Track a Quantity Through Changes
A measured quantity — container weight, water level, bar length, work done — changes as things are added, removed, or accumulate at a net rate; the unknown is recovered by following the running total. Learners handle before/after weight, net fill-with-leak, bouncing-ball fractions, submerged bars, and combined work rates. The thread is conservation: every change is accounted for.
grade 3–4 Measurement & dataBase-ten numbersFractionsOperations Draw a DiagramWork Backwards
Progression (7)
g3 1. Bouncing ball rises a fraction of its fall FractionsOperations
g3 2. Find container weight after adding or removing Measurement & data
g3 3. Net fill rate is inflow minus outflow Measurement & dataOperations
g3 4. Add poured water to find total capacity Measurement & data
g4 5. Add per-day work fractions to find combined output Fractions
g4 6. Use submerged and exposed parts to find bar length Fractions
g5 7. Use weight differences to find the empty container Base-ten numbersMeasurement & data
Bridges to competition (2)
Reasoning problems that extend this idea toward competition:
Set up the correct add/subtract equation Logic
Broken clock with constant drift Pattern & rule