Multiplicative Comparison and Unit Rate
How many times as much, and how much per single unit, are two faces of the same relationship. Learners find a per-unit value (per kilogram, per hour as speed, fraction of a number) and scale it up, including reading speed as the slope of a distance-time graph. Unit-rate reasoning underlies proportions and all later rate work.
grade 3–4 Measurement & dataBase-ten numbersFractionsOperations Analyze the UnitsConvert to Algebra
Progression (7)
g4 1. Distance grows in proportion to time Measurement & dataOperations
g4 2. Speed is distance per unit time Measurement & dataOperations
g3 3. Fraction of a number: divide then multiply FractionsOperations
g3 4. Find the per-unit-weight rate first OperationsMeasurement & data
g4 5. How many times the unit quantity OperationsBase-ten numbers
g4 6. Find the value of one unit Base-ten numbersOperations
g5 7. Slope of a time-distance line graph is speed Measurement & data
Bridges to competition (3)
Reasoning problems that extend this idea toward competition:
Broken Clock: Constant Error Rate Other
Meeting time of two movers Other
Comparing speeds and distances Other