Sunday, March 31, 2013

Mastering Basic Facts

Addition and Subtraction
Counting
  • Addition
    • Direct modeling
      • counting all
      • counting on from first
      • counting on from larger
    • Counting abstractly
      • counting all 
      • counting on from first 
      • counting on from larger
  • Subtraction
    • Counting objects
      • separating from
      • separating to 
      • adding on
    • Counting fingers
      • counting down
      • counting up
    • Counting abstractly
      • counting down
      • counting up
Reasoning 
  • Addition
    • Properties
      • a+0=a
      • a+1=next whole number
      • commutative property
    • Known-fact derivations
      • 5+6=5+5+1
      • 7+6=7+7-1
    • Redistributed derived facts
      • 7+5=7+(2+3)=(7+3)+2=10+2=12
  • Subtraction
    • Properties
      • a-0=a
      • a-1=previous whole number
    • Inverses.complement of know addition facts
      • 12-5 is known because 5+7=12
    • Redistributed derived facts
      • 12-5=(7+5)-5=7+(5-5)=7

Retrieval
  • Addition and Subtraction
    • Retrieval from long-term memory
Multiplication and Division
Multiplication
  • Facts can be mastered by relating to existing knowledge
    • Repeated addition
  • Doubles
    • 2 means double
  • Zeros and Ones
    • Any number multiplied by zero is zero
    • Any number multiplied by one is itself
  • Nifty Nines
    • Look for patterns
      • sum of digits is always 9
      • tens digit of product is one less the then other factor
  • Using Known Facts to Derive Other Facts
Division

  • Repeated Subtraction
  • How can we use multiplication to help with division?
Additional Resources
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