Maryland Math 7.AT.C.9.a
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.
Write inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.
Maryland College and Career Ready Standards for Mathematics (2025) · MODEL WITH AND SOLVE EQUATIONS AND INEQUALITIES.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students write an inequality from a word situation. They use a variable for an unknown amount, multiply it by a rate, add a fixed amount, and choose > or <.
What Mastery Looks Like
- Given a $2.50 fee, $1.25 per ride, and a total below $10, a student writes 1.25x + 2.50 < 10. They explain that x is the number of rides and that $10 is not included.
Common Misconceptions
- Some students write 1.25 + x + 2.50 instead of 1.25x + 2.50. Others reverse the sign because the words “less than $10” come before the cost in the sentence. Some use ≤ even though “below $10” excludes $10.
How to Assess It
- Exit ticket: A bike rental costs $3.50 to start and $2.25 per hour. Write an inequality for a total greater than $17, and define your variable.
Lesson moves
Ways to Teach It
Give pairs $2 entry cards, $1.50 ride tokens, and a $10 budget card; have them build the cost and write an inequality.
Ask: “A $3 fee plus $0.50 per ticket costs more than $9. Why does the inequality use >?”
Play a card match with word situations and inequalities such as 0.75x + 2 < 8; have students explain each match.
Show a tank with 20 liters that loses 1.5 liters per minute; ask students to write an inequality for more than 8 liters left.
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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.
- 7.NOS.A.2.b
Interpret quotients of rational numbers in context and represent division of signed numbers in different forms, such as −(p/q) = (−p)/q = p/(−q) when the diviso...
- 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.
- 6.AT.C.10.b
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.
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