How to Teach Pascal's Triangle
The number pattern found in Pascal's triangle has practical applications for expanding polynomials and also provides a good introduction to number patterns in general. The pyramid structure used to setup the pattern helps to explain the pattern to younger students or students who learn best visually. The triangle pattern also serves as a memory technique to help students remember the numerical pattern for advanced problems. You can also derive the Fibonacci sequence from Pascal's triangle.
Instructions
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Draw Pascal's triangle on the board for the students. The pattern for Pascal's triangle requires that you start the top of the triangle with the number 1. The next row should have two ones. Form subsequent rows by adding the two numbers diagonally above it to the left and right. A 1 should occur at the beginning and end of each row. For example, the third row is (1,2,1) and the fourth row is (1,3,3,1).
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Explain how to get each number in the triangle from the two numbers above it for the first three rows. Ask students how to fill in the fourth row.
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Provide students with worksheets containing partially completed Pascal's triangles. Some worksheets can require students to fill in rows after the fourth row, and other worksheets can require students to fill in the blanks in different rows in the triangle.
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Give students the formula for finding any number in Pascal's triangle after they have learned the basic visual pattern. The formula is the same one used to find combinations: n! /( k!*(n-k)! ), with "n" as the row number and "k" as the index of the item in the row.
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