Objects versus Gaps (Fencepost Counting)
Spacing objects along a line or loop ties the object count to the gap count: on an open path posts are one more than gaps, on a closed loop they are equal. Problems compute trees, posts, or intervals from length and spacing. The off-by-one fencepost relation is a classic trap the archetype trains learners to see.
grade 2–4 MDOA Draw a DiagramLook for a Pattern
Progression (5)
2-2 1. Gaps are one fewer than the objects 2.MD.B.5
3-1 2. Objects versus gaps when spacing along a line 3.OA.A.33.OA.D.8
3-2 3. Posts versus gaps on lines and loops 3.OA.A.33.MD.D.8
3-2 4. Count posts via length divided by spacing 3.OA.A.33.MD.D.8
4-1 5. Intervals differ on open paths versus closed loops 4.OA.A.34.MD.A.2