1. Today you will learn: How to multiply positive and negative numbers. How to Divide positive and negative numbers. Review for Exam on Monday Daily Goals Class Work Notes Handout

2. Multiplication Using Arrays

3. How many paper clips are here? I could count them, but there is an easier way!

4. Now, how many paper clips are here? I can count them by groups. 4 paper clips in each column 3 columns. That is 3 sets of 4. I can add 4 + 4 + 4 or I could say 3 x 4. Now how many are there?

5. How many are here? What is the number sentence? You could have said 3 + 3 or 2 + 2 + 2. Using multiplication You might have said 2 x 3 or 3 x 2. The answer will be the same for all!

6. Try this one. What is the number sentence using multiplication? If you said 3 x 4 or 4 x 3 you are correct. What is the answer?

7. Now try this one. What is the multiplication fact? Great! 2 x 4 or 4 x 2. What is the product? (that means answer when you are multiplying! Recorder/Reporter Task Manager Facilitator Resource Manager

8. To find out how many stars there are, you could add. + 2 red + 2 blue = 6 stars 2 yellow

9. However, if you have equal groups of something you can use

10. I see three groups of two. x 2= 6 stars 3 groups

11. If you are having a party and you want to have lots of sodas, you can use multiplication. Sodas come in groups of six.

12. Five groups of six would be 30 sodas. 5 x 6 = 30 sodas

13. Sometime multiplication can be used when objects are in rows or columns, or arrays. Here is an array of flowers.

14. There are 3 rows of 6 flowers. 3 x 6 = 18 flowers.

15. How many groups? How many in each group? There are 3 groups of 4 balloons.

16. Equal numbers are in each group. Multiplication can be used! 3 x 4 = 12 balloons

17. How many groups? How many in each group? There are 4 groups of 3 tires.

18. Equal numbers are in each group. Multiplication can be used! 4 x 3 = 12 tires

19. When combining EQUAL groups, the fastest way to get the total is by using…

20. I know how to do multiplication, but what about division? Don’t worry Woody, it is easy to relate multiplication and division.

21. Multiplication is a shortcut for addition. When you add, you combine amounts. When you have equal amounts to add, you can multiply to find the total.

22. Sample There are 5 bicycles that need new tires. How many tires is that? You could add 2+2+2+2+2 to find the total. 22222 ++++ 2 + 2 + 2 + 2 + 2 = 10

23. I can also multiply 2 by 5 to find the total. 2 is the number of tires on each bike. 5 is the number of bikes. 2x 5 =10 Total number of tires

24. is the operation of making equal groups and finding the number in each group or the number of groups. Wow!!!!!!! That sounds cool! Division

25. There are 12 stickers and 3 students. How many stickers can each student get so that they each have the same amount?

26. 12 ÷ 3 = 4 Total number of stickers Total number of students Number of stickers for each student.

27. Sample There are 18 cupcakes. How many cupcakes can you put into 3 boxes so each box has the same amount of cupcakes? 18 Total number of cupcakes ÷3= Total number of boxes 6 Total number of cupcakes for each box.

28. Just like subtraction is the opposite of addition, division is the opposite of multiplication. You can use what you know about multiplication to help you with division.

29. Multiplication Facts Related Division Facts 4x 5 =20 ÷5=4 5x4 = ÷ 4=5 I’ll do the multiplication facts. Ok, I’ll do the related division facts

30. Some people find multiplication easier than division. If you do, when you see division, think about multiplication. 24 ÷ 8 = Think: X 8 = 24 The number you need to write here is called the missing factor. = 3 So, you know Answer because3x8=24 ÷8=3 =3

31. Yeah! We did it !

32. Lisa IovinoMultiplying and Dividing Integers Ms. Iovino

33. Lisa IovinoMultiplying and Dividing Integers To Multiply and Divide Integers, We use the same set of rules.

34. Meet the Negative Family

35. Lisa IovinoMultiplying and Dividing Integers The negative people live in negativeland. In negativeland, you must follow the rules that are listed here.

36. Rules to NegativeLand There are only two things that you can do in negativeland (Shop or Math) You can only go shopping in negativeland, if you have ONE other friend to go with. If you don’t go shopping you stay home and do math (meaning you are in the answer).

37. Lisa IovinoMultiplying and Dividing Integers Let’s try a problem….. 4 x –2=

38. Lisa IovinoMultiplying and Dividing Integers Multiply, like you would without the negative sign. 4 x 2=8 How many negative signs do you see?

39. Lisa IovinoMultiplying and Dividing Integers One negative sign…… 4 x –2= One negative sign represents one negativeland resident. Does he have anyone to shop with?

40. Lisa IovinoMultiplying and Dividing Integers Nope, He doesn’t….. So he stays home in the answer. 4 x –2= -8

41. Try these problems….. -5 x –3= -8 x 3= 10/-2= -14/-2= -20/5= -3 x –4 x –1=

42. Here are the answers….. -5 x –3= 15 The two negative people go shopping. -8 x 3= -24 One negative sign makes a negative answer. 10/-2= -5 One negative sign, negative answer. -14/-2= 7 Two negative signs cancel out. -20/5= -4 One negative sign, negative answer. -3 x -4 x-1= -12 Two negative signs cancel out and one is left in the answer.

43. Lisa IovinoMultiplying and Dividing Integers In conclusion, when multiplying and dividing integers, every two negative signs cancel each other out.

44. Lisa IovinoMultiplying and Dividing Integers If you have an even number of negative signs, your answer is negative.

45. Lisa IovinoMultiplying and Dividing Integers If you have an odd number of negative signs, your answer is positive.

46. Lisa IovinoMultiplying and Dividing Integers