Maths Resource of the Week 28

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Estimation of Pi

  • How can we estimate pi?
  • What is it? - Pi is a very mysterious thing to many students (and to this teacher!). If encouraged to think about it, they are likely to be fascinated by the whole concept of an irrational number. How can the digits of pi never ever end? How come we can measure a diameter and we can measure a circumference, and yet the ratio between them is something we can never accurately write down? If you ask students how we can come up with an accurate value of pi, they are likely to suggest measuring circumferences as accurately as possible and dividing them by diameters. This simple little applet offers a completely different approach which, if your students can understand it, will not only spark their interest but also help reinforce important concepts in algebra and probability.
  • How could it be used? - If you have an able GCSE group you may wish to project the circle inside the square up on the board and give them five minutes to think of how such a simple diagram could be used to estimate the value of pi. It is very unlikely they will come up with the answer, but an interesting discussion could ensue. Then you may wish to take them step by step through the process, each time pausing to see if they can predict what will come next. They will need to know their area formula and have good skills at simplifying algebra. However, for me the real power of this applet is the ability to alter the number of dots fired. This gives you a great opportunity to discuss the nature of experimental probability and the effect more trials has on the outcome. Why will firing 200 dots give us a more accurate estimation of pi than firing just 10? Let’s see if it is true…
  • How have you used this resource? - Please share your ideas below.
  • Uploaded by TES Resource Team

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