The goal of this activity is to use the standard algorithm to find the products in which composition of a new unit happens once.  Students first calculate a three-digit-number-by-two-digit-number example, using a strategy of their choice, and then analyze the same example, with the composition recorded above the product. Students may use different strategies when they try on their own including:

• Partial products.
• Mentally accounting for the hundred that is composed when finding the product .

After students discuss how composing new units is recorded in the algorithm, they find the value of two multiplication expressions, using the standard algorithm.

When students interpret a new way of multiplying a three-digit number by a two-digit number, they use their understanding of place value to make sense of the method (MP7).

• Invite students to share how they interpret Lin’s work of finding .
• Display the image of Lin’s calculation.
• Circle the 2 in the number 723 in Lin’s calculation.
• “What does the 2 in the tens place represent?” (It’s 2 of the tens from .)
• “What does Lin do with the other 10 tens?” (She makes 1 hundred out of them and puts them together with the other hundreds when she multiplies 200 by 3.)
• Circle the 1 above 241 in Lin's work.
• "What does this 1 represent?" (It’s the hundred from .)
• Circle the partial product 4,820.
• “What does 4,820 represent in the calculation?” ( . The 2 from the factor 23 is in the tens place and so it represents 20.)
• “Now take a few minutes to solve the last two problems.”
• 4-5 minutes independent work time
• Invite students to share the products, and ask them what questions they have about the standard algorithm with composition.

The goal of this activity is to multiply numbers with no restrictions on the number of new units composed. Students first multiply a three-digit number by a one-digit number and a three-digit number by a two-digit number, with no ones. They then can put these two results together to find the product of a three-digit number and two-digit number ,with many compositions. They then solve another three-digit-number-by-two-digit-number example, with no scaffolding. Because these calculations have new units composed in almost every place value, students will need to locate and use the composed units carefully. It gives students a reason to attend to the features of their calculation and to use language precisely (MP6).

• Display the expression: .
• “How did you use the first two calculations to help with the third problem?” (They gave me the two partial products for the product , so I just had to add them up.)
• Invite students to share their responses for the last product, focusing on the newly composed units.