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 3–6 Measurement & dataBase-ten numbersFractionsOperations Analyze the UnitsConvert to Algebra
Progression (15)
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
g5 8. Express smaller units as larger using fractions FractionsMeasurement & data
g5 9. Decimals convert small units to larger ones Base-ten numbersMeasurement & data
g6 10. Find the daily gap between a clock and true time Number systemRatios
g7 11. Unit distance is total distance divided by time Ratios
g7 12. Set the whole job to 1 and write a day's work as a fraction RatiosNumber system
g7 13. Find the unit amount first Number systemRatios
g6 14. Change the unit using a decimal Number systemRatios
g6 15. Find the unit amount RatiosNumber system
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