# Dividing Decimals

This lesson can be used as a pre-lesson for the Diner DivisionLesson plan.

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This lesson can be used as a pre-lesson for the Diner DivisionLesson plan.

Students will be able to apply the standard algorithm for dividing decimals by a whole number to solve real-world maths problems.

##### Language

Students will be able to describe how to divide decimals by whole numbers using models and strategic pairings.

(5 minutes)
• Tell students you went grocery shopping yesterday and your total bill was forty-eight dollars and fifty-four cents. Ask them to represent the price in a different way on whiteboards rather than in word form (e.g., \$48.54 or a place value chart with four boxes in the tens place, eight boxes to represent the ones place, five lines to represent the value in the tenths place, and four dots for the value in the hundredths place).
• Allow students to share their ideas in partners. Write their ideas on the board as they discuss them.
• Tell students that your friends want to split the grocery bill three ways. Ask them to turn and talk to their elbow partner about what operation they would use to figure out how much each friend would need to pay. Choose students to share aloud and lead them to decide they need to divide \$48.54 into three different groups to represent the amount that each friend has to pay.
• Write the student-friendly language objective and have students choral read it with you: "I can describe how to divide decimals by whole numbers using models and strategic pairings." Draw images near the vocabulary terms to represent what they mean (e.g., a decimal number above "decimals," grid models above "model," and phrases students may use when they describe a process, like "First, I ____.").
(6 minutes)
• Distribute the vocabulary cards for TenthsAnd HundrethsAnd review the cards. Since the lesson will involve dividing monetary values, you can do a quick review of dimes representing the tenths place and pennies in the hundreths place, etc., while they draw the visuals on their white boards.
• Model how to solve \$48.54 ÷ 3On chart paper with the standard algorithm. Tip: as you solve both division problems, continue to refer to the correct value you are dividing. For example, when using standard algorithm for \$48.54 ÷ 3, for the first step you can say, "There is one group of three in the number 4, so I'll place the one above the four. One ten times three is three tens, so I will subtract three tens from the four tens."
• 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.
• Present another problem students will solve using the standard algorithm and then the longer place value division if time allows. For example, say, "Santiago spent \$24.44 on movie tickets for himself and three friends. They paid him for their tickets when they got to the theater. How much did each friend owe Santiago?"
(8 minutes)
• Ask students to solve the problem on copy paper with their partner, making sure to use the chart paper outline of the process for division. Encourage them to draw pictures to represent the total amount and the division between the four people who needed a ticket (e.g., tape diagrams or a part-part-whole model).
• Choose a student who has a firm grasp on using the standard algorithm 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 Instruction/Teacher Modeling section.
• Have students separate back into partnerships and reconsider their solutions. Then have partners take turns describing the process they used to solve their division problem with the standard algorithm in partners.
(12 minutes)
• Present a new problem and ask students to stop and think about how they will solve the problem. For example, "Santiago also bought some snacks to eat before the movie. He spent \$16.32 on the snacks he shared with his three friends. His friends repayed him for the snacks as well. How much did each friend pay?"
• 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., \$16.32 ÷ 4 = \$4.08). After they've represented the numbers and wrote down ideas for solving the problem, give them a minute to think about how they will share the information with their partners. 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 discussion 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. Afterwards, model asking clarifying questions to help pull more language from the presenter (e.g., "Why would you do ____?" or "How come ____?"). Then ask students to return to their same partners, but this time have the speaker present the information and the listener ask a clarifying question afterward. Finally, have them switch roles in the same partnership.

Beginning

• Allow students to use their home language (L1) or their new language (L2) in all discussions. Provide reference materials in their L1 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.
• Mention the values of the actual number as you model when dividing decimals with the standard algorithm. For example, with 2.3 ÷ 4You are dividing two and three-tenths into four different groups.
• Let them use place value charts and/or decimal grids to check their answers as they complete the division using standard algorithm. Allow students to refer to the visuals as they give their explanations.

• Pair students with mixed-ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate. Ask them to share their ideas first and provide possible language frames that correspond with the discussions.
• Allow them to compete problems with larger numbers. Have students estimate the quotient before they solve the problem and explain their reasoning.
(5 minutes)
• Ask students to separate into their last 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.
• Take notes about student conversations and questions on the board.
• Assess students' ability to refine their explanations and visual representations of the maths problem from their Pre-Write to their Post-Write sections.
(4 minutes)
• Share some of the student descriptions of how to solve the maths problem and some of their clarifying questions. Allow students to critique the quotes based on clarity and attention to detail.
• Ask students to share their insight on the benefits of repeatedly describing their answers and whether they thought changing partners was helpful.

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