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

Students bring prior knowledge of subtraction strategies from 3.NBT.A.2. This prior knowledge is extended to subtraction of whole numbers within 1,000,000 as students apply the standard algorithm for subtraction. A conceptual challenge students may encounter is understanding why the standard algorithm for subtraction sometimes requires composition of a new base-ten unit from ten smaller units, and the decomposition of a larger base-ten unit into ten smaller units.

The concept is developed through work with base-ten blocks which provide a visual model of why and how base-ten units are composed and decomposed when applying the standard algorithm for subtraction.

This work helps students deepen their understanding of number because it illustrates the fluidity of the base-ten system which allows numbers to be decomposed in multiple ways.

Students engage in Mathematical Practice 8 (Look for and express regularities in repeated reasoning) as they compose and decompose place values when the digit in the subtrahend is greater than the digit in the corresponding place value in the minuend.

**Key vocabulary:**

When modeling the standard algorithms for addition and subtraction avoid using language that is conceptually misleading such as “borrowing” and “carrying.” Replace such language with more mathematically appropriate language, such as trading, bundling/unbundling, composing/decomposing, or regrouping to describe the process of exchanging equivalent base ten units.

- algorithm
- compose
- decompose
- expression