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Integer Tiles in Multiplication and Division

Learn how to solve multiplication and division of integers with integer tiles, rules for operations, and number line representation. Practice and master the concepts with symbolic and pattern recognition methods.

jmikesell
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Integer Tiles in Multiplication and Division

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  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:

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