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Math 8

Math 8. Unit 2: Integers. Unit 2: Integers. What you’ll learn: Multiply and divide integers Use the order of operations with integers Solve problems involving integers. Unit 2: Integers. Why its important: Used with temperature (negative temperatures is where water freezes)

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Math 8

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  1. Math 8 Unit 2: Integers

  2. Unit 2: Integers What you’ll learn: • Multiply and divide integers • Use the order of operations with integers • Solve problems involving integers

  3. Unit 2: Integers Why its important: • Used with temperature (negative temperatures is where water freezes) • Used with finance (losing money is negative)

  4. Unit 2: Integers 2.1 Using Models to Multiply Integers

  5. 2.1 Using Models to Multiply Integers • Focus: Use a model to multiply two integers

  6. 2.1 Using Models to Multiply Integers • Remember that integers are positive and negative whole numbers. http://img.sparknotes.com/figures/5/50ca5e784bb7e4242910d5b8a571d103/number_line.gif

  7. 2.1 Using Models to Multiply Integers • Review addition of integers • When adding positive numbers go right • +2 + + 3= • -2 + + 3 =

  8. 2.1 Using Models to Multiply Integers • Review addition of integers • When adding negative numbers go left • +2 + - 3= • -2 + - 3 =

  9. 2.1 Using Models to Multiply Integers • Review subtraction of integers • When subtracting positive numbers go left • +2 - + 3= • -2 - + 3 =

  10. 2.1 Using Models to Multiply Integers • Review subtraction of integers • When subtracting negative numbers go right • +2 - - 3= • -2 - - 3 =

  11. 2.1 Using Models to Multiply Integers Remember • Multiplication is fast addition • 2 x 5 is the same as 2 + 2 + 2 + 2 + 2 or 5 + 5 • 3 x 4 is the same as 3 + 3 + 3 + 3 or 4 + 4 + 4 • 2 x – 5 is the same as -5 + -5 • - 3 x 4 is the same as – 3 + - 3 + - 3 + -3

  12. 2.1 Using Models to Multiply Integers • Write out the following multiplications as additions and solve • 3 x -2 • 4 x – 3 • 5 x – 4 • -3 x 2 • -4 x 3

  13. 2.1 Using Models to Multiply Integers • Write out the following multiplications as additions and solve • 3 x -2 = -2 + - 2 + -2 = -6 • 4 x – 3 = -3 + - 3 + - 3 + -3 = -12 • 5 x – 4 = - 4 + -4 + -4 + -4 + -4 = -20 We can’t make add negative times so reverse the number pattern • -3 x 2 = - 3 + -3 = -6 • -4 x 3 = - 4 + - 4 + - 4 = -12

  14. 2.1 Using Models to Multiply Integers • Homework

  15. Unit 2: Integers 2.2 Developing Rules to Multiply Integers

  16. 2.2 Developing Rules to Multiply Integers • Focus: Use patterns to develop rules for multiplying integers

  17. 2.2 Developing Rules to Multiply Integers • Fill in the highlighted part of the following table

  18. 2.2 Developing Rules to Multiply Integers What pattern do you notice about the numbers as we go down the columns? Fill in the rest of the column following the patterns going down.

  19. 2.2 Developing Rules to Multiply Integers Check your answers. What is the pattern going right to left?

  20. 2.2 Developing Rules to Multiply Integers Use the pattern to fill in the rest of the table.

  21. 2.2 Developing Rules to Multiply Integers Check your answers. Positive multiplied by a positive = Positive multiplied by a negative = Negative multiplied by a negative = Negative multiplied by a negative =

  22. 2.2 Developing Rules to Multiply Integers • Use your rules to solve: • Practice: • +4 x -5 = • -3 x +6 = • -2 x -8 = • +5 x + 6 =

  23. 2.2 Developing Rules to Multiply Integers The same rules apply to addition and subtraction • + 2 + + 3 is the same as 2 + 3 • + 2 + - 3 is the same as 2 – 3 • + 2 - + 3 is the same as 2 – 3 • + 2 - - 3 is the same as 2 + 3

  24. Unit 2: Integers 2.3 Using Models to Divide Integers

  25. 2.3 Using Models to Divide Integers • Focus: Use a model to divide integers

  26. Division is the opposite of multiplication quotient 8 ÷ 2 = 4 dividend divisor product 4 x 2 = 8 factor factor

  27. Investigate

  28. Unit 2: Integers 2.4 Developing Rules to Divide Integers

  29. 2.4 Developing Rules to Divide Integers • Focus: Use patterns to develop the rules for dividing integers

  30. 2.4 Developing Rules to Divide Integers Remember the rules for multiplying integers: • Positive multiplied by a positive is positive • Positive multiplied by a negative is negative • Negative multiplied by a positive is negative • Negative multiplied by a negative is positive • Same signs are positive • Opposite signs are negative

  31. 2.4 Developing Rules to Divide Integers Practice: • + 48 ÷ + 8 = • + 56 ÷ - 8 = • - 42 ÷ + 6 = • -36 ÷ - 6 =

  32. 2.4 Developing Rules to Divide Integers • Homework

  33. Unit 2: Integers 2.5 Order of Operations with Integers

  34. 2.5 Order of Operations with Integers • Focus: Apply the order of operations to integers

  35. 2.5 Order of Operations with Integers Remember • Order of operations: B E D M A S

  36. 2.5 Order of Operations with Integers Remember • Order of operations: Brackets Exponents Division Multiplication Addition Subtraction } Done at the same time from left to right } Done at the same time from left to right

  37. 2.5 Order of Operations with Integers • Scientific calculators do order of operations for you. • Check by doing the following: • 8 + 2 x 3

  38. 2.5 Order of Operations with Integers Practice = -10 ÷ 5 x - 2 ÷ 2 x - 3

  39. 2.5 Order of Operations with Integers Practice = -10 ÷ 5 x - 2 ÷ 2 x – 3 = -2 x - 2 ÷ 2 x – 3 = - 4 ÷ 2 x – 3 = - 2 x – 3 = 6

  40. 2.5 Order of Operations with Integers Practice • -5 x 2 + 3 • (-5 x 2) + 3 • -5 x (2 + 3) • 2 + 3 x – 4 • (2 + 3) x – 4 • 2 + (3 x – 4) =-7 =-7 =-25 =-10 =-20 =-10

  41. 2.5 Order of Operations with Integers • Homework

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