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# Decimal Placement with Division

Encourage learners to discuss decimal point placement with division and apply their understanding of standard algorithm decimal division. Use this lesson on its own or use it as support to the lesson Dividing Decimals Dash.
This lesson can be used as a pre-lesson for the Dividing Decimals Dash! lesson plan.

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This lesson can be used as a pre-lesson for the Dividing Decimals Dash! lesson plan.

Students will be able to divide decimals by whole numbers.

##### Language

Students will be able to discuss decimal placement in division problems using place value charts and peer supports.

(5 minutes)
• Display the following equation and tell students the quotient is missing a decimal point: 29.8 ÷ 73 = 8. Ask students to brainstorm in parters where they should put the decimal point in the quotient.
• Gather information on their background knowledge by listening for their understanding of the key terms ("quotient," "decimal point") and their ability to accurately place the decimal.
• Ask volunteers to share their answers and see if they can explain their reasoning. Some answers may focus on the fact that 298 ÷ 73 = 8, not 29.8 ÷ 73 = 8, and that they need to move the decimal to the left in the quotient to create the correct equivalency (29.8 ÷ 73 = 0.8).
• Tell students that by the end of the lesson, they should know how to explain their decimal placement by relating the decimal division problem to an equation of solely whole numbers.
(5 minutes)
• Display a place value chart, such as the Decimal Place Value Chart worksheet. Use the problem from the introduction (i.e., 29.8 ÷ 73 = 0.8), and provide context for the numbers, such as, "The cupcakes for the goodbye party cost the 5th grade classes \$29.80. Each of the 73 students split the cost of the cupcakes. Each student paid 80 cents, or \$0.80."
• Place the dividend (\$29.80) on the place value chart and ask students to discuss each digit and its value. Correct any misconceptions and restate their information so they use correct terms. Say, "The digit two is worth two tens, or twenty, and the digit nine is worth nine ones, or nine. The digit eight is in the tenths place, so it is worth eight-tenths."
• Review with students that the value of each of the digits is dependent on its placement on the chart in relation to the decimal point. Define the terms decimal point, place value chart, value, and other terms students struggle with in the introduction section.
• Remind students that the movement of the decimal place affects the value of the digit (10 times or divided by 10) and its placement on the place value chart. In other words, each place on the chart has a value of 10 times the place to its right.
• Model how to move the decimal to the left using a three-digit number and show them how it is equivalent to dividing the number by 10 to get the new value (use the standard algorithm). For example, 33.0 ÷ 10 = 3.30.
• Show them the change in values on the place value chart and use the correct terms, such as three tenths and 3 units, or ones. Do another example that requires you to add a zero to hold the place of the tenths or hundredths (e.g., 0.8 ÷ 100 = 0.008).
• Display the example problem from the Decimal Placement in Division worksheet. Ask students to turn and talk about what they notice about the different equations (e.g., "I notice when the decimal moves in the dividend, the decimal moves in the same direction in the quotient.").
• Model the division problems using the standard algorithm for each of the equations listed to prove your answers. Ask students to copy your teacher markings on their whiteboards or their math journals.
(6 minutes)
• Have a student model the process for dividing a decimal number by a whole number using the standard algorithm with one of the example equations from the Decimal Placement in Division worksheet. Ask another student to recount the steps the student took to solve the equation. Write their wording on the board, numbering the steps but also putting sequencing words and phrases on the board.
• Distribute the Decimal Place Value Chart worksheet. Write some three-digit numbers on the board with decimals and ask the students to divide the number by 10 or 100. Tell them to use their whiteboards if they need to do some work or check their answers.
• Have them place the dividend and quotient for each of the numbers on the place value charts and see the changes in the value of the numbers and discuss those changes. For example, "The number got smaller when I divided it by 10 and the decimal place moved one place to the left."
• Ask students to share observations about what happened to the decimal place as they divided the numbers by 10 or 100. They should understand that the decimal moved once or twice to the left, or the number got 10 or 100 times smaller. Record some of their phrases on the board for student reference throughout the lesson.
(15 minutes)
• Distribute the Decimal Placement in Division worksheet. Have students work in groups of four where each member is a number from 1–4. Have members work together to solve questions 1 and 2 and discuss what happened to the quotient when a decimal was added to the dividend.
• Challenge the students to make sure they can all explain their process for finding the quotient without doing the standard algorithm. Tell students you will choose a number 1–4 and the student who has that number will explain the process aloud so they should practice sharing in their groups. The student presenters can use any notes the group created to solve the problem in their explanations, including their own worksheets.
• Write sequencing phrases on the board:
• "First, I ____."
• "After I ____, I ____."
• "Then, I ____."
• "My next step was ____."
• Choose a student from each group to present the solution for question one and another student from a different group to present the same problem. Then, do the same process for question two. (Tip: select groups with advanced ELs first so they can model the explanation process for the class first and the other students can refine their answers.)
• Discuss as a group the effect the decimal placement in the dividend had on the quotient (e.g., "The decimal point was the same number of spaces away from the ones place in both the dividend and the quotient. The divisor did not have a decimal at all.").

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 students to use the vocabulary cards and terms in their conversations and writing. Allow them to draw pictures to support their understanding of the terms.
• Have them use the vocabulary terms and sequencing terms in their L1 before they try in their L2.
• Pair them with advanced students so they can model some of their phrasing and word choice.
• Review the process for standard algorithm division with decimals and ask them to tell you the steps. Point to sections of their work and ask them to tell you the values of the numbers within the standard algorithm.
• Allow them to use calculators to confirm their division problems since the focus on the lesson is to explain decimal place value and their thinking.

• Pair students with mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Encourage them to think about the relationship between moving the decimal to the right versus the left and share their ideas with a partner or aloud with the class in the closing section of the lesson.
(6 minutes)
• Ask students to complete the last two problems in the Decimal Placement in Division worksheet. Ask them to make sure they know how to explain their reasoning, using the sentence frames from the lesson.
• Tell them to practice saying their explanation to themselves before they say it to a partner.
• Ask for volunteers to share their ideas with the class.
(3 minutes)
• Try to have students draw conclusions from the lesson by asking them to consider the following question and discuss their answers in partners: "How does moving the decimal place in the dividend of an equation affect the quotient?"
• Have a student share their answers with the class and correct any misconceptions. Write some of their correct phrasing and logic on the board. For example, "If we move the decimal to the right in the dividend, then the number is increasing. That means the quotient will increase as well, so we can move the decimal to the right the same number of places we moved it in the dividend."