All 8 problems from "Tree Planting Problems" with complete step-by-step worked solutions: recognising the type, the idea, the working steps and the conclusion. Use this page to review with your child after the animated lesson, or let them check their own working against it.
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.
6 fence posts in a straight line — this time the gaps are asked for, not the posts.
Each gap sits between two posts, so there is always one fewer gap than posts.
Picture it: post, gap, post, gap, …, post.
Intervals = 6 − 1 = 5.
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.
Trees every 6 m along a 30 m path, starting from both ends.
Intervals first, then one extra tree for the far end.
Intervals: 30 ÷ 6 = 5.
Trees = 5 + 1 = 6.
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.
Trees every 10 m along a 100 m road, with trees at both ends.
Intervals first, then + 1 for the second end tree.
Intervals: 100 ÷ 10 = 10.
Trees = 10 + 1 = 11.
So: So there are 11 trees.
A 60 m road has trees every 5 m at both ends. There are ___ intervals and ___ trees.
Key idea: Find the intervals first: intervals = length ÷ spacing.
Trees every 5 m along a 60 m road at both ends — both the intervals and the trees are asked for.
Divide for the intervals; the trees are one more.
Intervals: 60 ÷ 5 = 12.
Trees = 12 + 1 = 13.
So: So there are 12 intervals and 13 trees.
Lampposts are placed every 8 m along a 96 m street (with lampposts at both ends). How many lampposts are there?
Key idea: Find the intervals first: intervals = length ÷ spacing.
Lampposts every 8 m along a 96 m street, with lampposts at both ends.
Same shape as the trees: intervals first, then + 1.
Intervals: 96 ÷ 8 = 12.
Lampposts = 12 + 1 = 13.
So: So there are 13 lampposts.
Trees are planted every 4 m along both sides of a 48 m road (with trees at all four endpoints). How many trees are there in total?
Key idea: Both sides: solve ONE side completely, then double it.
Trees every 4 m along BOTH sides of a 48 m road, with trees at all four endpoints.
One side is a normal both-ends problem; the other side is identical.
One side: 48 ÷ 4 = 12 intervals, so 12 + 1 = 13 trees.
Both sides: 13 × 2 = 26.
So: So there are 26 trees in total.
A circular track is 80 m around. Trees are planted every 10 m. How many trees are there?
Key idea: On a CIRCLE there is no extra endpoint: trees = intervals.
A circular track 80 m around with trees every 10 m.
The track closes on itself, so the + 1 endpoint tree disappears.
Intervals: 80 ÷ 10 = 8.
On a circle, trees = intervals = 8.
So: So there are 8 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:
