Florida B.E.S.T. MA.912.AR.9.6
The Standard
Given a real-world context, represent constraints as systems of linear equations or inequalities. Interpret solutions to problems as viable or non-viable options.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students define variables and turn limits, costs, capacities, or requirements into linear equations or inequalities. They test possible values and explain whether each choice meets every condition in the context.
What Mastery Looks Like
- Students define variables and write a complete system, including reasonable bounds such as nonnegative values. They test a proposed solution by substitution or graphing, then explain why it is viable or non-viable.
Common Misconceptions
- Students often reverse inequality signs for phrases such as "at least" and "no more than." They may accept a point that satisfies only one constraint. They also forget nonnegative or whole-number limits required by the context.
How to Assess It
- Exit ticket: A play can sell at most 120 tickets and needs at least $900. Adult tickets cost $10 and student tickets cost $6. Define variables, write the inequalities, and decide whether 50 adult and 60 student tickets is viable.
Lesson moves
Ways to Teach It
Tape a coordinate grid on the floor, assign two inequalities, and have students place counters only where both conditions are satisfied.
Ask, "Why can a point satisfy one constraint but still be unusable?" Students defend an example with substitution.
Run a constraint card sort where students match contexts, systems, graphs, and labeled viable or non-viable solution points.
Plan a school event using attendance, room capacity, ticket price, and budget limits, then identify feasible attendance and pricing choices.
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Related Standards
- MA.912.AR.9.7
Given a real-world context, represent constraints as systems of linear and non-linear equations or inequalities. Interpret solutions to problems as viable or no...
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Given a mathematical or real-world context, write and solve one-variable linear inequalities, including compound inequalities. Represent solutions algebraically...
- MA.912.AR.9.3
Given a mathematical or real-world context, solve a system consisting of two-variable linear or non-linear equations algebraically or graphically.
- MA.912.AR.2.8
Given a mathematical or real-world context, graph the solution set to a two-variable linear inequality.
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