Graphs of ratios
Target: Decide whether a point belongs to a ratio.
Language target: Name the factor for x and for y.
Likely miss: Students accept a point that is visually close but not a constant multiple of the base pair.
Ask: What factor takes the base x to this x?
If you see it: Ask, “What factor takes the base x to this x? Does that same factor work for y?”
Evidence to listen for: The student rejects a near point and names the shared factor.
Next: If graph points are unsteady, return to the table that generates them.
Observable student moves: names both quantities, uses the represented relationship, and revises after feedback. This companion is not a score.
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