In this final lesson on multiplication, students consolidate their understanding of the ideas from the previous lessons and generalize toward an algorithm that can be used to find the product of any pair of decimals.

Previously, students saw that we can multiply decimals by:

• Thinking of the decimals as products of whole numbers and fractions and multiplying those numbers.
• Multiplying the decimal factors by powers of 10 to make them whole numbers, finding their product, and dividing it by the same powers of 10.
• Representing decimal factors as side lengths of a rectangle, decomposing them by place value, finding partial products, and adding them.

Here, students make a generalization that we can also: multiply whole numbers with the same digits as the decimal factors, count the total number of decimal places in the factors, and place the decimal point in the product so that it has that number of decimal places. They see that the steps of this algorithm can be explained by prior reasoning about properties of base-ten numbers and the calculation result can be checked using other methods.

The lesson includes an optional activity that allows students to apply the multiplication algorithm both in and out of context.

The optional activity referred to in the Lesson Narrative is at the end of the lesson. In this course, another optional activity is included after the Warm-up. It provides additional practice decomposing decimal factors before students are introduced to a general multiplication algorithm in the following activity. Because both activities use the same numbers, including this optional one can help students make stronger connections between area diagrams, partial products, and the algorithm.