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Level 3: Figurative units 

At this stage the student counts forwards or backwards following a pattern of multiplese.g. “3, 6, 9, 12” or “12, 9, 6, 3” without reference to the individual items. The student uses composites figuratively, without visible individual items. That is, the student can calculate using composites when the individual items are screened. The student is removed one step from direct sensory experience where he or she no longer relies on counting by ones. 

Each group is represented by a single marker and needs to be formed prior to counting the total collection. 

For example, when presented with four sealed opaque containers with three counters in each, the student can determine the total number of counters. The containers act as perceptual markers for the composite units. The student can see the number of groups but cannot see the individual items in each group. Consequently, the student is forced to treat the individual items in each group figuratively. 

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Figurative units