Multiplication and Division
Arithmetical Strategies
Conceptual Constructs
Construct 0
Emergent
Construct 1
Initial Grouping
Construct 2
Perceptual Counting
in Multiples
Brief Description
Quantities are treated only in terms of the individual unit items,
no significance is placed on the groups. The student may be
unable to share items into groups of a given size or to share
items into a given number of groups.
The student is able to share items into groups of a given size,
and to share items into a given number of groups. The student
uses perceptual counting, by ones, to establish the numerosity
of a collection of equal groups. The student does not attend to
the structure of the groups when counting.
The student uses multiplicative counting (i.e. stress counting or
skip counting) to count visible items arranged in groups
The student uses multiplicative counting (i.e. stress counting or
skip counting) to count items arranged in groups without
Figurative Composite individual items visible. The student is able to re-present the
items with the groups, but relies on perceptual markers to
Grouping
represent each group.
Construct 3
Construct 4
Repeated Abstract
Composite Grouping
Construct 5
Multiplication and
Division as
Operations
The student uses multiplicative counting (i.e. stress counting or
skip counting) to count composite units in repeated addition
and subtraction. The student is able to use the composite unit a
specified number of times without visible markers for the
groups or the individual items.
The student can coordinate two composite units (i.e. the
number in each group and the number of groups) as an
operation. The student can recall or quickly derive many of
the basic facts for multiplication and division. The student
recognizes and applies the commutativity property of
multiplication and the inverse relationship of multiplication
and division.