Add/subtract that build on composing and composing numbers contributes to children's overall number sense

Easier and faster than standard algorithms and often done mentally

"Number talks" let children have opportunities to engage in solving and discussing alternative strategies to solve computation problems

Addition and subtraction are good context for learning place-value concepts

If children only understand computation as digit-by-digit, they make many more errors and are often unable to make reason of answer

Children develop place-value understanding as a result of their own methods of add and subtract multidigit numbers

Use of manipulatives, drawings,or fingers along with counting to directly represent numbers involved and meaning of operation

Children who consistently count by ones in addition most likely have not developed base-ten grouping concepts

When children have constructed of ten as a unit, they begin to use this idea to move from \direct modeling to invented

Any strategy other than standard algorithm, that doesn’t involve the use of physical materials or counting by ones

At times, invented become mental methods after ideas have been explored, used, discussed and understood

Studies show children in and out of school can construct methods of add and subtract multi-digit numbers without explicit instruction

Standard should be making sense of the prodcedure as a process and not learning a memorized series of steps

Standard may result in thinking there is only one best approach and one “right” algorithm but that is not true

Standard algorithms must be understood, delaying standard can help learn other algorithms, and cultural differences can influence on what algorithms work best