Lesson objective: Fluently multiply and divide decimals using the standard algorithm.

This lesson helps to build fluency with multiplying and dividing decimals. The standard algorithm is used here because it is the most efficient method for operations. This work develops students' understanding that rules for all operations with whole numbers and decimals are based on the place value system.

Students engage in Mathematical Practice 2 (Reason abstractly and quantitatively) as they notice how the placement of a digit in the algorithm, and in relation to the other numbers within the algorithm, gives it its place value - that the “place” it is in determines its “value”. Students engage in Mathematical Practice 7 (Look for and make use of structure) as they understand how the structure of the standard algorithm shows place value of each of the digits within the algorithm.

Teachers should frequently question student work so they can articulate understanding of the algorithm. Questions can be:

- "Why did you record your partial product here?" (
*Because it allows me to line up the place values that are the same.) *
- "What does this digit in your quotient mean?" (
*The 7 means 70 because it is in the tens place.) *
- "How do you know where to place your decimal in your product?" (
*I look at how many place value digits I have to the right of the decimals in my factors.)*

**Key vocabulary:**

- dividend
- divisor
- place value
- product
- quotient
- standard algorithm