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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  K-2 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. Next Steps: Successfully put two small collections together and find the sum Find the difference after taking a small amount from a collection POSSIBLE ACTIVITIES

 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. Next Steps: Begin to use ‘short-cuts’ to add two small collections, or to take a small amount from a collection (e.g.count on to find a sum, or count back, count down to, or count up from’ to find a difference) POSSIBLE ACTIVITIES

 Stage C: These children are beginning to use short-cuts to add two small collections, or to take a small amount from a collection. They only need part of a model, and either count on to find a sum, or count back, count down to, or count up from to find a difference.Next Steps: Begin to use 'simpler' thinking strategies to add and subtract (adding one or zero, using doubles, turning around the addends, sums to ten, or adding ten) Make Ten Towers of Ten Worksamples

 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. Next Steps: Use later thinking strategies (fact families, extending to larger numbers, near doubles, make to ten, adding nine). POSSIBLE ACTIVITIES

 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.