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Surface Areas and Volume

Surekha Waldia
Critical thinking, Problem Solving
Remember, Understand, Application, Analysis
Surface Areas and Volume
1. To learn to apply concept of Pythagorean Triples.2. To visualize that cylinder is three dimension form of two dimensional rectangle
The idea behind giving this type of problem sum is to develop the spatial intelligence of the students while applying multiple concepts of perimeter, surface
a cylinder of the specific measurement as given in the problem, A thread or a sketch pen to mark around the cylinder

Problem Stated:

Step 1: Make the students work in a group of 3-4 students and give them just 5 mins to solve this problem.

Step 2: Ask them to create a cylinder with a piece of paper of the measurement given above and mark with pen the thread around it.

Step 3: Once the time is over ask each group to show their working for the same.


Note: Twenty years ago, this puzzle appeared on a test administered to top-tier math students from 16 countries around the world. Only 10% of test takers got it right.

 New York Times’ Edward Rothstein wrote about this problem back in 1998:

It is actually a beautiful solution, simple and startling enough so one almost has to take an object in hand and think about why it makes sense… Nothing could be a better illustration of the value of teaching a mathematical way of thinking. It requires different ways of examining objects; it might mean restating problems in other forms. It can demand a playful readiness to consider alternatives and enough insight to recognize patterns. Anyone who solves this problem starts to think differently about the world itself.

1. Ask them what all concepts have they used in solving this question.
2. If they are unable to identify the concept then you can draw their attention toward Pythagorean Triples.
Accurate, Clearly explained, Complete, Knowledgeable, Methodical, Precise

Maths is all about developing spatial understanding. Therefore such questions when worked as group activity help students who are weak in grasping such abstract concepts.

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