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1-15.

Finding and using a pattern is an important problem-solving skill you will use in algebra. The patterns in Diamond Problems will be 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 you could 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.

  1. Diamond Problem. Left 2, Right 5, Top blank,  Bottom blank

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

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

  1. Diamond Problem. Left blank, Right 1 divided by 2, Top 4,  Bottom blank

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

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

See the diamonds below. In the example diamonds, notice how one row added
together equals the bottom number, while that row multiplied equals the top number. 

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

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

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

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

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

In the example diamonds, notice how one row added together equals the bottom number, while that same row multiplied equals the top number.