4.2+Studying+Multiplication+Patterns

Sudhir Mandarapu 4/26/09 Math7B __ Studying Multiplication Patterns  __ Problem 4.2 ** BIG Idea  ** Multiplication Patterns can help you do multiplication problems. ** Essential Questions  ** ** 1.)   ** Are multiplying, adding, and subtracting negative integers all the same?
 * 2.)  ** Are there any patterns that can really help you do multiplication with negative integers?
 * A.) ****Describe any patterns you observe in the way the products change as the integers multiplied by 5 get smaller.**

The first number in the equation is the same every time, as the second number gets smaller so does the product.

5  ´ (-1) = -5, Pattern: 5  ´  2= 10, 5  ´  1 = 5, 5  ´  0 = 0, 5  ´  (-1) = -5 5  ´ (-2) = -10, 5  ´  (-3) = -15, 5  ´  (-4) = -20, 5  ´  (-5) = -25
 * B.) ****1. Use the patterns you observed to predict 5** ** ´  (-1). Explain your reasoning. **
 * 2. Write the next four equations of the patterns. **


 * C.) ****Complete the equations below, and use them to help you in parts E & D.**

5 × (-4) = -20 4 × (-4) = -16 3 × (-4) = -12 2 × (-4) = -8 1 × (-4) = -4 0 × (-4) = 0 I observed that while the integers get smaller the answers get bigger. (-1) × (-4) = -4, 1 × (-4) and (-1) × (-4) are the same thing, even though the first number is a positive, the number will end up as a negative.
 * D.) Describe any patterns you observed in the way the products change as the integers multiplied by -4 get smaller. **
 * E.)1. Use the patterns you used to predict (-1) × (-4). Explain you reasoning. **


 * 2. ****Write the next four equations in the pattern.**

-2 × -4 = -8, -3 × -4 = -12, -4 × -4 = -16, -5 × -4 = -20 1.) -21 2.) -40 3.) 132 4.) 334
 * F.) Find the following products. 1.) -3 × 7 2.) 5 × -8 3.) -11 × -12 4.) -3.6 × 2.7 **

** Problem 4.2 Follow Up ** ** 1.) ****a. Find -6 × 7 and 7 × -6.**   -6 × 7 = -42, 7 × -6 = -42 No.
 * b. When you multiply integers, does the order of the integers matter?**

-6 + 7 = 1, 7 + -6 = 1
 * 2.) ****a. Find -6 + 7 and 7 + -6.**

**b. When you add integers, does the order of the integers matter?** No.

-6 – 7 = -13, 7- (-6) = 13
 * 3.) ****a. Find -6 – 7 and 7 – (-6).**

**b. When you add integers, does the order of the integers matter?**

Yes

 Yes, for example -2 × -5 = -10, or -7 × -6 = -42.
 * 4.) ****When you add two negative integers, you get a negative result. Is the same true when you multiply two negative integers? Explain.**