Pascal’s Percents

Teacher Notes:

• Have students research Pascal and Pascal’s Triangle using the Internet.
• Be sure that all students understand how Pascal’s Triangle is formed before they move
  to Step 2.

Answers:

Procedure for the Activity

Step 1  Each number in the triangle is found by adding two numbers in the row above.
For example, in Row 3, 2 is the sum of 1 and 1 in Row 2.

Step 2  (Note: The rows are shown but not in as a triangle.)

1
1  1
1  2  1
1  3  3  1
1  4  6  4  1
1  5  10  10  5  1
1  6  15  20  15  6  1
1  7  21  35  35  21  7  1
1  8  28  56  70  56  28  8  1

Step 3   

1
2
4
8
16
32
64
128
256

Step 4

100%
50%  50%
25%  50%  25%
12.5%  37.5%  37.5%  12.5%
6.25%  25%  37.5%  25%  6.25%
3.125%  15.625%  31.25%  31.25%  15.625%  3.125%
1.5625%  9.375%  23.4375%  31.25%  23.4375%  9.375%  1.5625%
0.78125%  5.46875%  16.40625%  27.34375%  27.34375%  16.40625%  5.46875%  0.78125%
0.390625%  3.125% 10.9375%  21.875%  27.34375%  21.875%  10.9375%  3.125%  0.390625%

Wrapping Up the Activity

Check students’ paragraphs.

Some patterns are: The percents in each row add to 100%. The first percent in each row is one half of the first percent in the row before. In a row with an even number of terms, the term that is repeated is 0.75 of the middle term in the row before.