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Decimal Comparisons

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

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

Students will be able to use their knowledge of place value to compare decimals.

Language

Students will be able to compare decimals to the hundredths place using visuals and review their comparative language.

(5 minutes)
• Write the following numbers on the board: 0.56, 0.09, 0.75. Gather background information by asking students to place the numbers in order from least to greatest.
• Have them work on their own using scrap paper. Observe their strategies (number line, converting to fractions, etc.) and whether they got the right answer.
• Tell students to turn and talk to their partner about their chosen order. Monitor their language use and write some examples on the beginning section of the anchor chart Lesson Language. Make sure to note an example that needs improvement to ask students for their input later on in the lesson.
• Choose a student to share the order aloud and have other students put their thumb up if they agree, thumb sideways if they're unsure, and thumb down if they disagree.
• Tell students today they will compare only two decimals to determine which fraction is closer to 1.00.
(8 minutes)
• Model ordering the decimals from the introduction section (i.e., 0.09, 0.56, 0.75). Use a place value chart, empty number line, or base 10 grid paper to give students a visual representation of the decimal values.
• Emphasize using correct comparative language (e.g., "____ is greater than/less than ____ because ____.") and saying the decimals correctly (e.g., 0.75 is seventy-five hundredths).
• Take the comparison to the next level by asking students which number is closer to 1.00. Allow them to share their ideas with their partners, but they should come to the understanding that the greatest number (i.e., 0.75) is closer to 1.00 because none of the numbers are above 1.00.
• Ask students if they can explain why 0.75 is the number closest to 1.00. Then refine their explanations and rephrase their words so that they understand there are two more tenths in 0.75 than in 0.56. The number 0.09 has no tenths, therefore it is the smallest number.
• Use a random number generator, such as Random.org, to get random numbers. Think aloud how to rearrange the two numbers to create a decimal closest to 1.00.
• Review the language students used when comparing decimals that you wrote on the anchor chart Lesson Language from the introduction section. Correct a sentence that misuses the language or is imprecise, such as "This number is bigger than that number." Change the sentence to add more precise language, like "Seventy-five hundredths is greater than fifty-six hundredths."
(8 minutes)
• Create a new random number and ask students to work in partners to talk about how to create a decimal to the hundredths place that is closer to 1.00 but less than one. Have them use the place value chart or number line to compare the two values they provide. For example, if they have numbers 4 and 9, they would create 0.49 and 0.94 and should conclude 0.94 is the closest number to 1.00.
• Choose a student to model explaining their process for choosing the greatest decimal. Additionally, have another student add onto the explanation by either adding precise information (numbers) or giving a visual to support the answer.
• Allow another partnership to share their explanation too.
• Monitor their language use and write some examples on the middle section of the anchor chart Lesson Language.
(8 minutes)
• Tell students they will now find decimals that are closer to 1.00 using a pair of dice. Remind them they will only have two dice, so they should create a decimal with the numbers only in the hundredths and tenths place.
• Pass out the dice and a sheet of copy paper.
• Tell students to fold the paper in half twice so that they have four boxes.
• Have them roll the two dice to get two numbers, one on each die.
• Ask them to create a number that is the closest to 1.00 and a smaller number using those two numbers for the tenths and hundredths place.
• Repeat this process four times so that they have two decimal number in each of the copy paper boxes (i.e., four pairs of numbers)..
• Tell them to draw a visual for each of the four sets of numbers, whether it's a number line or place value chart, to show the two numbers they can create and which is the greatest.
• Choose a partnership to share one of their numbers with the class and encourage them to use some of the language from the Lesson Language anchor chart if they need assistance.
• Have students share their eight numbers with their partners. ("My first number is ____. It's greater than ____ because ____.")
• Write more language frames you overhear from peer conversations in the last section of the anchor chart.

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 use visual models, a number line, or converting the decimal into a fraction to help them provide evidence for their explanations.

• Pair students with mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Choose them to model their comparative language.
• Have students give examples of sentence frames they can use in their partner discussions before they separate into partnerships.
(6 minutes)
• Ask a volunteer to provide another decimal to the hundredths place.
• Distribute a scrap paper and ask students to write a new number that is closer to 1.00.
• Tell them to draw a visual or write a reason they know the number is closer to 1.00.
• Have students share their numbers and explanation with partners.
(5 minutes)
• Choose students to share their assessments aloud.
• Review the last section from the Lesson Language anchor chart and ask students to make observations to their partners about how the language changed from the beginning to the end of the lesson (e.g., "The sentences got longer," or "I notice the sentences have more specific information.").
• Ask volunteers to share their partner's ideas with the class ("____ thinks...").

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