Across grades 2 and 3 students move from concrete modelling of addition, to flexible strategies, to the standard algorithm and mental proficiency.

 Grade 2 Grade 3 Two Digit Add and subtract two digit numbers using concrete materials, student generated algorithms, and the standard algorithm. Add and subtract two digit numbers using mental strategies. Three Digit Add and subtract three digit numbers using concrete materials, student generated algorithms, and standard algorithm.

Most of the methods included here develop student’s understanding before the standard algorithm in grade 2. In grade 3, they provide the background to develop mental proficiency.

The methods used before the standard algorithm should enhance the students understanding of place value. That is, they require the student to decompose one or both of the numbers in order to add the hundreds, tens, and ones.

Methods that require both numbers to be decomposed can be called Number Splitting. When just one number is decomposed, for example to add on tens and then ones, these are called jump strategies.

 Addition Progression This is an excerpt from a Calculation Progesssion package from Cuddington Community Primary School (UK). They’ve done a fantastic job of laying out a linear progression of addition skills K-3 with ties to various models and methods.