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State Numeracy Programs Conference 20102
The Multiplication and division aspect of the learning framework underpins:
Count Me In TooCounting OnTaking Off With Numeracy
State Numeracy Programs Conference 20103
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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State Numeracy Programs Conference 20105
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.NES1.3PAES1.1
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State Numeracy Programs Conference 20106
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.NS1.3PAS1.1
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State Numeracy Programs Conference 20107
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.NS1.3PAS1.1
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State Numeracy Programs Conference 20108
Level 4: Repeated abstract composite unitThe 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, NS2.3PAS1.1, PAS2.1
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State Numeracy Programs Conference 20109
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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State Numeracy Programs Conference 201011
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.
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