Maryland Math 7.AT.C.8
Standard Cluster
Use variables to represent quantities and write and solve equations to model and reason about relationships in context. Write equations of the form px + q = r and p(x + q) = r where p, q, and r are specific rational numbers. Solve equations of these forms flexibly and efficiently. Explain the solution process and how it connects to the original statement of equality. Solve word problems leading to equations of these forms and interpret the solution in terms of the context.
Maryland College and Career Ready Standards for Mathematics (2025) · MODEL WITH AND SOLVE EQUATIONS AND INEQUALITIES.
Cluster contents
Standards in This Cluster
7.AT.C.8 is a cluster heading. These are the individual standards under it.
- 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.AT.C.8.b
Solve equations of these forms flexibly and efficiently. Explain the solution process and how it connects to the original statement of equality.
- 7.AT.C.8.c
Solve word problems leading to equations of these forms and interpret the solution in terms of the context.
Teacher's field guide
What This Cluster Means
What Students Need to Do
- Students use a letter for an unknown amount in a story, then write and solve an equation. They show how each step keeps the two sides equal and explain what the answer means in the story.
What Mastery Looks Like
- For three rides at the same price plus a $2 entry fee, a student writes 3x + 2 = 20 and finds that each ride costs $6. They check the total and know that 3(x + 2) = 20 would charge the fee for every ride.
Common Misconceptions
- Students may put a one-time fee inside parentheses, which charges it more than once. They may change only one side of an equation or give a number without saying what it measures.
How to Assess It
- Exit ticket: A taxi charges $3 per mile plus a $2 pickup fee. The fare is $17. Write and solve an equation, then check what your answer means.
Lesson moves
Ways to Teach It
Give pairs 17 counters and three paper cups; place two counters outside, share the rest equally, and write the matching equation.
Ask, "How do 3(x + 2) = 21 and 3x + 2 = 21 tell different stories about a $2 fee?"
Post 0.5(x + 2) = 4 and 0.5x + 2 = 4; students solve both, then compare answers with a partner.
Show a $16.50 receipt for three identical smoothies and a $1.50 fee; students find the price of one smoothie.
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Printable 7.AT.C.8 Worksheet
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Related Standards
- 7.AT.C.9
Use variables to represent quantities and write and solve inequalities to model and reason about constraints and conditions in context.
- 6.AT.D.11
Use variables to represent two quantities in context that change in relationship to one another.
- 5.AT.B.3.c
Use tables, ordered pairs, and graphs to represent the relationship between quantities.
- 6.AT.C.8
Solve problems in context by writing and solving equations and interpreting the solutions in context.
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