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# Doubling Multiples for Division

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This lesson can be used as a pre-lesson for the Partial Quotients MethodLesson plan.

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This lesson can be used as a pre-lesson for the Partial Quotients MethodLesson plan.

Students will be able to divide two-digit divisors by listing doubled multiples.

##### Language

Students will be able to present an opinion about multiples involving divisors using sentence stems and peer conversations.

(5 minutes)
• Present a thought-provoking generalization about division on chart paper, such as, "It's better to guess the smallest multiples for the divisor to answer a division problem quickly."
• Read the generalization aloud and ask students to consider if they agree or disagree with the statement. Have them think on their own for 30 seconds before turning to their partners to discuss it. (I think the statement is correct because...)
• Choose partnerships to share their ideas aloud and take notes on the the chart paper. (Note: it is typically faster to guess the largest number you can share into the different groups or sets in the beginning to minimize the number of steps to solve a division problem.)
• Gather information about their language use and their understanding of the vocabulary terms to guide how much intervention and review you should do throughout the lesson. (Tip: provide the meaning of "multiples" and "divisor" if the conversation is stalling.)
• Tell students that today they will learn a strategy for division that involves them listing the doubles of multiples for the divisor before beginning the division problem. They will also think critically about which multiples they should choose to use with division problems.
(8 minutes)
• Display the vocabulary cards for Divisor, Dividend, Quotient, Multiples, and FactorsAnd review the terms with the students. Ask students to reread the meanings and use the terms in sentences with their elbow partners.
• Write a division expression on the board (e.g., 7,892 ÷ 36) and solve the problem. Complete the problem using the standard, digit-by-digit division method, where you think aloud possible multiples and make guesses about which multiple to subtract from the dividend, using one digit at a time.
• Refer back to the division expression 7,892 ÷ 36. List some of the multiples and their expressions for the divisor 36 (e.g., 36 x 100 = 3,600, 36 x 200 = 7,200, and 36 x 400 = 14,400). Ask students to think about what the multiples have in common and raise their hands to share their ideas. ("I notice there is a pattern to the multiples (x2) and that one factor doubles too.")
• Solve the division problem again, but this time use the closest multiple to the total dividend as a starting point (i.e., 7,200). Think aloud your process, emphasizing that the choice between 7,200 and 14,400 has to do with not being able to share over the dividend amount (7,892). (Tip: you can list multiples to the 10th power, such as 36 x 10 = 360And 36 x 20 = 720, to help you estimate the other factor to use.) Continue to solve the problem until you can no longer share equally with 36 groups.
• Consider the use of 100 as a factor. Mention that you know the answer will be in the hundreds place because you cannot equally share the 7,000 (number in the thousands place) into 36 groups.
• Ask students to turn and talk about which process they think would have been better: starting out with multiples with 10 or multiples of 100 as the factor? Allow them to share their ideas aloud. Rephrase some of their opinions so they contain transition words and evidence.
(7 minutes)
• Distribute and display the Division: Listing Multiples worksheet and review the instructions with the students. Look at the teaching component and sample problem, and ask students to reflect on the information in partners ("I notice... I see the... There are... The problem has...").
• Allow students to share their ideas aloud and encourage student input on the presenter's answers. Have them share their agreement or disagreement or add to the conversation ("I agree, but I would also add..." or "I would like to add...").
• Have students consider the choice of multiples and decide if they think they're helpful in solving the division problem ("I believe..." or "I would prefer...").
• Write down some phrases students can use for expressing their opinions on the board for use throughout the lesson.
(10 minutes)
• Have students complete the next two problems from the Division: Listing Multiples worksheet on their own. The first is scaffolded with a lot of the doubled multiples filled in. Have students discuss with their partners how to complete the equations and then solve the division problem using the best multiple. (Tip: if students need the scaffolds for the next problem, fill in some of the equation frames).
• Choose volunteer partnerships to share their answer for the first problem aloud. Ask for student input about the chosen multiple and discuss other potential multiples they can use to solve the problem. ("I think I would use ____Because...")
• Have students complete the second problem with their partners.
• Give an opportunity for students to ask questions about the process based on the feedback they get on their papers or the whole-class discussion.

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.
• Read the vocabulary terms and preteach the words, such as "generalizations," "conclusions," "multiples," "factors," "divisor," "dividend," "quotient," and "opinion."
• Model how to use the sentence stems throughout the lesson, or ask an advanced student to model using the language.

• Ask students to share their opinion phrases aloud and add them to a list on the board.
• Ask them to share their ideas first as an example for students in appropriate language for the assigned task.
• Pair students with mixed-ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
(7 minutes)
• Write another division problem on the board, such as 392 ÷ 17With listed multiples for the divisor 17 times factors of 1,000 (i.e., 17 x 1,000 = 17,000, 17 x 2000 = 34,000, etc.).
• Ask students to evaluate the division problem by determining if the choice in multiples is helpful or not.
• Ask students to use their whiteboards and solve the problem with the listed multiples, and then solve it again with different multiples. Then have them discuss their opinion with their elbow partner.
• Possible sentence stems include:
• "Having multiples of 17 to the thousands place is...."
• "I think ____Is a better strategy because..."
• "This is/is not helpful because..."
• "While listing multiples can be helpful..."
• Listen to their conversations and take notes on the language and content they hear throughout their discussion.
(3 minutes)
• Review the notes on the chart paper for the thought-provoking question in the Introduction section. Read through some of the ideas students had about the statement and confirm or deny some of the assumptions.
• Add additional information from ideas in this lesson based on student feedback.
• Choose students to explain how doubling the multiples in long division problems can help them quickly solve division problems and eliminate some stress when solving multi-digit division problems. Mention that this strategy is also good when they need to estimate quotients.

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