Mathematicians learned the basic addition and subtraction facts of numbers to 20 through a variety of strategies such as part-part-whole, counting on, related facts, doubles, and properties. They learned about place value of numbers to 40. With this foundation of addition and subtraction and the knowledge of numbers to 40, children progress in this unit to the standard vertical form for addition and subtraction of numbers to 40.
Students are taught vertical form based on place value that can be used to add or subtract numbers without regrouping. The frequent use of place-value charts in this unit leads children away from a dependence on concrete representations. Students are also taught that addition can be used to check subtraction.
Lastly, the learning of addition and subtraction without regrouping is applied to real-world problems. Students may still use manipulatives for assistance, however they should gradually be able to work out the problems without the use of manipulatives.
Students are taught vertical form based on place value that can be used to add or subtract numbers without regrouping. The frequent use of place-value charts in this unit leads children away from a dependence on concrete representations. Students are also taught that addition can be used to check subtraction.
Lastly, the learning of addition and subtraction without regrouping is applied to real-world problems. Students may still use manipulatives for assistance, however they should gradually be able to work out the problems without the use of manipulatives.