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This problem is good to encourage systematic thinking - working from a simple start : twosticks, three, four . . .

Encourage questions like "what could come before . . . . . and what before that" ?

Working backwards from the goal is a mathematical thinking skill.

Especially encourage explanation - accounting for pattern.

There is lots of interest in this simple mechanical process - look out for the triangle numbers!

Above all, if possible, let each insight prompt fresh questions to consider, each new question will illuminate more of the structure.