Arrays and factors

Lessons

In this lesson, we will learn:

• Factors, Products, Multiplication Statements
• Writing a product for a given array
• Drawing arrays to find factors
• Using an array to describe the distributive property of multiplication

Notes:

Factors

• Numbers we can multiply to get another number
• Numbers we can multiply to get another number

• two numbers that we multiply together to get a certain product

Ex. 3 x 4 = 12 

3 and 4 are both factors of 12 and 3 and 4 are a factor pair

$\quad$ 2 x 6 = 12 

2 and 6 are also factors of 12, 2 and 6 are a factor pair

BUT be careful! 2 and 4 are not a factor pair of 12 even though they are both factors of 12 because:

2 x 4 DOES NOT EQUAL 12

Tips for finding factors

• Every number has 1 as a factor
• Every number has itself as a factor 

Product

• The term product in this section is used for both an expression involving multiplication and the evaluation of that expression 

$\qquad \qquad$ Ex. The product of 2 and 5 is: 2 x 5 and 10

Arrays

• An array is a diagram which represents a product 
• You can draw an array with dots or with squares 

Writing a product for a given array
The product is created by writing the number of rows times the number of columns
The product for the above array would be 2 x 3 or 6

• 1.
  Products and Arrays
  Write a product for each array
  a)

  
  
  
  
  b)

  
  
  
  
  c)

  
  
  
  
  d)

  
  
  
  

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• 2.
  Find Factors using Arrays
  Draw an array to find the factors of
  a)

  12
  
  
  b)

  6
  
  
  c)

  7
  
  

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• 3.
  Arrays and the Distributive Property
  

  1. Write a product for the entire diagram, the unshaded squares and the shaded squares
  2. Write an equation for the entire diagram (using the distributive property)
  a)

  
  
  
  
  b)

  
  
  
  

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• 4.
  Rewriting products in expanded form
  Rewrite each product in expanded form (rewrite as a sum)
  a)

  6 x 12
  
  
  b)

  3 x 128
  
  
  c)

  7 x 408
  
  

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• 5.
  Distributive Property of Multiplication (multiplying by 1-digit)
  Use the distributive property to find the product:
  a)

  4 x 36
  
  
  b)

  3 x 825
  
  
  c)

  401 x 9
  
  

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• 6.
  Distributive Property of Multiplication (2-digit x 2-digit)
  Use the distributive property to find the product:
  a)

  14 x 12
  
  
  b)

  65 x 34
  
  

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