Guided Lessons
Explore

# The Partial Products Strategy for Multiplication

The partial products strategy is essential for students to build a foundational understanding of place value as it relates to multiplication. This lesson may be taught on its own or used as a pre-lesson to Multiplying Multiples.
This lesson can be used as a pre-lesson for the Multiplying Multiples lesson plan.

No standards associated with this content.

Which set of standards are you looking for?

This lesson can be used as a pre-lesson for the Multiplying Multiples lesson plan.

Students will be able to solve multi-digit multiplication with the partial products strategy.

##### Language

Students will be able to discuss the meaning and process of the partial products strategy to multiply, using partner work and sentence starters.

(3 minutes)
• Ask students to consider the multiplication problem: "There are 52 rows with 25 seats in each row in the school's auditorium. How many people can the auditorium seat?"
• Give students time to discuss the problem with a partner. Have them explore how they might approach solving it.
• Gather students' responses and acknowledge their background knowledge on multiplication. Students may mention the standard algorithm, area models, repeated addition, or other strategies they know. Jot down their ideas and allow for student exploration and interaction with the various strategies to solve the problem and reach the conclusion that the auditorium can fit 1,300 people.
• Tell students that today they will learn how to multiply multi-digit numbers with a useful strategy called partial products.
(10 minutes)
• Show students each vocabulary card on the document camera. Read the word, its definition, and describe the image if available. Leave the vocabulary cards on display for students to use as a reference during their work time.
• Have students stand in two lines, facing each other. Call out one of the vocabulary terms and have them verbally restate the meaning or give an example of the word to the classmate standing in front of them. Tell students that both partners should share information about the word to each other. Have the students in one line move to the right so that they are facing a new partner, and repeat the process with another vocabulary term until you have gone through all of the words. Have students return to their seats.
• Distribute the An Introduction to Partial Products worksheet to each student. Display a teacher copy on the document camera.
• Direct students' attention to the first explanatory page.
• Read aloud the definition and explanation of partial products on this page. Emphasize the importance of place value in the partial products strategy. Explain that we are basically breaking apart each factor into its pieces, based on place value, and then multiplying each piece of the numbers to get partial products which we then add to get the total product.
• Highlight keywords such as "multiply," "full value," "tens place," "ones place," "parts," and "add," and tell students to underline or circle these words also.
• Review the steps of the strategy, and have students rephrase the steps to a table partner.
• Read aloud the "Why do we use this strategy?" teaching box and restate the sentence in more manageable, student-friendly terms. For example, say, "We use this strategy because it helps us understand the value or amount of each digit when we multiply multi-digit numbers. This strategy makes us stronger and more flexible math thinkers. It also helps us understand the steps in the standard algorithm on a deeper level."
• Ask students if they have any questions or concerns regarding the first page. Address any issues that arise.
(10 minutes)
• Have students turn their attention to the second page of the worksheet. Go over the sample multiplication problem and point out how the numbers were color coded to help them understand the components or pieces of the factor they are multiplying in each step.
• Distribute colored pencils to each student and tell them to underline the numbers in the parentheses on the second sample problem so that they match the color of the factor they represent.
• Place students into groups of four, assign each student a number from 1–4, and tell them to solve the rest of the multiplication problems on their worksheet.
• Call on a number from 1–4 for the student with that assigned number to demonstrate and explain the problem. Have them share the process with the other members in their group. Review and display these sentence starters that students will use as they present and discuss their answers:
• "First, I multiplied..."
• "Then, I found the product of ____ and ____ to get ____."
• "After that, I..."
• "Finally, I added the partial products to get a total product of ____."
• Circulate to assist students who need further guidance.
• Tell the students in the audience of each group to use the following sentence stems/frames to provide feedback to their classmate's work:
• "I like how you ____ when you solved the problem using the partial products strategy."
• "I think you made a mistake when you ____. You can fix it by ____."
• Give a chance for students to modify their solutions based on peer feedback.
• Listen in on students' conversations and compliment them for their academic math language.
(10 minutes)
• Have students continue working in their group of 4. Remind them of the vocabulary cards displayed from earlier in the lesson. Instruct students to use the cards and the resources from the first two pages of the worksheet to help them fill in the blanks in the sentences on page 3.
• Read aloud sentences 1–4 on this page and clarify the definition of any unfamiliar terms in the sentences.
• Tell students to complete or answer these first four questions/sentences.
• Give students sentence stems to help them answer the fifth and sixth question:
• "One reason to use this strategy is..."
• "I would tell Peter to..."
• Review students' responses as a whole group and correct any misconceptions.

Beginning

• Have students repeat the directions in their home language (L1) or in English (L2) before beginning the work.
• Give students access to bilingual glossaries and online dictionaries for them to look up unfamiliar words throughout the lesson.
• Place students with more advanced ELs for group or partner work.
• Pull aside a small group of students as they work on the group work and guide them through the process.
• Allow students to work on the formative assessment with a helpful partner.

• Encourage students to speak and write their answers without using the sentence frames/stems.
• Allow students to be the first to share their ideas or rephrase their classmates' contributions to class discussions.
• Have students create and display a word/phrase bank with helpful terms from the lesson for reference purposes (with images if applicable).
(5 minutes)
• Hand out an index card to each student. Write the following problem on the board and read it aloud: "The school ordered new individual whiteboards for students. They ordered 35 boxes and each box has 14 whiteboards. How many whiteboards are there in all?"
• Make sure students understand the word problem, and have them solve it on their index card using the partial products strategy.
• Collect the index cards to check for understanding.
(2 minutes)
• Have students discuss the following prompts with a partner first before facilitating a whole group conversation:
• What do you think of the partial products strategy? ("I like/dislike the partial products strategy because...")
• How does the partial products strategy help you understand multiplication? ("The partial products strategy helps/does not help me understand multiplication because it...")