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Exploring Pascal || Student Center || Teachers' Place
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Exploring Pascal's Triangle

Intermediate Level

Pascal Petals

Working with a partner, study the following number pattern in Pascal's triangle.

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Notice that the gray cell is surrounded by 6 other cells. These six cells make up the petals on Pascal's flower.

Starting with the petal above and to the left of the gray center, alternating petals are colored yellow and numbered 5, 20, and 21.

The three remaining petals around the chosen center are colored orange and numbered 6, 10, and 35.

The product of the numbers in the yellow petals is 5 x 20 x 21 = 2100.

The product of the numbers in the orange petals is 6 x 10 x 35 = 2100.

The products are the same. Can you explain this?

Write the prime factorization of each of the numbers in the yellow petals.

_______________   _______________   _______________

Write the prime factorization of each of the numbers in the orange petals.

_______________   _______________   _______________

Compare the prime factorizations of the two sets of numbers. Write an explanation of your discovery.

Share your discoveries with the group.


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What if a different center number were chosen? Would the results be the same?

Choose ANY cell on Pascal's triangle that is surrounded by 6 other cells. Shade this cell using your black pencil.

Starting with the petal above and to the left of the gray center, alternating petals are colored yellow. The numbers are: _____, _____, and _____.

Color the three remaining petals around the gray center orange. The numbers are: _____, _____, and _____.

The product of the numbers in the yellow petals is __________. The product of the numbers in the orange petals is __________. Are the products the same? Can you explain this?

Write the prime factorization of each number in an orange petal.

_______________   _______________   _______________

Write the prime factorization of each number in a yellow petal.

_______________   _______________   _______________

Compare the prime factorizations of the two sets of numbers. Write an explanation of your discovery.

Share your discoveries with the group.


Questions, Answers, and Discussion

Questions? Write to the workshop facilitators.

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Math Forum * * * * 28 April 1998