less than $20 to spend; students solve and list possible game counts.

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