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2-16.

Finding patterns is an important problem-solving skill used in mathematics. You will use the patterns in Diamond Problems to solve other problems later in the course. Can you discover a pattern for the numbers in each of the four diamonds below?

Diamond Problem. Left 5, Right 2, Top 10,  Bottom 7

Diamond Problem. Left 2, Right 8, Top 16,  Bottom 10

Diamond Problem. Left 8, Right 7, Top 56,  Bottom 15

Diamond Problem. Left 1, Right 4, Top 4,  Bottom 5

Copy the Diamond Problems below and use the pattern you discovered to complete each of them.

Notice that the top number is the product of the middle numbers and the bottom number is the sum.
Now complete the diamonds in parts (a) through (d) using this pattern.

  1. Diamond Problem. Left 3, Right 4, Top blank  Bottom blank

    Diamond Problem. Left 3, Right 4, Top 12, Bottom 7

  1. Diamond Problem. Left 2, Right 3, Top blank,  Bottom blank

    Diamond Problem. Left 2, Right 3, Top 6, Bottom 5

  1. Diamond Problem. Left blank, Right 2, Top 12,  Bottom blank

  1. Diamond Problem. Left blank, Right blank, Top 28,  Bottom 11

    What two numbers have a product of and a sum of ? Try factoring and check factors to see which two add up to .