CCSS.Math.Content.7.EE.B.4a
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 specific 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.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn a word problem into an equation with one unknown, then solve using inverse operations. They also solve the situation arithmetically and compare the order of steps in both methods.
What Mastery Looks Like
- A student writes an equation that matches the quantities and solves it accurately, including with fractions or decimals. The student checks the answer in context and explains how the arithmetic and algebraic steps correspond.
Common Misconceptions
- Students may match numbers to symbols without checking what the unknown represents. They may distribute to only one term, undo operations in the wrong order, or make sign errors with fractions and decimals.
How to Assess It
- Exit ticket: A taxi ride costs $4 plus $3.50 per mile and totals $18. Find the miles using arithmetic and an equation, then list each operation.
Lesson moves
Ways to Teach It
Use cups and counters to model 3(x + 2) = 18, then separate the groups and identify x.
Students write and defend two solutions to 4(x − 3) = 28, one dividing first and one distributing first.
Create a card match with scenario, equation, solution, and operation-sequence cards for eight two-step problems.
Use a phone plan with a monthly fee and per-gigabyte charge to find an unknown number of gigabytes from a total bill.
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Printable 7.EE.B.4a Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.7.EE.B.4a, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.6.EE.B.6
Students must use variables for unknown quantities before writing and solving one-step or two-step equations from word problems.
- CCSS.Math.Content.7.NS.A.3
Solving px + q = r with rational numbers requires adding, subtracting, multiplying, and dividing rationals accurately.
- CCSS.Math.Content.6.EE.B.7
Solving one-step rational equations prepares students for the inverse operations needed in two-step word-problem equations.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.8.EE.C.7a
Fluently undoing operations and using equivalent equations carries into simplifying linear equations to one solution, no solution, or infinitely many.
- CCSS.Math.Content.8.EE.C.7
Solving one-step and two-step rational equations prepares students for the broader linear equation methods required in grade 8.
- CCSS.Math.Content.8.EE.C.7b
Solving one-variable equations with rational numbers and distributive steps is required before handling multi-step equations with like terms.
- CCSS.Math.Content.7.G.B.5
Solving angle equations depends on fluently representing relationships and solving linear equations like x + 35 = 90 or 2x = 180.
- CCSS.Math.Content.8.NS.A.1
Solving linear equations with rational numbers supports the algebra used to turn repeating decimals into fractions.
Keep exploring
Related Standards
- CCSS.Math.Content.HSA-APR.D.6
Rewrite simple rational expressions in different forms; write a(x /b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the ...
- CCSS.Math.Content.7.EE.B.4b
Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the...
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