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1-18.

Finding and using a pattern is an important problem-solving skill necessary for your study of mathematics. The patterns in Diamond Problems are used later in the course to solve other types of algebraic problems.

Look for a pattern in the first three diamonds below. For the fourth diamond, explain how to find the missing numbers (?) if you know the two numbers (#).

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

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

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

Diamond Problem. Left #, Right #, Top unknown,  Bottom unknown

Copy the Diamond Problems below onto your paper, then use the pattern you discovered to complete each one.

What do you do to each of the (#) numbers to get to the (?) numbers?

  1. Diamond Problem. Left 3, Right 5, Top blank,  Bottom blank

    Diamond Problem. Left 3, Right 5, Top 15,  Bottom 8

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

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

  1. Diamond Problem. Left blank, Right blank, Top 8,  Bottom 6

    Diamond Problem. Left 2, Right 4, Top 8,  Bottom 6

  1. Diamond Problem. Left 8, Right 1 divided by 2, Top blank,  Bottom blank

    Diamond Problem. Left 8, Right one half, Top 4,  Bottom 8 and one half

  1. Diamond Problem. Left blank, Right blank, Top 12,  Bottom negative 7

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