PCMI, Summer 2004 High School Teacher Program
[download: 10coins.doc 10coins.xls]
The following is an example of using an area model to solve a probability problem.
- Draw a square, 32 x 32 units in dimension. (There are 210, or 1024, outcomes. (1024)_ =32, so a 32 x 32 unit square gives 1024 boxes)
- Divide the square in half, representing the first coin flip.
- Divide each rectangle in half again, representing the second coin flip.
- Continue dividing each section to represent the 10 coin flips. Stop dividing the sections any time two heads are flipped in a row since two heads is a ÒloseÓ and it makes no sense to continue. The next two flips (four rounds total) are shown below:
This method isn't exactly elegant and is definitely a bit time consuming, but an interesting fractal-type pattern emerges. It's also very accessable for students. I use the area model extensively with my freshmen in Interactive Math (IMP) 1. I did the original model by hand on graph paper and redid it in Microsoft Excel. The complete area model shows the winning boxes as unshaded. The numbers on the right side of the area model are simply where I counted up the winning boxes. Cheers! PCMI@MathForum Home || IAS/PCMI Home
With program support provided by Math for America This material is based upon work supported by the National Science Foundation under Grant No. 0314808 and Grant No. ESI-0554309. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. |