Compare your answers.

For each of the following,

  • Identify a pattern in the information given.
  • Use your pattern to make a conjecture.
  1. A relationship between angles in a parallelogram

    A good start may be to draw several different parallelograms and measure their interior angles.




    There are several angle patterns you might see within the parallelograms. One pattern is that adjacent angles in the parallelograms add to 180°. Conjecture: The adjacent angles in a parallelogram will always add to 180°.

  2. The sum of the digits for multiples of 9

    Begin by writing some multiples of 9 and determining the sum of their digits.

    Multiples of 9 9 18 27 36 45 54 63
    Sum 9 1 + 8 = 9 2 + 7 = 9 3 + 6 = 9 4 + 5 = 9 5 + 4 = 9 6 + 3 = 9


    The sums of the digits of all the multiples of 9 shown are 9.

    Conjecture: The sum of the digits of a multiple of 9 will be 9.



  3. The data in the table below.



    There is a lot of information in this table and many patterns are possible. The following table lists some possibilities.

    PatternConjecture
    No batting average of the top 9 players was above 0.280. No one on the entire team will have a batting average above 0.280.
    J. Bautista played RF in 2012. J. Bautista will play RF in 2013.
    The top 9 players had a total of 165 home runs. The top 9 players on the Boston Red Sox will have a total of about 165 home runs.