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 2–6 Measurement & dataFractionsOperations Draw a DiagramIdentify Subproblems
Progression (8)
g2 1. Subtract the overlap from total length Measurement & data
g3 2. Overlap shrinks the total length Measurement & dataOperations
g3 3. Overlaps are one fewer than the strips Measurement & dataOperations
g4 4. Subtract the overlap when joining fraction lengths Fractions
g5 5. Both A and B is part of A or B Fractions
g5 6. Overlaps equal tape count minus one Base-ten numbers
g6 7. Use the overlap as the unit to find a figure's area GeometryExpressionsFractions
g7 8. Equal after removing the shared part means equal to begin with GeometryExpressions
Bridges to competition (2)
Reasoning problems that extend this idea toward competition:
Length of overlapping strips Counting
Total Length with Gaps or Overlaps Other