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# Decimal Multiplication Estimations

This lesson can be used as a pre-lesson for the Multiply Decimals with Models lesson plan.

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This lesson can be used as a pre-lesson for the Multiply Decimals with Models lesson plan.

Students will be able to estimate decimal products.

##### Language

Students will be able to estimate decimal multiplication using peer conversations and paragraph frames.

(5 minutes)
• Display two models on the board, one hundredths model with 0.85 shaded in yellow and one tenths model with 0.60 shaded in blue.
• Ask students which model has more shaded. (Tip: do not share any vocabulary as you will be gathering background knowledge and accessing their prior knowledge to inform you on what vocabulary to focus on in this lesson.)
• Ask them to use a whiteboard to copy the models and then use a greater than or less than symbol to show the relationship between the two numbers.
• Have students share their answers with each other and then choose volunteers to share their whiteboard answers and rationale with the class.
• Jot down some of the phrases the students use while in peers or presenting to serve as a model for future language use.
(7 minutes)
• Review how to write the decimals from the two models displayed on the board. Write down the key vocabulary you used to describe the models (hundredths, tenths, zero, decimal point, models, etc.) to serve as a word bank for student explanations.
• Solicit definitions from students for key vocabulary students did not discuss during the Introduction section and review vocabulary with which your students may need more instruction.
• Review the ideas behind more than and less than with whole numbers, and then add additional decimal digits to the same numbers to emphasize their value both on a number line and with the models. (Note: each square model for tenths and hundredths represents one, so the number 3.5 will have three models completely shaded with the fourth model having only five of the ten rows shaded.)
• Display the Estimating Decimal Products worksheet with only the boxed problem for #1 shown and none of the sentence frames. Ask students to consider the problem and share their ideas in partners. Choose students to share some of their ideas aloud with the group.
• Explain to students that one way to look at multiplication or division of decimals is to consider what the decimal numbers would be as whole numbers to determine a reasonable answer for the decimal multiplication problem. For problem #1, 1.85 is close to two and 3.4 is close to three. When I multiply the whole numbers 2 x 3, the product is six. (See the answer sheet for more ideas.)
(5 minutes)
• Ask students to turn and talk to their partners about how the product for problem #1 is more than 10, and how they know they have the right answer.
• Display the Estimating Decimal Products worksheet and read through the paragraph frame for problem #1. Ask students for help with completing the paragraph frame given their understanding of the expression and its product.
• Distribute the Estimating Decimal Products worksheet and allow students to write their answers for problem #1. Tell students to read their answer to their partners.
• Choose others to share their answers aloud to the class. Model rephrasing their explanations as necessary and write sentence stems on the board for students who may not be using the sentence frames in their oral explanations (i.e., intermediate or advanced ELs). For example, "I think the answer will be..." or "When I multiply the whole numbers..."
(12 minutes)
• Have students complete the next two problems on the worksheet Estimating Decimal Products in partners. Remind them to continue to relate the decimal numbers to the nearest whole number as well as the corresponding whole number multiplication problem.
• Review the answers with the students and ask students to add to explanations and write more notes in the empty lines under the problems.
• Ask students to give you ideas on what makes a "good" explanation (visuals, examples, non-examples, etc.) and what makes a "needs improvement" explanation (unclear, lacking transition words, no examples, etc.).
• Tell students to practice saying their new explanations aloud for a problem of their choice while in partnerships.

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.
• Give them a chance to use the blank models to visualize the decimal amounts and assist in their estimation explanations.
• Allow them to use a calculator or multiplication chart to confirm their whole number products so they can focus on their explanations for their estimations and not their multiplication facts memory.

• Pair students with mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Encourage students to complete their justifications without the sentence frames on lined paper. Have them write the expression and the question to accompany their justification on their papers.
• Have students read their written justifications if they have a new format or style that students can observe or comment on after the presentation.
(6 minutes)
• Tell students they will now practice giving justifications for their answers in partners for a problem of their choice (#1â€“3 on the Estimating Decimal Products worksheet). Tell them to remember what they had practiced in their group work.
• Take notes on their explanations using the Formative Assessment: Peer Persuasion Checklist. Make sure to have notes on each student.
(5 minutes)
• Share one exemplary explanation and one that needs improvement. Ask students to help you adjust the explanation to make it more clear (e.g., add a model or number line to show the decimal placement, transition words, etc.).
• Ask students to think about how they can relate decimals to whole numbers in real-world situations (e.g., timed races, timed sporting events, cooking, and measurements and material needing estimations).

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