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Thinking With
Numbers
Goals and Teaching Strategies
Edward C. Rathmell
Larry P. Leutzinger

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Grade K Focus

Help students

  • learn to count up and back fluently
  • learn to partition numbers up to ten
  • learn to count on to add and to count back to subtract
  • learn to solve word problems concretely

Teaching strategies/models include

  • pose word problems about numbers each day (use a variety of problem structures)
  • use ten frame to represent numbers
  • use part-part-whole language
  • hide part of the counters so students cannot count


Grade One Focus

Help students

  • learn partitions of numbers to ten
  • learn to efficiently count on to add
  • learn to efficiently count back and count up to subtract
  • extend these strategies/partitions to use with larger numbers
  • explore the use of derived fact strategies

Teaching strategies/models include

  • pose word problems to solve each day (use a variety of problem structures)
  • use a ten frame to represent numbers
  • use part-part-whole language
  • hide part of the counters so students cannot count
  • roll number cubes and add the numbers
  • use the empty number line


Grade Two Focus

Help students

  • learn to partition numbers to twenty
  • learn to efficiently count up to subtract
  • learn to efficiently use doubles/near doubles to add
  • learn to efficiently use make ten to add
  • learn to efficiently use ten to subtract
  • learn to efficiently think addition to subtract
  • extend these strategies/partitions to use with larger numbers

Teaching strategies/models include

  • pose word problems to solve each day (use a variety of problem structures)
  • use ten a frame to encourage derived fact strategies
  • use part-part-whole language
  • hide part of the counters so students cannot count
  • roll number cubes and add the numbers
  • use the empty number line
  • use incredible equations/number of the day


Grade Three Focus

Help students

  • learn to partition numbers to one hundred
  • learn to efficiently use make ten to add
  • learn to efficiently use ten to subtract
  • learn to efficiently think addition to subtract
  • learn to count up to subtract with larger numbers  (and make change)
  • learn to efficiently use tens to add and subtract with larger numbers
  • extend these strategies/partitions to use with larger numbers
  • learn to skip count
  • learn to use repeated addition for easy multiplication facts
  • learn to split a problem into parts for harder multiplication facts
  • learn to think multiplication to divide
  • learn to multiply by tens

Teaching strategies/models include

  • pose word problems to solve each day (use a variety of problem structures)
  • use a ten frame to encourage derived fact strategies
  • use part-part-whole language
  • hide part of the counters so students cannot count
  • roll numbers cubes and add the numbers
  • use the empty number line
  • use incredible equations/number of the day
  • use graph paper to split problems into parts
  • pose lots of problems involving thinking multiplication to divide
  • pose lots of problems involving multiplication/division by tens


Grade Four/Five Focus

Help students

  • learn to efficiently use addition to subtract
  • learn to efficiently use tens to add and subtract with larger numbers
  • extend these strategies/partitions to use with larger numbers
  • learn to split a problem into parts for harder multiplication facts
  • learn to think multiplication to divide
  • learn to multiply/divide by tens

Teaching strategies/models include

  • pose word problems to solve each day (use a variety of problem structures)
  • use a ten frame to encourage derived fact strategies
  • use part-part-whole language
  • use the empty number line
  • use incredible equations/number of the day
  • use graph paper to split problems into parts
  • pose lots of problems involving thinking multiplication to divide
  • pose lots of problems involving multiplication/division by tens

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