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