The purpose of this activity is for students to connect an algorithm that uses partial products to the standard algorithm when multiplying a three-digit number by a two-digit number. The standard algorithm shows two partial products while the other algorithm shows six partial products. While the products are recorded differently, the same six partial products are still part of both calculations, and this activity gives students a chance to see this common structure while also appreciating the different way the standard algorithm records the calculations.

Students use the common structure in the two algorithms (MP7) to make sense of the standard algorithm before they use it themselves in the next activity.

• Invite students to share what was alike in the two algorithms, highlighting:
  • All six partial products are calculated in both.
  • They are calculated in the same order.
  • Both need to add up their partial products at the end.
• Invite students to share what was different in the two algorithms highlighting:
  • One algorithm lists each partial product on a separate line while the standard algorithm lists some of them on the same line.
• Circle the first partial product (413) in the standard algorithm.
• “What does the first partial product 413 represent?” (It's .)
• Circle the second partial product (8,260) in the standard algorithm.
• “What does the second partial product 8,260 represent?” (It's .)

The purpose of this activity is for students to practice multiplying a three-digit number by a two-digit number, using the standard algorithm. The problems do not involve composing new units so that students can practice the procedure of multiplying each place in one factor by each place in the other factor. In the last problem, students look at incorrect work for which the value of the digit in the tens place has not been accounted. This problem encourages students to use estimation to assess the reasonableness of their answers and is the focus of the Lesson Synthesis.

• “How did you decide that Diego's answer makes sense?”
• “Which equation would represent each partial product in Diego's work?”

• Invite students to share their solution for .
• “How is multiplying 122 by the 3 in the ones place of 33 the same as multiplying 122 by the 3 in the tens place?” (In both cases I get 366.)
• “How is it different?” (The 3 in the tens place represents 30 and so the 366 needs to shift one place to the left because it is really 366 tens or 3,660.)