1. Solve problems involving patterns and recreational problems following Polya's four steps.

2.Organize your methods and approaches for proving and solving problems

Problems

1. In a class experiment, Miguel rolls one ordinary 6-sided die repeatedly. Keeping track of each number he rolls, he decides to stop as soon as one number is rolled three times. Miguel stops after the 12th roll, and the sum of these rolls is 47. Which number occurred for the third time? (An ordinary 6-sided die has the numbers from 1 through 6 on its sides)

2. How many squares of all sizes are there on a standard 8-square by 8-square checkerboard?

3. How many toothpicks will be needed to make a 7 7 square?