2-1 6th grade math

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2-16th grade math

• Multiplication Properties

2
Objective

• To use multiplication properties and mental math
  strategies to compute mentally.
• Why? To help you solve multiplication problems
  faster w/o using a paper and pencil and/or to get
  an estimated answer in your head before you
  actually solve the problem

3
California State Standards

• AF 1.3 Apply the commutative, associative, and
  distributive properties and justify each step
  in the process
• MR 3.3 Develop generalizations of the results
  obtained and the strategies used and apply them
  in new problem situations

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Vocabulary

• Commutative Property
• The order in which numbers are multiplied does
  NOT affect the product
• (switch the order)
• 5 x 20 20 x 5
• Associative Property
• The way in which factors are grouped does NOT
  affect the product
• (all must be x and keep the same order, just
  flip the () around)
• 3 x (2 x 5) (3 x 2) x 5
• Identity Property
• The product of 1 and any other number is that
  number
• 45 x 1 45
• Property of Zero
• The product of 0 and any number is zero
• 9,999 x 0 0
• Distributive Property
• Multiplying a factor by a group of addends yields
  the same result as multiplying that factor by
  each addend and then adding the products
• (a number is x to a group of numbers being
  ) (distribute pass/give out)
• 6 x (5 4) (6 x 5) (6 x 4) or 6(5 4)
  (6 x 5) (6 x 4)

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How to Use Mental Math in Solving Multiplication
Problems- Break Apart Method

• Used with distributive property
• 1) Recognize how numbers can be broken apart in
  order to compute quickly
• 2) Break apart a number to give you easier
  numbers with which to work
• 3) Use the distributive property to multiply

• 3 x 17
• 17 10 7
• (3 x 10) (3 x 7)
• 30 21
• 51

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How to Use Mental Math in Solving Multiplication
Problems- Compatible Numbers

• Used with commutative and associative properties
• 1) Look for two numbers that may be rearranged
  to be computed in your head commutative prop
• 2) Multiply using the associative prop
• 3) Check your work

• 2 x (386 x 5)
• 2 x 5 are compatible
• (2 x 5) x 386
• 10 x 386
• 3,860

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How to Use Mental Math in Solving Multiplication
Problems- Compensation

• Used with distributive property and when one of
  the factors is close to be rounded
• 1) Look for a number that may be rounded to the
  nearest whole number and can be solved in our
  head
• 2) Use distributive prop to multiply the added
  number to the factor,
• 3) And then multiply the subtract amount from
  the factor
• 4) Multiply

• 4 x 598
• 598 is close to 600 (by 2 counts)
• 4 x 600
• 4 x (600 2)
• (4 x 600) (4 x 2)
• 2400 8
• 2,392

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Try It!

• 4 x 253
• Use the break apart
• (4 x 250) (4 x 3)
• (1000) 12
• 1012
• 2) 13 x 5
• Use the break apart
• (10 x 5) (3 x 5)
• 50 15
• 65

• Use multiplication properties and mental math to
  simplify each expression.
• 4 x 253
• 13 x 5

9
Try Some More!

• 3) 6 x 393
• Use the compensation
• 6 x (400 7)
• (6 x 400) (6 x 7)
• 2400 42
• 2,358
• 4) 4 x (7 x 25)
• Use the compatible numbers
• (4 x 25) x 7
• 100 x 7
• 700

• 3) 6 x 393
• 4) 4 x (7 x 25)

10

• 5) (5 x 188) x 2

• 5) (5 x 188) x 2
• Use compatible numbers
• (5 x 2) x 188
• 10 x 188
• 1880

11
Objective Review

• To use multiplication properties and mental math
  strategies to compute mentally.

• Why? You can now solve multiplication problems
  faster w/o using a paper and pencil and/or to get
  an estimated answer in your head before you
  actually solve the problem.

12
Independent Practice

• Complete problems 7-17
• Copy original problem first.
• Show all work!

• If time, complete Mixed Review 18-23
• If still more time, work on Accelerated Math.