NY Next Generation Math NY-7.EE.4.a
The Standard
Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students solve word problems that lead to equations shaped like px + q = r or p(x + q) = r with rational numbers. They compare algebraic steps with arithmetic reasoning.
What Mastery Looks Like
- The student writes and fluently solves a matching equation, including any needed simplification on one side. The student identifies the operation sequence in both an algebraic and arithmetic solution.
Common Misconceptions
- Students may divide before removing the added or subtracted amount in px + q = r. They may distribute incorrectly in p(x + q) or introduce variables on both sides.
How to Assess It
- A rectangle has perimeter 54 centimeters and length 6 centimeters. Ask students to find its width using an equation and compare with an arithmetic solution.
Lesson moves
Ways to Teach It
Model 3(x + 2) = 21 with equal groups of tiles, then connect each move to an algebraic step.
Ask students to compare solving 4x + 7 = 31 by undoing operations and by reasoning from known facts.
Run an equation relay with rational-number problems in both px + q = r and p(x + q) = r forms.
Write and solve an equation for a rental cost with equal group charges and one fixed fee.
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Printable NY-7.EE.4.a Worksheet
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Related Standards
- NY-7.EE.4.b
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Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), us...
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