1 / 46

USING: INTEGER- TILES

USING: INTEGER- TILES. Multiplication and Division. MULTIPLICATION and DIVISION of INTEGERS:. 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 . .

jmikesell
Download Presentation

USING: INTEGER- TILES

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. USING: INTEGER- TILES Multiplication and Division

  2. MULTIPLICATION and DIVISION of INTEGERS:

  3. 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 . . . . . . (-3)(+2) = -6 (-3)(+1) = -3 (-3)(0) = 0 (-3)(-1) = +3 (-3)(-2) = +6 . . . . . . What have you noticed???

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

  5. 0 7 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 Multiplication on the number line: (+3)(+2) = +6 +6 . .

  6. 0 7 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 Multiplication on the number line: (+2)(-3) = -6 -6 . . OR

  7. 0 7 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 Multiplication on the number line: (-3)(+2) = or (-)(3)(2)= -6 -6 +6 . . Note: Negative changes to opposite direction

  8. 0 7 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 Multiplication on the number line: (-3)(-2) = or (-)(-)(3)(2)= +6 -6 +6 +6 . . Note: Negative changes to opposite direction Note: Negative changes to opposite direction

  9. +10 +2 = 0 7 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 Division on the number line: +5 . How many moves of (2) will get you from 0 to 10

  10. -10 -2 = 0 7 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 Division on the number line: +5 . How many moves of (-2) will get you from 0 to -10

  11. (-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 . . . . . . Let’s Look at this pattern… What have you noticed???

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

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

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

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

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

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

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

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

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

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

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

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

  24. DIVISION of INTEGERS:

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

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

  27. - 2

  28. - 4

  29. +2

  30. + 5

  31. Try a few more... -2 +4 -3 +2 +7

  32. Extension! for multiplication and division

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

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

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

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

  37. - 2 Place 8 zero’s on the mat! Hint:(The dividend will tell you, how many zero’s). Remove4 equal groups, leaving behind +8 on the mat. (Hint: Opposite sign of the dividend, tells you what to remove from the mat).

  38. + 2 Place 8 zero’s on the mat! Hint:(The dividend will tell you, how many zero’s). Remove4 equal groups, leaving behind -8 on the mat. (Hint: Opposite sign of the dividend, tells you what to remove from the mat).

  39. - 2 Place 4 zero’s on the mat! Hint:(The dividend will tell you, how many zero’s). Remove2 equal groups, leaving behind +4 on the mat. (Hint: Opposite sign of the dividend, tells you what to remove from the mat).

  40. COLOURS in CONFLICT (factors oppose) ALWAYS WHITE (Negative) P R O D U C T REMEMBER!! Coloured tiles are POSITIVE and White tiles are NEGATIVE Hint Wrap up Algebra-tiles

  41. BLACKLINE MASTERS

  42. BLACKLINEMASTERS

  43. Add and Subtract number lines: 0 0 0 0 0 0 7 7 7 7 7 7 -12 -12 -12 -12 -12 -12 -11 -11 -11 -11 -11 -11 -10 -10 -10 -10 -10 -10 -9 -9 -9 -9 -9 -9 -8 -8 -8 -8 -8 -8 -7 -7 -7 -7 -7 -7 -6 -6 -6 -6 -6 -6 -5 -5 -5 -5 -5 -5 -4 -4 -4 -4 -4 -4 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 9 9 9 9 9 9 10 10 10 10 10 10 11 11 11 11 11 11 12 12 12 12 12 12

  44. Add and Subtract number lines: 0 0 0 0 0 0 0 7 7 7 7 7 7 7 -12 -12 -12 -12 -12 -12 -12 -11 -11 -11 -11 -11 -11 -11 -10 -10 -10 -10 -10 -10 -10 -9 -9 -9 -9 -9 -9 -9 -8 -8 -8 -8 -8 -8 -8 -7 -7 -7 -7 -7 -7 -7 -6 -6 -6 -6 -6 -6 -6 -5 -5 -5 -5 -5 -5 -5 -4 -4 -4 -4 -4 -4 -4 -3 -3 -3 -3 -3 -3 -3 -2 -2 -2 -2 -2 -2 -2 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 3 3 4 4 4 4 4 4 4 5 5 5 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7 8 8 8 8 8 8 8 9 9 9 9 9 9 9 10 10 10 10 10 10 10 11 11 11 11 11 11 11 12 12 12 12 12 12 12

  45. Multiplication and Division mat:

More Related