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

Ajwad Khan April 27, 10 Math 7B
 * Big Idea: Negative numbers help us to model many real world situations. **
 * Essential Questions: How do I multiply and divide integers? **

__Problem 4.3__


 * Play the game with a partner. Look for interesting patterns and ideas that might help you devise a winning strategy. Make notes of or observations.**

To me, going second is probably better than going first because you get the first pick on the board. It’s best to get squares toward the center because you then have more options of which direction you want to make your row of four. Then you are not stuck in the corner. You should actually go in multiple directions incase your opponent blocks you out even though you should start making a row of four. You can always get a positive or a negative number on the board. The two factors that are there before do not matter. You just have to move it to the correct positive or negative. For example if the paper clips are on -4 and 8. You can get a positive number or a negative number, but you may not get the exact integer you want. That’s why you have to try to match the integers and use the factors that were there from before.

__Problem 4.3 Follow-Up__


 * 1.** **Give every combination of two factors from the factor list that will give each of the following products.**

a. 5: 5 and 1, -5 and -1 b. -12: 4 and -3, 3 and -4, 6 and -2, 2 and -6 c. 12: 4 and 3, 6 and 2, -4 and -3, -6 and -2 d. -25: 5 and -5


 * 2**. **Your opponent starts the game by putting a paper clip on -4. What products are possible on your turn?**

4, -4, -8, 8, 12, -12, 16, -16, 20, -20, 24, -24


 * 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?**

I would move the -2 to 3. 3 x -5= -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?**

I would move -3 to 3 or -2 to 2.


 * 5**. **Why doesn’t -35 appear on the board?**

-35 doesn’t appear on the board because there is no -7 or 7 as a factor which could be multiplied with -5 or 5.