Patterns & Reasoning

Problem

Intervals differ on open paths versus closed loops

Along a straight 200 m road, trees are planted every 20 m starting at one end and continuing to the other end, with a tree at each end. Find the total number of trees.
...... 20 m 200 m
OperationsMeasurement & data
Your answer
How to solve
Strategy Draw a Diagram — Interval-counting is best seen with a diagram: the figure shows trees at both ends of an open road, so the count of trees is the count of gaps plus 1. Trying a tiny case (a short road with a couple of gaps) makes the plus-one rule obvious before applying it to 200 m.
1STEP 1

Count the gaps

Divide the road length by the spacing to find how many 20 m gaps fit: 200 / 20 = 10 gaps.

200 ÷ 20 = 10 gaps
2STEP 2

Add 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.

10 + 1 = 11 trees
Answer
11 trees
200 ÷ 20 + 1 = 11
Check with the spacing: 11 trees make 10 gaps of 20 m, which is 10 x 20 = 200 m, exactly the road length. The plus-one matches the figure showing a tree at each end.
Takeaway

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
Where next?
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