Math · Stage 3

Planting-trees problems (both ends, one end, closed loop)

Plant trees along a path and the trees are not the gaps — both ends means trees = gaps + 1, one end means trees = gaps, and a closed loop means trees = gaps too.

✦ Math📘 Stage 3 · S3⏱ ~12 min🧒 Ages 7–8★ Free to start

I can solve planting-trees (gaps-and-posts) problems.

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Kavi Plants the Park Path 🌳

Kavi is planting trees along a 20-metre path, one tree every 5 metres — with a tree at each end. "Easy — 20 ÷ 5 = 4 trees!" hoots a friend. But Kavi counts the trees and the gaps between them: 4 gaps, but 5 trees! "The trees sit on the ends of the gaps," says Kavi. "With both ends planted, the trees are always one more than the gaps."

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What your child will learn

1A row of trees, both ends plantedHere is a straight path with a tree at both ends and the rest spaced evenly: 5 trees in the row — 1, 2, 3, 4, 5. Now point to each gap between two neighbouring trees.

2The gaps are the hopsPut the trees as marks on the path, 0 to 20, one every 5 metres. Tap Hop +5 and watch each hop jump the gap between two trees: 5, 10, 15, 20. The hops are the spaces between the trees.

3Both ends: gaps + 1 = treesFlip it into a number bond: the gaps plus 1 make the trees, when both ends are planted. For 4 gaps: 4 gaps + 1 = 5 trees.

4One end, and the closed loopNot every path has both ends planted! One end only (e.g. trees from a wall, nothing at the wall end): the trees pair up with the gaps — trees = gaps. A closed loop (trees around a round pond): the last tree joins back to the first, so trees = gaps too.

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A peek inside

A 20 m path has a tree every 5 m, with a tree at both ends 🌳. How many trees?

gaps = 20 ÷ 5 = 4 · both ends → trees = gaps + 1 = 4 + 1

Try this at home: A 40 m path has a tree every 8 m, with a tree at both ends. How many trees?

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

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Part of Math · Stage 3 · S3 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.