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MF.PR.6 Challenge MF-020-A12-V03

Find and interpret the constant of proportionality in multiple representations.

Match representations by constant of proportionality

Problem

Evaluate every card against \(c~=~2.4p\), where \(c\) is cost in dollars and \(p\) is weight in pounds.

Card A: Equation \(c~=~2.4p\)
Card B: Table with \(p\text{-}\text{values}\) \(5,~10,~15\) and \(c\text{-}\text{values}\) \(12,~24,~36\)
Card C: Graph of \(c\) versus \(p\) passing through the \(\text{origin}\) and the point \((4,~9.6)\)
Card D: Context: In a proportional relationship, the cost \(c\) is \(\$24\) when the weight \(p\) is \(10~\text{pounds}\).
Card E: Equation \(c~=~p~+~2.4\)
Card F: Table with \(p\text{-}\text{values}\) \(2,~4,~8\) and \(c\text{-}\text{values}\) \(4.8,~8.8,~19.2\)
Card G: Context: In a proportional relationship, the cost \(c\) is \(\$2.40\) when the weight \(p\) is \(5~\text{pounds}\).

Report the complete set of cards with the same constant of proportionality.

A target statement c = 2.4p is shown above seven cards A through G arranged in two rows. The cards include an equation, a table, a graph through (4, 9.6), contexts, a nonproportional equation, and a table with one mismatched row so students can compare constants of proportionality. Open full size
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Four variants of this problem type
Curriculum context
Standard
MF.PR.6
Category
Proportional Reasoning
Domain
Representations
Objective
Find and interpret the constant of proportionality in multiple representations.
Problem type
Match representations by constant of proportionality