Overlap Reduces the Total
When pieces are joined with overlap, the combined length is the sum of the parts minus the overlapping portion — and with several strips the overlaps number one fewer than the strips. The idea runs from taped lengths to multiplied strips to fraction distances. It is the first taste of inclusion-exclusion.
grade 2–4 MDNFOA Draw a DiagramIdentify Subproblems
Progression (4)
2-2 1. Subtract the overlap from total length 2.MD.B.52.MD.A.4
3-1 2. Overlap shrinks the total length 2.MD.B.53.OA.D.8
3-1 3. Overlaps are one fewer than the strips 3.MD.D.83.OA.D.8
4-2 4. Subtract the overlap when joining fraction lengths 4.NF.B.3