4.3+Playing+the+Integer+Product+Game+0910

4/26/10
 * Seung Hyun Kong

4.3 Playing the Integer Product Game

Big idea** Positive+****Positive=****Positive** Negative+****Negative=****Negative**
 * Negative numbers help us to model many real world situations.**
 * Notes from class -
 * Positive+Negative=Negative
 * Negative+****Negative+Positive=****Negative**
 * So if there are odd numbers of negatives in a number sentence, the answer would be a negative number, and if there are even number of negatives the answer would be positive.**

The integer product game Factors - -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 **Game rules - 1.Player A puts a paper clip on a number in a factor list. Player A does not cover a square on the product grid because only one factor has been marked; it takes 2 factors to make a product.**
 * Question: Play the game with a partner. Look for interesting patterns and ideas that might help you devise a winning strategy. Make notes of your observation.**
 * 1 || -1 || 2 || -2 || 3 || -3 ||
 * 4 || -4 || 5 || -5 || 6 || -6 ||
 * 8 || -8 || 9 || -9 || 10 || -10 ||
 * 12 || -12 || 15 || -15 || 16 || -16 ||
 * 18 || -18 || 20 || -20 || 24 || -24 ||
 * 25 || -25 || 30 || -30 || 36 || -36 ||


 * 2. Player B puts the other paper clip on any number in the factor list (including the same number marked by Player A) and then shades or covers the product of the 2 factors on the product grid.**


 * 3. Player A moves either one of the paper clips to another number and then shades or covers the new product using a different color from player B.

4. Each player, in turn, moves a paper clip and marks a product. If a product is already marked, the player does not get a mark for that turn. The winner is the first player to mark 4 squares in a row-up and down, across, or diagonally.**

ways to win - try to use your opportunity to block your opponent's row or try to get 4 squares in a row.

1. Give every combination of 2 factors from the factor list that will give each of the following products.** a. 5: 5X1, -1X(-5) b. -12: 1X-12, -1X12, -2X6, 3X-4 c. 12: 12X1, -12X-1, 2X6, -2X-6, -3X-4, 3X4 d. -25: 1X-25, 5X-5 24, 20, 16, 12, 8, 4, -4, -8, -12, -16, -20, -24 -5X3 -3X-2, -2X-3 It is because there are no 2 factors multiplied and get a -35. If there should be one, the available factors should have a 7 or -7 to get a -35
 * F.U
 * 2. Your opponent starts the game by putting a paper clip on -4. What products are possible on your turn?**
 * 3. At the end of your opponent's turn, the paper clips are on -5 and -2. What move would you make to get a product of -15?**
 * 4. At the end of your opponent's turn, the paper clips are on -3 and -2. What move would you make to get a product of 6?**
 * 5. Why doesn't -35 appear on the board?**

even number of negative numbers would result a positive number and odd number of negative numbers in a number sentence would result a negative number.
 * Summary:**