Trees and Equal Intervals

1. 1Find the Intervals FirstDivide the road into equal spaces of 5 m and count each space as it appears. Notice: we are counting intervals, not trees — counting intervals and counting trees are two different jobs.60 ÷ 5 = 12 intervals
2. 2Plant One Tree at the Start of Each IntervalPlant one tree at the start of each interval. That gives us 12 trees for 12 intervals; the far endpoint is still open.12 intervals → 12 trees so far
3. 3Close the Far EndAdd the 13th tree exactly at the far endpoint, so both ends of the road have a tree.12 trees + 1 closing tree = 13 trees
4. 4Count the Trees One by OneCount the trees slowly from one end to the other: there are 13 trees. Set the two counted numbers side by side: 12 intervals — 13 trees.12 intervals → 13 trees
5. 5The Tree RuleFrom the two numbers we counted: with a tree at both ends, the trees always outnumber the intervals by exactly 1.Trees = 60 ÷ 5 + 1 = 13 trees
6. 6Check the AnswerWork backwards to check: 13 trees make 12 intervals; at 5 m each, the road is 12 × 5 = 60 m — exactly the given length.(13 − 1) × 5 = 60 m ✓

Change the numbers to test the engine with any sum & difference problem: