4.2+Studying+Multiplication+Patterns+0910

CA 4/25/10


 * Big Idea****:** Negative numbers help us model many real-world situations**.**


 * Essential Question:** How can I study multiplication patterns with integers?


 * __Problem 4.2:__**

5x5= 25 5x4=20 5x3=15 5x2=10 5x1=5 5x0=0 5 x-4=? 4 x-4=? 3 x-4=? 2 x-4=? 1 x-4=? 0 x-4=? -20 -16 -12 -8 -4 0
 * A.** **Describe any patterns you observe in the way the products change as the integers multiplied by 5 get smaller.** As the integers got smaller, the product decreased by 5 each time. For example, 5x5=25, 5x4=20. 20 is 5 less than 25.
 * B.** **1. Use the patterns you observed to predict 5 x-1. Explain your reasoning.** 5x-1= -5. Since the integer decreased by 1 (-1 is 1 less than 0), the answer will decrease by 5. Since 5x0=0, 5 must be taken from 0 to get -5.
 * 2. Write the next 4 equations in the pattern.** 5 x-2=-10, 5 x-3= -15, 5 x-4=-20, 5 x-5=-25
 * C. Complete the equations below and use them to help you answer parts D&E.**
 * D. Describe any patterns you observe in the way the products change as the integers multiplied by -4 get smaller.** The products all decrease by 4 as the integer decreases by 1. For example: 5 x-4= -20, and 4 x-4=-16. -16 is 4 less than -20.
 * E. 1. Use the patterns you observed to predict -1 x-4. Explain your reasoning** -1 x-4= 4. A negative multiplied by a negative makes a positive. Since -1 and -4 are both negative, their product will be positive.
 * 2.** **Write the next 4 equations in the pattern.** -1 x-5=5, -1 x-6=6, -1 x-7=7, -1 x-8=8
 * F. Find the following products:**
 * 1. -3 x7 2. 5 x-8 3. -11 x -12 4. -3.6 x 2.7** -21 -40 -132 -9.72

The order matters because if the numbers are switched, you are taking different quantities from different numbers. For example, 3-1. You are taking 3 from 1. But, if you switch it to 1-3, it is a completely different problem. You are now taking 3 from 1. The order of the numbers matters in subtracting integers.
 * __Problem 4.2 Follow-up:__**
 * 1a. Find -6x7 and 7x-6 -**6x7= -42 7x-6= -42
 * 1b. When you multiply integers, does the order of the number matter?** No, it does not. Multiplication has the commutative property, which means that the numbers can be switched around, and the answer will not change.
 * 2a.** **Find -6+7 and 7+-6** -6+7= 1 7+-6= 1.
 * 2b. When you add integers, does the order of the numbers matter?** No, it does not. Addition also has the commutative property. The numbers can be in any order and the answer will remain the same.
 * 3a. Find -6- 7 and 7- -6.** -6-7= -13 7- -6= 13
 * 3b. When you subtract integers, does the order of the numbers matter?**
 * 4. When you add two negative integers, you get a negative result. Is the same true when you multiply two negative integers? Explain.** No, it is not true. A negative multiplied by a negative is a positive.