Finding the Longest
The longest road in a tree is found by walking away from anywhere twice — a guess by eye, then a count to check it.
- Grades
- 1–6
- Subjects
- Counting & Estimating, Logic
- Kind
- Two-player game
- Cost
- Free, no account, no ads
What it is
A tree of roads covers the board, with one big dot somewhere on it. Two spots in that tree are farther apart than any other pair, and the board asks for them. Tap a spot and its road back to the dot draws itself, counting the steps — steps along the roads, not distance across the paper, so a spot sitting right beside the dot can be a very long way round.
What it gives you to practise
The method is one of the small, good facts about trees: walk away from anywhere to the farthest point you can reach, then walk away from there, and the second walk is the longest road in the whole tree. The board plays that in two rounds instead of telling you about it. A wrong tap costs a second but leaves its step count behind on the board, so a guess is never wasted — it turns into evidence for the next one.
In a classroom
The question worth asking after a few boards is why the first walk is allowed to start anywhere at all. It is not obvious, and a class that has played six boards has the evidence in front of it to argue either way.
The rules
A tree of roads, and one big dot. Somewhere in the tree two spots are farther apart than any others — find them.
Tap a spot and its road from the dot draws itself, counting the steps. Steps along the tree, not distance across the board — a spot right next to the dot can be a long way round.
First, the spot farthest from the big dot. The dot moves there.
Then the spot farthest from the new dot — and the road between the two is the longest in the whole tree.
A wrong tap adds a second to the clock, but it leaves its step count behind, so a guess is never wasted. Each board keeps your best time.
Near it on the shelf
- Finding ZeroEvery number turned over says how far zero is, so the hunt closes in by reasoning rather than guessing.
- Slug SaladEach slug eats a number equal to everything it has eaten before it — addition with a reason to check and go back.
- Stained GlassSkip-counting turned into a picture: the pattern each times table draws across a hundred square.