Proportional Relationships Later Transfer

Try this on a later occasion. These are constructed models, not measured product data. Ribbon has a stated uniform mass of 3 grams per meter. The model allows ribbon lengths from 0 to 8 meters. Ignore every other mass.

Model A counts ribbon mass only. Model B counts ribbon plus one 4-gram bag; the bag is included even at zero ribbon length. Let x be ribbon length in meters and y be the stated total mass in grams.

• Complete both columns and write both rules. Which mass is proportional to ribbon length? Use positive-input quotients and zero-input meanings.
• Explain each model’s point at one meter. Find both masses at 8 meters.
• Is a result at 10 meters guaranteed by this stated domain? Give a qualified conclusion.

For squares with side length from 0 to 4 centimeters, area equals side length multiplied by itself. A zero side is the limiting zero-area case in this mathematical model. The table is constructed.

Fictional learner Jo says, “The graph includes (0, 0), so area is proportional to side length.” Evaluate that claim using at least two positive-side quotients. Test Jo’s proposed rule A = 3 × s at a different displayed pair. Then find the area of a square with side length 4 centimeters using the supplied area rule. Explain why a zero pair alone cannot decide proportionality.