The Structure of Measurement Units

The machinery for restating one quantity in another unit gets organized here. Volume relationships between cm³ and L, m³ and kL, and kL and L are confirmed, along with weight relationships between g and mg and between kg and t, and time conversions turning fractional hours into minutes and minutes and seconds into mixed-number minutes.

Confusing the factor of 1000 for length with the factor of 1000000 for volume, as in taking 1 m³ for 1000 cm³, leaves the answer three zeros short. With time, thinking in hundreds rather than sixties makes 0.5 hours into 50 minutes, which is standard. Converting minutes into fractional hours, children multiply by 60 instead of dividing.

Interest moves from counting to organizing units. After the focus on counting in Number of Cases, this stage brings the conversions for volume, weight and time together and checks them all at once. In Traveler Problems, which follows, the feel for time units settled here becomes the common ground for calculations involving speed and time.