CCSS.Math.Content.7.RP.A.2d
The standard
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Common Core State Standards for Mathematics
What this standard means
Students need to read a graph of a proportional relationship and explain what any point means in the context. They should connect x and y to the two quantities, not just say the ordered pair. They also need to know why the graph goes through (0, 0) and why (1, r) shows the unit rate.
Mastery looks like clear sentences tied to the situation, such as “4 hours costs $36,” and “1 hour costs $9.” Students often mix up x and y, treat (1, r) as just another point, or say (0, 0) means “nothing” without explaining zero of both quantities.
Ways to teach it
- Hands-on activity: Use price cards for 1, 2, 3, and 4 notebooks, graph the points, then label what each point means.
- Discussion prompt: Ask, “On this graph, what does the point (1, 2.5) tell us, and how do you know?”
- Quick assessment: Show a proportional graph with point (6, 18) marked, and have students write one sentence explaining it in context.
- Real-world connection: Use a miles driven and gallons used graph, and identify the point that shows miles per 1 gallon.
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Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
- CCSS.Math.Content.7.RP.A.2a
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- CCSS.Math.Content.7.RP.A.2c
Represent proportional relationships by equations.