Maryland Math 6.AT.C.10.b
The Standard
- 6.AT.C.10
- Solve problems in context by writing and solving inequalities and interpreting solution sets in context.
Write and solve one-step inequalities of the form x + p > q, x − p > q, px > q and x/p > q (using ≥, >, ≤, <) where p and q are nonnegative rational numbers.
Maryland College and Career Ready Standards for Mathematics (2025) · REASON ABOUT AND SOLVE ONE-VARIABLE EQUATIONS AND INEQUALITIES
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students write an inequality from a short situation and find all values that work. They undo addition, subtraction, multiplication, or division by a positive number, then show the solutions on a number line.
What Mastery Looks Like
- Given 'three times a number is more than 7.5,' a student writes 3x > 7.5 and solves x > 2.5. They mark 2.5 with an open circle, shade right, and check a value by substitution.
Common Misconceptions
- Some students flip the sign when dividing by a positive number, or read 'at least' as > instead of ≥. Others give only the boundary value or include it when the inequality is < or >.
How to Assess It
- Exit ticket: 'A number minus 1.5 is at most 3.' Write and solve the inequality, graph the solutions, and check whether 4.5 works.
Lesson moves
Ways to Teach It
Lay floor tape marked in halves; students place an open circle at 2.5 and stand at values satisfying x + 1.5 > 4.
Ask, 'Does 2.5 belong in the solution to 2x > 5?' Have students explain by substituting 2.5.
Give pairs cards with x − 1/2 ≥ 2, 3x ≤ 9, and x/2 < 3; match each to a solution card.
A bus pass has $10 left and rides cost $2.50 each; students write 2.50x ≤ 10 and find possible ride counts.
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Related Standards
- 7.AT.C.8.a
Write equations of the form px + q = r and p(x + q) = r where p, q, and r are specific rational numbers.
- 6.AT.C.8.b
Write and solve one-step equations of the form x + p = q, x − p = q, px = q and x/p = q for cases in which p, q and x are all nonnegative rational numbers.
- 7.AT.C.9.a
Write inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.
- 6.AT.C.9
Write an inequality of the form x > c (using ≥, >, ≤, <) represent a constraint or condition in context. Recognize that inequalities of this form have infinitel...
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