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 MDNBTNFOA Draw a DiagramWork Backwards
Progression (7)
3-2 1. Bouncing ball rises a fraction of its fall 3.NF.A.13.OA.A.2
3-2 2. Find container weight after adding or removing 3.MD.A.2
3-2 3. Net fill rate is inflow minus outflow 3.MD.A.23.OA.A.3
3-2 4. Add poured water to find total capacity 3.MD.A.2
4-2 5. Add per-day work fractions to find combined output 4.NF.B.3
4-2 6. Use submerged and exposed parts to find bar length 4.NF.B.3
4-2 7. Use weight differences to find the empty container 5.NBT.B.74.MD.A.2