Structures of Multiplication and Division

1
Structures of Multiplication and Division

• Equal Groups Whole Unknown (Multiplication)
• Equal Groups Size of Groups Unknown (Partition
  Division)
• Equal Groups Number of Groups Unknown
  (Measurement Division)
• Comparison Product Unknown (Multiplication)

• Comparison Set Size Unknown (Partition Division)
• Comparison Multiplier Unknown (Measurement
  Division)
• Combinations Product Unknown
• Combinations Size of a Set Unknown

2
Multiplication can be

• Repeated Addition
• (sets of equal amounts)
• Rate (jumps on a number line, speed,)
• Arrays (area models)

3
Division can be

• Repeated Subtraction (sets)
• The Number of Sets
• Fair-Sharing
• The Number in Each Set
• Rate
• Arrays ( the missing dimension)

4
Grade 5 Outcomes

• B2 multiply 2-, 3-, and 4-digit numbers by
  1-digit numbers
• B3 find the product of two 2-digit numbers
• B4 divide 2-, 3-, and 4-digit numbers by single
  digit divisors and investigate division by
  2-digit divisors
• B5 find simple products of whole numbers and
  decimals
• B6 divide decimal numbers by single digit whole
  numbers
• B9 solve and create multiplication and division
  problems involving whole numbers and/or decimals

5
Grade 6 Outcomes

• B1 compute products of whole numbers and decimals
• B2 model and calculate the product of two
  decimals
• B3 compute quotients of whole numbers and
  decimals
• B4 model and calculate the quotient of two
  decimals
• B7 Solve and create relevant addition,
  subtraction, multiplication, and division
  problems involving whole numbers
• B8 Solve and create relevant addition,
  subtraction, multiplication, and division
  problems involving decimals
• B12 calculate products and quotients in relevant
  contexts using the most appropriate method

6
Modeling ideas

• Base ten materials
• Grids
• Area models
• Number lines
• Ten frames