Problem
Span A-to-C covers AB and BC; span B-to-D covers BC and CD. Add them and the middle piece BC lands in both, so it is counted two times.
Drawing the two bars on the same line shows the shared middle plainly, the way a Grade 2 length-line picture does.
2.MD.B.5Draw A DiagramFirst add the lengths A-to-C and B-to-D together.
Three-digit addition is exactly the regrouping skill practiced in Grade 3.
3.NBT.A.2Identify SubproblemsBecause the middle part B-to-C was counted twice, take it away one time to get the true length from A to D.
Removing the extra copy of the overlap is a single three-digit subtraction.
3.NBT.A.2Identify SubproblemsTaking the overlapping middle B-to-C away one time from the joined spans A-to-C and B-to-D leaves exactly the true length from A to D.
The two joined spans hold the middle piece B-to-C two times, while the real line from A to D holds it only once, so one extra copy must come off.
Span A-to-C is the piece A-to-B joined with B-to-C, and span B-to-D is the piece B-to-C joined with C-to-D, so adding the spans lays B-to-C down twice.
A span split into its pieces with no gap and no overlap is just those pieces added back together.
The whole line from A to D is the pieces A-to-B, B-to-C, and C-to-D set end to end with no gap, so it contains B-to-C a single time.
The extra B-to-C was piled into the total by adding, so taking it away with subtraction undoes that extra and brings back the true length.
When two lengths overlap, add them and subtract the shared middle once -- just Grade 3 add-and-subtract!