1. Bell Ringers Solve the following equations and write the commutative property equation and solve: (-74) + 54 (-87) + (-32) Solve the following equations and write the associative property equation and solve. ((-42) + (-10)) + (-68) (82 + 91) + (-48) Solve the following equations using the rule of subtraction (-76) – (-39) 61 – 86

2. Multiplication of Integers

3. Today I will be able to apply my knowledge of repeated addition and multiplication of positive whole numbers to solve problems involving the multiplication of rational numbers.

4. How does addition relate to multiplication? Talk in your group about how addition is related to multiplication. How can we use addition to solve multiplication problems? Such as 3 x 4 = How do you think we can use this knowledge to help us when multiplying integers? (-3) x 4

5. What do you notice? Let’s use repeated addition to solve the following problems. 1.3 x 5 2.(-3) x 5 3.(-3) x (-5)

6. What did we notice? When we multiplied two positive integers we got a positive product or answer. When we multiplied one positive and one negative integer we got a negative product. When we multiplied two negative integers we got a positive product.

7. Just like addition and subtraction of integers there are rules for multiplying integers We can use the following concepts to help us remember the outcome of multiplying integers. 1.When a good thing happens to a good person we believe that they deserve it and it’s a good thing. 3 x 5 = +15 1.When a bad thing happens to a bad person we believe that they deserve it and it’s a good thing. (-3) x (-5) = +15 1.When a good thing happens to a bad person we believe that they don’t deserve it and it’s a bad thing. 3 x (-5) = (-15) 1.When a bad thing happens to a good person we believe that they don’t deserve it and it’s a bad thing. (-3) x 5 = +15

8. Rules for multiplying integers To multiply integers, always multiply the absolute values and use these rules to determine the sign of the answer: 1.The product of two positive integers or two negative integers is positive. 2.The product of a positive integer and a negative integer is negative.

9. Let’s Practice (-3) x 9 I3I x I9I 3 x 9 =27 Negative thing happens to a good person that’s bad, so my product is negative. Answer: -27

10. Discuss this in your groups (-6) x (-8) Answer:

11. Your turn Take turns holding up the positive and negative sign at your tables to show the sign of the product of the following equations. For example: If I showed the equation 3 x 3 we would hold up the __________ sign.

12. (-8) x (-9)

13. 5 x 7

14. (-4) x 7

15. (-9) x 8

16. (-2) x (-4)

17. 10 x 12

18. (-7) x (-7)

19. Multiplication War You will be put into groups of two or three. Each group will be given a deck of cards. The red cards in this deck represent negative cards and the black cards represent positive cards. Two players will play the card game war, but with a little twist. 1.Divide the cards evenly between the two players. 2.Each player shuffles their cards and keeps them facing down. 3.Each play will flip over their top card and place it in front of them. The first person to correctly state the product (don’t forget the sign) gets the cards. The person with the most cards when the timer goes off wins. 4.If you are in a group of 3 the third person is the judge to decide who answered the fastest and if the answer was correct. This player will get a turn after the timer goes off.

20. Exit Ticket Explain how you determine the product of two integers.