Virginia SOL 6.PFA.2.c
The Standard
Determine whether a proportional relationship exists between two quantities, when given a table of values, context, or graph.
Virginia Standards of Learning for Mathematics · The student will identify and represent proportional relationships between two quantities, including those in context (unit rates are limited to positive values).
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide whether two quantities change by the same constant factor. They check for equal ratios in tables, a constant rate in situations, or a straight graph through the origin.
What Mastery Looks Like
- Students correctly classify tables, graphs, and situations and support each decision with evidence. They can show a constant unit rate or explain why changing ratios or a nonzero graph intercept rules it out.
Common Misconceptions
- Students may think any straight graph is proportional, even when it does not pass through the origin. They may check for equal differences instead of equal ratios, or reverse the quantities when finding a unit rate.
How to Assess It
- Exit ticket: A table shows 2 tickets cost $7, 4 cost $14, and 6 cost $22. Ask whether the relationship is proportional and require ratio evidence.
Lesson moves
Ways to Teach It
Use measuring cups to make juice with one cup concentrate for every three cups water, then record totals and test the ratios.
Discuss: “A taxi charges $4 plus $2 per mile. Is cost proportional to miles? Defend your answer with two representations.”
Play a card sort matching tables, graphs, and situations, then label each set proportional or not and write one piece of evidence.
Compare two grocery packages using price per ounce, then decide whether each store’s price table represents a proportional relationship.
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Related Standards
- 7.CE.2.a
Given a proportional relationship between two quantities, create and use a ratio table to determine missing values.
- 6.PFA.2.d
When given a contextual situation representing a proportional relationship, find the unit rate and create a table of values or a graph.
- 6.PFA.2.a
Identify the unit rate of a proportional relationship represented by a table of values, a contextual situation, or a graph.
- 6.PFA.1.f
Create a table of equivalent ratios to represent a proportional relationship between two quantities, when given a contextual situation.
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