3. (3)(2) = 6 (3)(1) = 3 (3)(0) = 0 (3)(-1) = -3 (3)(-2) = -6.. Let’s Look At This… (-3)(2) = -6 (-3)(1) = -3 (-3)(0) = 0 (-3)(-1) = +3 (-3)(-2) = +6.. (-3)(+2) = -6 (-3)(+1) = -3 (-3)(0) = 0 (-3)(-1) = +3 (-3)(-2) = +6.. What have you noticed???

4. for Multiplication (+)(+) = + (-)(+) = - ( +)(-) = - (-)(-) = + SYMBOLIC:

5. Multiplication on the number line: 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 (+3)(+2) =. +6.

6. Multiplication on the number line: 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 (+2)(-3) =. -6. OR

7. Multiplication on the number line: 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 (-3)(+2) = or (-)(3)(2)=. +6. -6 Note: Negative changes to opposite direction -6

8. Multiplication on the number line: 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 (-3)(-2) = or (-)(-)(3)(2)=. +6. Note: Negative changes to opposite direction -6 Note: Negative changes to opposite direction +6

9. 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12. +10 +2 = How many moves of (2) will get you from 0 to 10 +5 Division on the number line:

10. 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12. -10 -2 = How many moves of (-2) will get you from 0 to -10 +5 Division on the number line:

11. Let’s Look at this pattern… What have you noticed??? (-8) (-2) = +4 (-6) (-2) = +3 (-4) (-2) = +2 (-2) (-2) = +1 (0) (-2) = 0 (+2) (-2) = -1 (+4) (-2) = -2 (+6) (-2) = -3 (+8) (-2) = -4.

12. SYMBOLIC: for Division (+) (+) = + (-) (-) = + ( +) (-) = - (-) (+) = -

13. AREA = Length X Width WIdthWIdth L e n g t h (+3)(+2) = What does this mean?? ADD: Three groups of +2 or 2+2+2= + 6 Product = factor x factor

14. (+4)(+3) = The product is ? ADD: Four groups of positive 3 +12

15. (+4)(- 3) = ADD: Four groups of negative three. - 12

16. (+3)(-2) = - 6

17. (- 5)(+ 2) = - 10 Add: two groups of -5

18. When COLOURS of the factors are in CONFLICT (Oppose) the product is ALWAYS WHITE ( negative) METHOD : 2 Remember there are ONLY two colours – White or Coloured

19. (- 3)( + 2) = - 6 Yes! Therefore, WHITE ! ARE product of the COLOURS in CONFLICT??? (Oppose)

20. (- 2)(- 3)= + 6 No! Therefore, Coloured ! ARE the product of the COLOURS in CONFLICT??? (Oppose)

21. (- 3)(-4) = + 12 No! Therefore, Coloured ! ARE the product of the COLOURS in CONFLICT??? (Oppose)

22. When the product of the COLOURS of the factors are in CONFLICT (Oppose) the product is ALWAYS WHITE ( negative) otherwise COLOURED!

23. 1. (-4)(+2) = 2. (+6)(+3) = 3. (-5)(-3) = 4. (+6)(-2) = 5. (-3)(+8) = - 8 + 18 + 15 - 12 -24

25. + 3 REMEMBER RULE!! Hint If the product is COLOURED the factors are the SAME! NOTE: It is the converse of Multiplication!

26. - 3 REMEMBER RULE!! Hint When the product is COLOURED the factors are the SAME colour!

27. - 2

28. - 4

29. +2

30. + 5

31. -2-2 +4+4 -3-3 +2+2 +7+7

33. METHOD # 2 : -3 x 2 = The negative means, to take out three groups of + 2 - 6 What are you left with on the mat?

34. -3 x -2 = The negative means, take out three groups of - 2 + 6 What are you left with on the mat?

35. + 3 Add to the mat, two equal groups to give you + 6.

36. Add to the mat, two equal groups to give you - 6 - 3

37. Remove 4 equal groups, leaving behind +8 on the mat. (Hint: Opposite sign of the dividend, tells you what to remove from the mat). - 2 Place 8 zero’s on the mat! Hint: (The dividend will tell you, how many zero’s).

38. Remove 4 equal groups, leaving behind -8 on the mat. (Hint: Opposite sign of the dividend, tells you what to remove from the mat). + 2 Place 8 zero’s on the mat! Hint: (The dividend will tell you, how many zero’s).

39. Remove 2 equal groups, leaving behind +4 on the mat. (Hint: Opposite sign of the dividend, tells you what to remove from the mat). Place 4 zero’s on the mat! Hint: (The dividend will tell you, how many zero’s). - 2

40. COLOURS in CONFLICT (factors oppose) ALWAYS WHITE (Negative) PRODUCTPRODUCT REMEMBER!! Coloured tiles are POSITIVE and White tiles are NEGATIVE REMEMBER!! Coloured tiles are POSITIVE and White tiles are NEGATIVE Hint Algebra-tiles

42. BLACKLINEMASTERSBLACKLINEMASTERS

43. 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 Add and Subtract number lines:

44. 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 Add and Subtract number lines: 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12 0 123456 7 789101112-10-9-8-7-6-5-4-3-2-11-12

46. Multiplication and Division mat: