Lesson objective: Fluently add and subtract multi-digit numbers while choosing the most efficient solution strategy and justifying the choice.

This lesson helps to build fluency with the standard algorithms for addition and subtraction and mental math.** **The standard algorithm is used here because it is frequently the most efficient strategy for solving addition and subtraction problems. Mental math is also used here because sometimes it is a more efficient strategy for solving addition and subtraction problems than the standard algorithm. This work develops students' understanding that the standard algorithms for addition and subtraction are efficient ways to add and subtract that use place value concepts.

Students engage in Mathematical Practice #2, reason abstractly and quantitatively as they make choices about strategies for solving various addition and subtraction problems based on the numbers within the problem. Students should examine the numbers and operations within a problem and determine if the standard algorithm is the most efficient strategy to use or if another strategy (mental math) would be more effiecient. Students engage in Mathematical Practice #3, construct viable arguments and critique the reasoning of others as they give reasoning for their choice of solution strategy based on the numbers in the problem. This takes place as students discuss with one another their strategy choice and reasoning and also by participating in teacher-guided whole class discussions.

**Key vocabulary:**

- decompose
- justify
- standard algorithm
- strategy