Lesson objective: Understand the role of place value in the standard algorithm for addition.

Students bring prior knowledge of addition strategies from 3.NBT.A.2. This prior knowledge is extended to addition of whole numbers within 1,000,000 as students apply the standard algorithm for addition. A conceptual challenge students may encounter is that regrouping is required when the sum of a place value column of digits exceeds 9.

The concept is developed through work with a parallel example of addition using the partial sums method, which clarifies the role of place value in the standard algorithm for addition.

This work helps students deepen their understanding of number because it illustrates how all methods of addition require composing and decomposing numbers by place value, regardless of how the steps are recorded.

Students engage in Mathematical Practice 8 (Look for and express regularities in repeated reasoning) as they compare the partial sums method and the standard algorithm for addition, understanding that base-ten operations require composition and decomposition into base-ten units.

**Key vocabulary:**

- algorithm
- compose
- decompose
- expression
- regroup
- vertical