Georgia 7.PAR.3.2
The Standard
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 specific rational numbers. Graph and interpret the solution based on the realistic situation that the inequalities represent.
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 turn a real situation with a limit or requirement into an inequality with one variable. They solve it, graph the solution on a number line, and explain what the values mean in the situation.
What Mastery Looks Like
- A student can define a variable, write the correct inequality, and solve it using inverse operations. The student graphs the solution with the correct endpoint and shading, then explains which values make sense in context.
Common Misconceptions
- Students may confuse phrases such as “at most” and “more than,” or use the wrong open or closed circle. They may forget to reverse the inequality sign when multiplying or dividing by a negative number. They may also include negative or fractional answers that do not make sense in the situation.
How to Assess It
- Give this exit ticket: A skating rink charges $6 plus $2.50 per hour, and Jordan can spend at most $18.50. Write and solve an inequality, graph the solution, and state the greatest whole number of hours Jordan can skate.
Lesson moves
Ways to Teach It
Build a floor number line with tape, then have students place an open or closed circle and shade each solution set.
Ask how “at most” changes an inequality and its graph, then have students answer with a scenario and example.
Run a card-sort race matching scenario cards, inequality cards, solution cards, and number-line graphs.
Compare two phone plans by writing inequalities to find which plan fits a fixed monthly budget.
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Related Standards
- 7.PAR.3.1
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 ...
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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.
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Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequality.
- 6.PAR.7.4
Recognize and generate inequalities of the form x > c, x ≥ c, x ≤ c, or x < c to explain situations that have infinitely many solutions; represent solutions of ...
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