Inverse proportional relationships as quantities scaling in anti-tandem, y = r/x¶

Theory · All theories
Evidence · no claims cited

Description¶

The paper extends the framework to inverse variation: 'Two measurable quantities in a scenario are said to be in an inverse proportional relationship if changing the measure of one quantity by a factor k causes the measure of the other to change by a factor 1/k.' It shows such data satisfies y = r/x, illustrated by volunteers stuffing envelopes, cake sharing, window washing, and the cats-and-rats teaser.

Design Implications¶

Context¶

Requirements¶

• Learners must recognize which quantity varies inversely with which, by common sense about the scenario

Constraints¶

• The paper treats inverse variation as a distinct relationship from direct proportionality, requiring anti-tandem rather than tandem scaling

Target Learners¶

• middle grades and secondary mathematics students

Target Learning Objectives¶

• distinguish direct from inverse proportional relationships and reason with y = r/x

Claims¶

Related Theories¶

• Scaling in tandem as the foundational way of thinking for proportional relationships

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