Billiards

QUESTIONS

1. Draw four different tables whose lengths are even and whose widths are odd numbers.
   1. Note the path of the ball on each table.
   2. Record the corner in which the ball ends up.
   3. Make up a corner-predicting rule for a table whose length is even and whose width is odd.
   4. State your rule as a complete sentence.
2. Draw four different tables whose lengths are odd and whose widths are even.
   1. Note the path of the ball on each table.
   2. Record the corner in which the ball ends up.
   3. Make up a corner-predicting rule for a table whose length is odd and whose width is even.
   4. State your rule as a complete sentence.
3. Draw four different tables whose lengths are odd and whose widths are also odd numbers.
   1. Note the path of the ball on each table.
   2. Record the corner in which the ball ends up.
   3. Make up a corner-predicting rule for a table whose length and width are both odd.
   4. State your rule as a complete sentence.
4. Draw three tables whose lengths and widths are even and whose dimensions are listed below:
   
   
   1. 6W X 10L
   2. 4W X 14L
   3. 10W X 12L
   
   On the basis of these three tables, does there seem to be a corner-predicting rule for a table whose length and width are both even?
   
5. The ratio of the length to the width of table A is 10/6.
   1. This ratio can be reduced to 5/3.
   2. Draw a table whose length is 5 and whose width is 3. Note the path of the ball on each table.
   3. Record the corner in which the ball ends up.
   4. You previously stated a corner-predicting rule for the table you just drew. Does that rule correctly predict the corner in which the ball ended up?
6. The ratio of the length to the width of table B is 14/4.
   1. Reduce this ratio to lowest terms. A ratio is in lowest terms if there is no whole number larger than 1 that will divide evenly into both x and y.
   2. Draw a table whose length and width are given by the numbers in the reduced ratio. Note the path of the ball on each table.
   3. Record the corner in which the ball ends up.
   4. Do any of the corner-predicting rules that you previously wrote correctly predict the corner the ball ended up in? If so, state the rule.
7. The ratio of the length to the width of table C is 12/10.
   1. Reduce this ratio to lowest terms.
   2. Draw a table whose length and width are given by the numbers in the reduced ratio. Note the path of the ball on each table.
   3. Record the corner in which the ball ends up.
   4. Do any of the corner-predicting rules that you previously wrote correctly predict the corner the ball ended up in?
   5. If so, state the rule.
8. If the length and width of a billiard table are both even, what should you do before trying to predict the corner in which the ball will end up?
   
   The numbers below represent giant billiard tables. In which corner of each table do you think the ball would end up? Tell why you chose each corner.
9. 85W x 95L
10. 100W X 105L
11. 110W X 120L
    
    
12. As a billiard ball travels around the table, it hits the cushions a number of times. How many times depends on the dimensions of the table. Counting the original and final corner positions as “hits,” a square table has two hits.
    1. Draw two tables, one with length 12 and width 9 and the other with length 4 and width 3. Note the path of the ball on each table.
    2. Record the hits.
    3. Why do both tables have the same number of hits?
    4. From these two tables, try to guess a rule for predicting the number of hits on a table on the basis of its dimensions. Test your rule on some of the other tables of this lesson.
    
    How many hits do you think there would be on each of the giant tables whose dimensions are listed below?
13. 95W X 96L
14. 100W X 110L
15. 90W X 105L
16. Explain your thinking in 12 words or less.