Working with a partner, study the following number pattern in Pascal's triangle. Exploring Pascal's Triangle
Intermediate Level
Pascal Petals
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.
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
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