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Level 4: Repeated abstract composite units 

The student uses composite units in repeated addition and subtraction. Such a student can use a composite unit a specific number of times as a counting (iterable) unit, unprompted. Using a composite unit repeatedly a specific number of times is the basis of repeated addition and repeated subtraction, 3 + 3 is 6, 6 + 3 is 9, 9 + 3 is 12. 

At this stage the student uses abstract composite units to find out how many elements are in a number of composite units without items visible, e.g. a double count is used when finding out how many threes are in eighteen, “3 is 1; 6 is 2; 9 is 3...18 is 6”. The student sees the overall pattern of composites. The student needs to use (enact) the counting unit repeatedly because he or she does not fully coordinate two composite units. 

Double counting is a common strategy at this stage. Fingers or markers may be used to assist in tracking the groups, but these are used as the counting occurs.

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Repeated composites