Six common contexts where proportional relationships arise¶

Design · All designs
Evidence · 1 claim (1 for) · 1 study (1 theoretical), q2 · 0 of 1 report an effect size · 1 claim rests on one study

Description¶

The paper enumerates the everyday and mathematical settings where, in its words, 'common sense informs us that a proportional relationship is at play': unit conversion and exchange rates, constant rates, percentages, scaled drawings and maps, similar figures in geometry, and ratios. Each context is worked with the same scaling-in-tandem reasoning rather than with cross multiplication.

Design Implications¶

Context¶

Requirements¶

Each context must involve two measurable quantities that plausibly scale in tandem

Constraints¶

The paper cautions that constant-rate statements concern changes in quantities, not absolute values: distance from home is not proportional to clock time

Target Learners¶

middle grades and secondary mathematics students

Learning Goals¶

recognize proportional structure across varied contexts

Claims¶

Data from any proportional relationship satisfies an equation of the form y = rx, and conversely [+W]

Examples¶

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Key Sources¶

James Tanton, Ted Coe, April Ström, Kyle Pearce. (2022). Proportional relationships decluttered—at last! White paper. https://www.nwea.org

Page metadata

Field	Value
`type`	`design`
`id`	`proportional-relationship-common-contexts`
`title`	`Six common contexts where proportional relationships arise`
`description`	`The paper enumerates the everyday and mathematical settings where, in its words, 'common sense informs us that a proportional relationship is at play': unit conversion and exchange rates, constant rates, percentages,...`
`status`	`review`
`generated`	by `process:settle-candidates` on `2026-10-09`
`trust`	unverified — no one has confirmed this page's content
`sources`	1 — `james-tanton-2022`

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