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 more information on using these centers in your classroom see the ECAM Centers page.
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.
- Successfully put two small collections together and find the sum.
- Find the difference after taking a small amount from a collection.
Bears in the Cave
Show One Less
Make 5 on the Five Frame
Shake 5 and Spill
Towers of Five
Hide the Cubes
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.
- 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).
Count On One (ver. 1)
Count On One (ver. 2)
Count On Two (ver. 1)
Count On Three (ver. 1)
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.
- 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).
Doubles Cover Up (ver. 2)
Towers of Ten
Make 10 on the Ten Frame (ver. 1)
Four in a Row Subtraction
Part Part Whole Cards
Turn Around Dominoes
Turn Around Trains
Add To: Result Unknown Problems (within 10)
Both Addends Unknown Problems (within 10)
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.
- Use later thinking strategies (fact families, extending to larger numbers, near doubles, make to ten, adding nine).
Making Ten (ver. 1)
Four in a Row with Near Doubles (ver. 1)
Race Around -10 (ver. 1)
Add to: Change Unknown Word Problems (within 20)
Take From: Change Unknown Word Problems (within 20)
Bunk Bed Problem
Double Decker Bus Problem
3x3 Magic Square
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.
Subtract Multiples of Ten
2-Digit Addition Trains (ver. 1)
Base Ten Bag: Addition
Base Ten Pictures
2-Digit Addition Split
3-Digit Addition Split
Add To: Result Unknown (within 100)
Take From: Result Unknown (within 100)
4x4 Magic Square
5x5 Magic Square
Magic Star Puzzle