Problem
Count the gaps
Divide the road length by the spacing to find how many 20 m gaps fit: 200 / 20 = 10 gaps.
Each 20 m piece is one gap, so dividing the total length by 20 counts them.
4.OA.A.3Solve An Easier Related ProblemAdd one for the open-road end tree
On an open road with a tree at both ends, trees = gaps + 1 because both ends get a tree: 10 + 1 = 11.
Drawing posts and the gaps between them shows there is always one more post than gap on an open path.
4.MD.A.2Draw A DiagramOn a straight open road with a tree at both ends, the number of trees is one more than the number of 20 m gaps.
Why?
The trees split into two groups that never overlap — one tree that closes each gap, plus the lone first tree that closes no gap — so adding the two counts gives every tree.
Why?
Each gap ends at exactly one tree and no two gaps end at the same tree, so the closing trees pair with the gaps one for one and are equal in number to the gaps.
Why?
Sorting the trees into the gap-closing trees and the single first tree leaves none out and counts none twice, so the total is the gap count plus one.
This only needs Grade 4 dividing -- count the gaps, then remember an open road has one more tree than gaps!
- Count the gaps
- Add one for the open-road end tree