Maryland Math 7.AT.C.8.b
The Standard
- 7.AT.C.8
- Use variables to represent quantities and write and solve equations to model and reason about relationships in context.
Solve equations of these forms flexibly and efficiently. Explain the solution process and how it connects to the original statement of equality.
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
- Solve equations such as 3x + 5 = 20 and 3(x + 5) = 24, including cases with negative numbers or fractions. Choose a useful first step, keep both sides equal, and check the answer in the original equation.
What Mastery Looks Like
- For 4(x - 2) = 12, a student can divide by 4 first or distribute first and get x = 5. They substitute 5 into the original equation and explain why doing the same operation to both sides keeps it true.
Common Misconceptions
- Students may subtract 5 first in 3(x + 5) = 24, as though the 5 were outside the parentheses. They may divide only one side, lose a negative sign, or check an answer in a later equation rather than the original.
How to Assess It
- Exit ticket: Solve 2(x - 3) = 10 two ways, then check your answer in the original equation. Explain why dividing both sides by 2 keeps them equal.
Lesson moves
Ways to Teach It
Use three paper cups for unknowns and two counters against 14 counters; remove two from each side, then split 12 among the cups.
Ask students: Why can you divide both sides of 4(x + 2) = 20 by 4 before subtracting 2? How else could you solve it?
Give pairs cards with 5x - 3 = 17 and -2(x + 4) = 10; award a point for each solution checked by substitution.
Show a receipt with a $3 fee and four equal-price tickets totaling $23; students write 4x + 3 = 23 and find the ticket price.
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Printable 7.AT.C.8.b Worksheet
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Related Standards
- 7.AT.C.8.c
Solve word problems leading to equations of these forms and interpret the solution in terms of the context.
- 6.AT.C.10
Solve problems in context by writing and solving inequalities and interpreting solution sets in context.
- 7.AT.C.7
Analyze contextual situations to determine whether an equation or inequality best represents the relationship between quantities. Justify the choice based on th...
- 6.AT.C.8
Solve problems in context by writing and solving equations and interpreting the solutions in context.
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