Problem
Write each length in centimeters so they can be combined.
Same-unit lengths add and subtract cleanly.
2.MD.B.5Draw A DiagramAdd A-C and B-D to get 544 cm, but this counts the middle part B-C twice.
Combining the two measured pieces gives a total that includes the overlap region twice.
2.MD.A.4Identify SubproblemsTake one overlap B-C (150 cm) out of 544 to get 394 cm, the true length A-D.
Taking out the part counted twice leaves the full stretch from A to D exactly once.
2.MD.B.5Identify SubproblemsTaking one copy of the overlap B-C (150 cm) out of the summed total (544 cm) leaves the exact length from A to D.
The summed total counts the whole path from A to D once but counts the middle overlap B-C a second time, so it is exactly one overlap too big.
The path from A to D is three touching parts in a row — A-B, then B-C, then C-D — with no gaps and no overlaps, so those parts add up to the whole path.
Span A-C is the parts A-B and B-C joined, and span B-D is the parts B-C and C-D joined, so adding the two spans lays the middle part B-C down twice while every other part is laid down once.
Subtracting one overlap takes back exactly the amount the second span piled on top, undoing the extra count and leaving A to D measured just once.
When two lengths overlap, add them and take the overlap back out once — Grade 2 length adding and subtracting!