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
What this standard means
Students need to turn word problems into one-step and two-step equations with rational numbers, then solve them accurately. They should handle forms like a rate times an unknown plus a fee, or a multiplier outside parentheses. They also need to explain what each number means in the situation.
Mastery looks like writing the equation, solving it, checking the answer in the story, and comparing algebra steps with arithmetic reasoning. Students often get stuck choosing the unknown, placing parentheses, and reversing operations in the right order, especially with negatives, fractions, and decimals.
Ways to teach it
- Use algebra tiles or paper balance mats to model 3x + 5 = 20, then have students write matching story problems.
- Ask students to solve a word problem two ways, with an equation and with arithmetic, then write how the steps match.
- Give an exit ticket with one problem in the form p(x + q) = r and ask for the equation, solution, and check.
- Use a phone plan with a monthly fee and cost per gigabyte, then have students find the number of gigabytes from a total bill.
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Related standards
- CCSS.Math.Content.7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers.
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- 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...