Lesson objective: Understand that a group of addends always has the same sum regardless of what strategy is used to add them.

Students bring prior knowledge that when adding two-digit numbers, we add tens with tens and ones with ones from 1.NBT.C.4. This prior knowledge is extended to adding up to four two-digit numbers as students discover that the sum is always the same no matter what addition strategy is applied when solving the problem. A conceptual challenge students may encounter is understanding that addends can be decomposed and recombined in many different ways.

The concept is developed through work with previously learned addition strategies, which are applied in various ways to addition problems with up to four two-digit numbers.

This work helps students deepen their understanding of equivalence because numbers can be decomposed in different ways and still have the same value; addends can be added in different ways and always get the same sum.

Students engage in Mathematical Practice 1 (Make sense of problems and persevere in solving them) as they solve problems using a variety of strategies, sometimes finding many ways to solve the same problem. Mathematical Practice 8 (Look for and express regularity in repeated reasoning) is also featured in this lesson as students use strategies they have practiced in addition problems with two addends and apply them to situations that involve three and four addends.

**Key vocabulary:**

- addend
- compose
- decompose
- strategy