Georgia 7.PAR.3.1
The Standard
Construct algebraic equations to solve practical problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Interpret the solution based on the situation.
Georgia's K-12 Mathematics Standards · Represent authentic situations using equations and inequalities with variables; solve equations and inequalities symbolically, using the properties of equality.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students translate practical situations into two-step equations with rational numbers. They solve the equations by keeping both sides equal, then explain what the solution means in the situation.
What Mastery Looks Like
- Students identify the unknown, fixed amount, rate, and total in a situation. They write and solve the matching equation using valid steps. They state the solution with units and check it in context.
Common Misconceptions
- Students may swap the fixed amount and the rate when writing an equation. They may distribute a factor to only one term or undo operations in the wrong order. Some report a number without checking its unit or whether it makes sense.
How to Assess It
- Give this exit ticket: “A taxi charges $3.50 plus $2.25 per mile for a $17 trip. Write and solve an equation. Explain your answer.”
Lesson moves
Ways to Teach It
Use cups, counters, and balance mats to model and solve equations with a multiplier outside a grouped expression.
Ask students to explain whether 4(x + 2) = 28 fits a ticket, meal, or distance situation, then write the story.
Give pairs equation cards and situation cards to match, solve, and check against an answer key.
Compare two phone plans with activation fees and monthly charges, then find how many months produce a given total cost.
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Printable 7.PAR.3.1 Worksheet
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Related Standards
- 7.PAR.3.2
Construct algebraic inequalities to solve problems, leading to inequalities of the form px ± q > r, px ± q < r, px ± q ≤ r, or px ± q ≥ r, where p, q, and r are...
- 7.NR.1.2
Show and explain p + q as the number located a distance ∣q∣ from p, in the positive or negative direction, depending on whether q is positive or negative. Inter...
- 6.PAR.7.3
Solve problems by writing and solving equations of the form x + p = q, px = q and x/p = q for cases in which p, q and x are all nonnegative rational numbers.
- 8.PAR.3.6
Use algebraic reasoning to fluently manipulate linear and literal equations expressed in various forms to solve relevant, mathematical problems.
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