# Lesson 17

Calculating Products of Decimals

### Lesson Narrative

In this culminating lesson on multiplication, students continue to use the structure of base-ten numbers to make sense of calculations (MP7) and consolidate their understanding of the themes from the previous lesson. They see that multiplication of decimals can be accomplished by:

• thinking of the decimals as products of whole numbers and fractions;
• writing the non-zero digits of the factors as whole numbers, multiplying them, and moving the decimal point in the product;
• representing the multiplication with an area diagram and finding partial products; and
• using a multiplication algorithm, the steps of which can be explained with the reasonings above.

### Learning Goals

Teacher Facing

• Interpret a description (in written language) of a real-world situation involving multiplication of decimals, and write a multiplication problem to represent it.
• Use an algorithm to calculate the product of two decimals, and explain (orally) the solution method.
• Use an area diagram to represent and justify (orally and in writing) how to find the product of two decimals.

### Student Facing

Let’s multiply decimals.

### Required Preparation

Some students might find it helpful to use graph paper to help them align the digits for vertical calculations. Consider having graph paper accessible for the activity: Calculating Products of Decimals.

### Student Facing

• I can use area diagrams and partial products to represent and find products of decimals.
• I know how to use a product of whole numbers to find a product of decimals.

Building On