The triangle challenge

7th January 2005 at 00:00
Figure 1: remove any two matchsticks to form two triangles.

Questions you could ask children before setting the challenge might include:

* How many trigons (triangles) can you see? (There are five: four small ones and the perimeter triangle that makes up the shape as a whole.)

* What types of triangle can you see? Acute-angled or equilateral?

* Subtract the number of matchsticks that make up the perimeter from a baker's dozen. Is your answer less than the fourth prime number? (13 - 6 = 7. Number 7 is the fourth prime number.)

* Count the matchsticks. How many more would you need to make a score?

* Give your name as a shape name (11 could be "hendecagon" or "undecagon").

* If each matchstick measured 2.5cm, would all the matchsticks measure more than a 30cm ruler if they were laid end to end? (No, because 9 x 2.5cm = 22.5cm.)

* What is the quotient of the number of matchsticks that make up the exterior divided by the interior? (6 V 3 = 2) Figure 2: Remove any four matchsticks to form five triangles.

When the children are ready, set them the challenge:

* Ask them to make the shape.

* Encourage them to plan what to do before trying to solve the problem.

* If they are struggling, provide prompts and clues after five minutes by indicating one of the matchsticks that could be removed.

* Award points for each puzzle solved according to difficulty.

* Ask one child to use an OHP to demonstrate the solution.

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