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# Describe the Partial Products Method

Have students describe the process for solving multiplication problems and ask clarifying questions while in partnerships. Use this lesson as a standalone lesson or as support to the lesson Eye See... Multiplicity.
This lesson can be used as a pre-lesson for the Eye See... Multiplicity lesson plan.

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This lesson can be used as a pre-lesson for the Eye See... Multiplicity lesson plan.

Students will be able to multiply whole numbers using the partial product method.

##### Language

Students will be able to describe how to use the partial products method using graphic organizers and peer discussions.

(3 minutes)
• Write and circle "multi-digit multiplication" on the board. Have students talk about the ideas related to those words. Write their ideas on the board and create a word web where all the ideas about the words stem from the middle circled words.
• Add an example or visual next to every detail students say (e.g., draw an area model or array for multiplication expressions).
• Tell students today they will review the partial products method for multiplying numbers and then describe the steps needed to complete the process.
(10 minutes)
• Review the vocabulary terms as necessary based on their usage in the Introduction section. Allow students to provide examples and nonexamples of each of the new terms they explore.
• Explain to students that the partial products method for multiplying larger numbers is another strategy for successfully multiplying numbers that relies on the place value of each number. For example, when multiplying 224 x 3, you multiply 3 x 4, 20 x 3, and 200 x 3. Next you list all their products under the line, one on top of the other. Then, you add up the partial products to get the total product or answer.
• Model how to solve 224 x 3 on chart paper using the partial products method. Write the numbers on a place value chart to review the values of the digits and write the multiplication problems from the chart. (Tip: as you solve the multiplication problem, continue to refer to the correct value you are multiplying.)
• Write down some of the phrases you used while modeling the problem for student reference. For example:
• "First, I ____,"
• "After I ____, I ____."
• "Then, I ____."
• "My next step was ____."
• Ask students to use your example to describe in pairs the process you used to solve the problem. Choose a student to share the description with the whole class and write some key phrases the student uses on the board.
• List the steps needed to solve the partial products multiplication problems on the chart paper. Ask students to help complete the list.
(8 minutes)
• Write a new multiplication story problem on the board, first with the written context, and then explain how to write the expression. For example, "The marathon has six heats with 189 people in each heat. How many people participated in the marathon?"
• Ask students to solve the problem on scrap or graph paper with their partner, making sure to use the chart paper outline of partial products method. Encourage them to use a place value chart to to verify the values of the digits if necessary.
• Choose a student who has a firm grasp on multiplying with partial products to model solving the problem for the class and explain the process throughout. Reinforce that student's presentation by rephrasing the explanation to include sequencing words and key vocabulary listed in the Explicit section.
• Have students separate back into partnerships and reconsider their solutions. Then have partners take turns describing the process they used to solve their partial products method in partners.
• Restate a potential student explanation:
• "First, I wrote the number on the place value chart. Then, I multiplied the bottom digit in the ones place (6) by the top digit in the ones place (9) and wrote the product under the line (54). Then, I used that same digit in the ones place (6) to multiply by the digit in the tens place (80) and wrote the product under the 54 (e.g., 80 x 6 = 480). Next, I multiplied the bottom digit in the ones place (6) by the top digit in the hundreds place (100) and wrote the product under the number 480 (e.g., 100 x 6 = 600). Then, I added up all the products (54 + 480 + 600 = 1,134) to get the final answer of one thousand one hundred thirty-four."
(7 minutes)
• Present a new multiplication problem and ask students to stop and think about how they will solve the problem. For example, "Each class raised at least \$240 for hurricane relief efforts. There are 8 classes in all of the school. What is the minimum amount they raised?"
• Distribute the worksheet Describe in Pairs and ask them to write ideas in the Pre-Write section about how they will solve the problem (i.e., \$240 x 8). After they've represented the numbers and written down ideas for solving the problem, tell them to solve the problem.
• Give students a minute to practice aloud to themselves how they will share the information with their partners (e.g., I think the expression is \$240 x 8. Each class raised at least \$240 and there are 8 classes total. I drew a part-whole model to show \$240 eight times.) Then, allow them to share their Pre-Write section with a partner without looking at their notes.
• Provide sentence frames as necessary and listen to student discussions to add more language frames to the board based on their discussions (e.g. "I think I should ____ first, and then ____.").
• Have a student share an explanation of how to solve the problem. Afterward, model asking clarifying questions to help pull more language from the presenter (e.g. "Why would you do ____?" or "How come ____?").
• Ask students to return to their same partners, but this time have the speaker present the information and then the listener asks a clarifying question afterwards. Finally, have them switch roles in the same partnership.
• Give students one minute to write notes or ideas their partners gave them in the Notes After Sharing with Partners section.

Beginning

• Allow students to use their home language (L1) or their new language (L2) in all discussions. Provide bilingual reference materials to assist in their vocabulary word acquisition.
• Encourage them to use the vocabulary cards and terms in their conversations and writing. Allow them to draw pictures to support their understanding of the terms.
• Scaffold their multiplication problem-solving by drawing lines and numbering each step needed in the standard algorithm for partial products. Make sure the numbers on the chart paper of the model correspond with the numbers you list on their partial products work. See the worksheet Partial Products Method Part 1 for an example of how to draw grid lines to accommodate each step.

• Pair students with mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Challenge advanced ELs who have a firm grasp of the partial products method to describe the steps for three-digit-by-two-digit multiplication and draw a chart paper model similar to the one in the Explicit Instruction section to show students in the Review and Closing section.
(7 minutes)
• Ask students to separate into a new partnership as they explain again how they solved their problem. Then, have them write their explanations in the Post-Write section of the Describe in Pairs worksheet.
• Monitor students' explanations as well as the listener's ability to ask questions that will solicit more language from the speaker (e.g., "What do you mean by ____," "What do you think about taking away/adding____," "Why did you____?") .
• Take notes about students' conversations and questions on the board.
• Assess students' ability to refine their explanations and visual representations of the math problem from their Pre-Write to their Post-Write sections.
(5 minutes)
• Conduct a "Connect, Extend, and Challenge" exercise in pairs where students answer the following three questions:
• How do the new ideas about the partial products method connect to what you already knew? ("The partial products method is similar to the way I think about place value and expanded form.")
• What new ideas did you get that extend or push your thinking in new ideas? ("I wonder if I can use the same strategy for larger numbers or multiplication with fractions.")
• What is still challenging for you to understand? ("I still don't understand...")
• Have students share their answers with their partners, taking turns to share one answer at a time. Choose advanced students to share one answer to the questions.