Guided Lessons

# Dissecting Decimals

Challenge students to think about decimals while identifying numbers to the hundredths and thousandths. They'll discuss decimal attributes too. Use this lesson on its own or as support to the lesson Dividing Decimals: Estimation.
This lesson can be used as a pre-lesson for theDividing Decimals: EstimationLesson plan.

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This lesson can be used as a pre-lesson for theDividing Decimals: EstimationLesson plan.

Students will be able to round a decimal to a whole number to estimate a quotient.

##### Language

Students will be able to create decimal numbers closer to a given decimal number using number lines and peer discussions.

(3 minutes)
• Post a number line partitioned into tenths so that the hundredths are the smaller dashed lines, or use a ruler and display it with a document camera.
• Ask students to think about what they are seeing and then try to make a guess about the day's lesson topic. Create a word web with all the ideas they have when they look at the number line (e.g., ruler, decimals, measuring, calculations, etc.).
• Confirm correct answers after all ideas are shared and then tell students that today they'll use number lines to find decimal numbers closer to the given decimal numbers.
(7 minutes)
• Review the terms Tenth, Hundredth, Thousandth, and Number lineWith the students. Allow them to share their ideas and then have them repeat the meanings. Show students the fractional representation for tenth (1/10), hundredth (1/100) and thousandth (1/1000).
• Place a number to the tenths place (e.g., 10.7) on the number line from the Introduction section and then ask students to think about numbers that are closer to that number than the whole number (e.g., 10), such as 10.3. Then, ask students if there are numbers even closer to 10 they can find on the number line. (Tip: continue to refer to the fractional equivalent of the decimal number if students have a solid understanding of fractions.)
• Have students share their ideas with partners and allow them to find the number on the number line to confirm their answer.
• Ask students if there are numbers that are even closer to 10 but that they cannot find on the drawn number line. Choose students to share their ideas. They should understand that the thousandths place is not visible, but that the number 10.001 is even closer to 10.
• Have students talk to their elbow partner about a number that is closer to 11 this time. Have them find numbers closer to 11 little by little until they identify a closer number (e.g., 10.9).
• Ask students if there is a number closest to 11 that they cannot find on the number line (e.g., 10.999).
• Give students time to ask questions and give other students the opportunity to answer the question before answering it yourself.
(9 minutes)
• Pose some questions that require students to make a choice:
1. Is 4.56 closer to 5 than 4.506?
2. Is 95.3 closer to 95 than 95.33?
3. Can you think of a number in the tenths place that is closer to four than five?
• Pass out a whiteboard to each student to allow them to take notes or draw a number line to confirm their ideas. Answer the questions as a class.
• Provide the following sentence stems:
• "I think ____Is closer to ____Because..."
• "Also, ____Is close to ____."
• "I agree with ____Because..."
(10 minutes)
• Assign the Always, Sometimes, Never: Decimal Questions worksheet to partners.
• Explain to students that they need to read the cards to each other and determine if the statement is always true, sometimes true, or never true. Tell them to write an example to support their answers on the back of the card and then place the card in the corresponding column in the table.
• Ask partners to "correct" another partnership's answers. Have partners move to another partnership's table and review the card placements. Explain that if they disagree with the card placement, they should move them off the chart. When students come back to their table, ask them to review the disagreements and see if they have questions.
• Ask students to share if they had cards moved off of their table and then discuss the correct answer. ("Can you help me with card ____? I think the answer for card ____Is ____.") Correct misconceptions as necessary after students have tried to help partnerships correct their answer.
• Review the card placements on the chart and discuss the cards in detail that have the most debate between students.

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.
• Have students work with sympathetic, advanced ELs to help them read the Always, Sometimes, and Never cards.
• Allow students to use a number line visual to help them explain their answer.

• 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 to help model language use.
• Write down some language examples ELs use in their discussion to serve as examples for other students.
• Ask them to create their own Always, Sometimes, and Never card for decimals and have them switch with another student to answer each other's card with an example to support their ideas.
(6 minutes)
• Post the following idea and ask students to determine if it's "Always True," "Sometimes True," or "Never True": "The number 4.5 is between the number four and five." Read the statement aloud to students.
• Distribute a sheet of copy paper and ask students to justify their answer with a visual or number line.
• Have partners share their ideas with each other and circulate around the room to assess student understanding.
(5 minutes)
• Distribute index cards and ask students to write one question about decimals.
• Collect the index cards, read them aloud, and have students vote 1–5 based on the questions they want to answer (5 is "I really want to answer it!").
• Remind students that the digits in the decimal period, or lack thereof, can change the value of the entire number.