Grades5
Tree-planting problems are a small topic with a big trap in Grades 4–5: planting along a road, staking out a plot, or spacing objects evenly along a line — the answer is always off by exactly one from a straight division, and which way it leans depends on whether one end, both ends, or a closed loop is planted. There is one key: count the gaps first and derive the number of trees second. This page teaches the type on an animated road that counts every gap and every tree, so children stop guessing whether to add or subtract one.
Spot the planting family whenever objects are spaced evenly along a line: trees along a road, fence posts, nails, or a ribbon cut into equal pieces. The question always turns on three quantities — the total length, the length of one gap, and the number of objects — and knowing two of the three is exactly when the plus-or-minus-one care is needed.
A road is 20 m long with trees every 5 m (including both ends). How many trees are there?
Key idea: Find the intervals first: intervals = length ÷ spacing.
Trees along a 20 m road every 5 m, with trees at BOTH ends.
Count the intervals first — the trees come one step later.
Intervals: 20 ÷ 5 = 4.
Trees = intervals + 1 = 4 + 1 = 5.
So: So there are 5 trees.
If there are 6 fence posts in a straight line, how many gaps (intervals) are between them?
Key idea: Running backwards: intervals = posts − 1 when both ends are planted.
So: So there are 5 gaps.
A 30 m path has trees planted every 6 m, starting from both ends. How many trees are planted?
Key idea: Find the intervals first: intervals = length ÷ spacing.
So: So 6 trees are planted.
A straight road is 100 m long. Trees are planted every 10 m with trees at both ends. How many trees are there?
Key idea: Find the intervals first: intervals = length ÷ spacing.
So: So there are 11 trees.
A straight road is 60 meters long. Trees are planted at equal intervals of 5 meters, with a tree at both ends. How many trees are planted?
Shortcuts: Space (play), Arrow keys (step), R (reset), F (fullscreen)
The straight road is 60 m long. Trees will be planted at equal 5 m intervals, with a tree at both ends. The big question of this lesson: will there be as many trees as intervals, more, or fewer?
Keep the question in mind — we will answer it by counting, not guessing.
Change the numbers and watch the diagram redraw itself:
Because the first tree stands before the first gap, and each later gap adds exactly one tree at its far end. Counting the gaps first and then adding the opening tree is the order that never goes wrong.
On a closed loop (around a pond or a yard) trees equal gaps, and planting at only one end does too. On an open line whose far end stays empty, trees are one fewer than gaps. A quick sketch of the road with both ends marked separates the cases at once.
The type appears in Grades 4–5 and is a regular guest in olympiad papers and selective Grade 6 entrance exams — small, quick, and used to reward candidates who are careful rather than fast.
