Students investigate the path of a ball on a billiard table with sides of whole number length when the ball starts in a corner and always travels at a 45 degree angle. They make a table which records the length and width of the billiard table, the number of hits against the perimeter, and the number of squares passed through, for billiard tables of various sizes, and look for relationships. The number of hits against the perimeter of the table, including the first and last corners, is the sum of the width and the length of the billiard table divided by their greatest common factor. Investigate the relationships among fractions, decimals, and percents, and use all of them appropriately. Given a circle graph of some interesting data, students estimate the size of each section of the graph as a fraction, a percent, and as a decimal.
Students also create their own circle graphs.
Identify, derive, and compare properties of numbers. Find five examples of numbers that have exactly three factors. Repeat for four factors, and then again for five factors. Students explore perfect numbers, those numbers that are equal to the sum of all of their factors including 1 but excluding themselves. Interestingly, the next one has 2 digits, the third has 3 digits and the fourth has 4 digits.