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This page provides examples of math center activities aligned with the Early Childhood Assessment in Mathematics (Board of Education of the City of New York, 2001; State Education Department) continuum for addition and subtraction. These activities can be used by teachers or parents to support students' progress within a stage or to promote movement to the next stage on the continuum. For paper and pencil practice to further develop a framework of mental strategies on which more advanced thinking techniques can be built see K2 Addition and Subtraction Strategies.
Stage A: These children are just
beginning to understand the concepts of putting small collections
together, or taking a small amount from a collection. They are not yet
successful in finding sums or differences.

POSSIBLE ACTIVITIES Build Five Towers 
Stage B: These children can
successfully put two small collections together and find the sum. They
can also find the difference after taking a small amount from a
collection. They need to fully model, and count from one by ones to find
their answers.

POSSIBLE ACTIVITIES Plus One Game 
Stage D: These children are able to
add and subtract small amounts using 'simpler' thinking strategies
(adding one or zero, using doubles, ‘turning around’ the addends, sums
to ten, adding ten). They are able to mentally add and subtract small
numbers without making a model.

POSSIBLE ACTIVITIES
Four in a Row with Near Doubles (Ver. 1) 
Stage E: These children are able to extend their thinking strategies to include larger numbers, and more difficult calculations with small numbers. They add and subtract mentally, using thinking strategies such as fact families, ‘near doubles’, build to ten, and adding nine. 
POSSIBLE ACTIVITIES 
More Addition and Subtraction Resources