Florida B.E.S.T. MA.8.AR.3.1
The Standard
Determine if a linear relationship is also a proportional relationship.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use tables, graphs, equations, and contexts to check whether y/x stays constant. They connect a constant ratio with an equation y = kx and a graph through (0, 0).
What Mastery Looks Like
- Given any representation, a student checks for a zero starting value and supports the answer with a ratio, equation, or graph. The student explains that y = mx + b is proportional only when b = 0.
Common Misconceptions
- Students may call every straight-line graph proportional. They may focus only on constant slope and ignore a nonzero starting value, or calculate x/y instead of y/x.
How to Assess It
- Exit ticket: Decide whether the table (x: 0, 2, 4; y: 3, 7, 11) is proportional. Justify your answer using the starting value, an equation, or ratios.
Lesson moves
Ways to Teach It
Use cups and counters to model y = 2x and y = 2x + 3, then record both in tables and graphs.
Students write a response to the prompt, “Explain why y = 4x + 5 is linear but not proportional.”
Run a card sort with tables, graphs, equations, and situations; pairs match representations and label each set proportional or nonproportional.
Compare a taxi fare with a starting fee to fruit sold at a fixed price per pound, then decide which relationship is proportional.
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Printable MA.8.AR.3.1 Worksheet
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Related Standards
- MA.7.AR.4.1
Determine whether two quantities have a proportional relationship by examining a table, graph or written description.
- MA.7.AR.4
Analyze and represent two-variable proportional relationships.
- MA.8.AR.3
Extend understanding of proportional relationships to two-variable linear equations.
- MA.7.AR.4.2
Determine the constant of proportionality within a mathematical or real-world context given a table, graph or written description of a proportional relationship...
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