The Learning Framework In Number: Multiplication

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The Learning Framework In Number Multiplication
Division

• Chris Francis

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The Multiplication and division aspect of the
learning framework underpins

• Count Me In Too
• Counting On
• Taking Off With Numeracy

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Structure

• Early multiplication and division strategies
  focus on the structure and use of groups of
  things.
• A composite unit is formed when a student takes a
  group of items and treats it as a unit.
• Recognising units is not sufficient. It is
  necessary to develop ways of coordinating the
  groups that are formed.

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Typical progression
Not intended to be aligned
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Level 1 Forming equal groups

• The student
• uses perceptual counting and sharing to form
  equal groups
• finds the total of the groups, counting by ones
• does not take notice of the structure of the
  groups when finding the total.
• NES1.3
• PAES1.1

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Level 2 Perceptual multiples

• The student
• uses items to form equal groups
• finds the total of the groups through rhythmic,
  skip or double counting, only when the items are
  visible
• cannot deal with concealed items.
• NS1.3
• PAS1.1

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Level 3 Figurative units

• The student
• does not rely on items being visible
• counts forwards or backwards using multiples (or
  a combination of multiples and rhythmic counting
  )
• uses perceptual markers (e.g. fingers) to keep
  track of the groups
• reconstructs the groups before counting.
• NS1.3
• PAS1.1

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Level 4 Repeated abstract composite unit

• The student
• uses repeated addition or subtraction to find the
  total
• does not need perceptual markers to represent the
  groups
• might use fingers to keep track as they count
• might use skip counting or a double count.
• NS1.3, NS2.3
• PAS1.1, PAS2.1

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Level 5 Multiplication division as operations

• The student
• recalls a wide range of multiplication and
  division facts
• uses multiplication and division as inverse
  operations to solve problems
• explains the composite structure in a range of
  contexts not simply recalling facts.
• PAS2.1
• NS2.3

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Observations

• Students are usually confident with some
  multiples over others.
• Strategy use is strongly dependent on knowledge
  of multiples.
• Students may use a combination of strategies.
• Students typically appear more confident with
  multiplication than division.
• Modeling of strategies is needed.
• The use of arrays is useful in developing
  visualisation.