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Place Value and Rounding

This lesson can be used as a pre-lesson for the What is My Place Value? lesson plan.
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This lesson can be used as a pre-lesson for the What is My Place Value? lesson plan.

Students will be able to determine the place and the value of a digit in a number and round the number to the nearest 10 or 100.

Language

Students will be able to explain the value of digits in a number and how to round to the nearest 10 or 100 using discussion supports and sentence stems.

(5 minutes)
• Write the words "What Do You Notice?" on the board, and underneath, display a series of numbers in which a specific digit has a different place value in each number. (e.g., 50,000, 5,000, 500, 50, 5)
• Facilitate a think-pair-share based on the information on the board. Have students think about what they notice about the numbers, and then instruct them to turn and talk to a partner about their ideas. Call on students to share what they discussed with their partner. Provide a sentence stem to support student sharing. For example, "We noticed that ____."
• Ask the following questions to further elicit discussion between partners and in the large group: "Which number would you want if the numbers represent apples and you have to choose a number that can feed the most people in your town or city? Why would you choose that number?"
• Listen for students to reveal what they know about place value in their conversations.
• Share a student-friendly language objective and have students repeat it aloud.
(8 minutes)
• Tell students that there are some key terms they will use as they explain the value of digits in a number and how to round to the nearest 10 or 100.
• Introduce the tiered words using the Vocabulary Cards. Hand out a set to each individual and use a teacher set to display on the document camera during discussion.
• Read aloud each word and have students repeat it. Then, invite the class to choral read the definitions. Instruct students to turn and talk to a partner about the images on each card. Ask them to think of any other images they could add to the card, and provide a sentence frame to support their sharing. For example, "Another image for the word ____ could be ____."
• Display a copy of the Place Value: What is the Value? worksheet on the document camera and think aloud about each of the questions regarding the place value of specific digits in the numbers given. Use the Place Value Mat: Five-Digit Numbers to write each of the numbers. Explain that the Place Value Mat is a tool they can use to help them organize the digits in numbers to better understand their placement and value.
• Explain that sometimes we need to come up with a number that is simpler than, but still close to the original number. Mention that when ordering large numbers of products, you often have to order a rounded number. Tell the class that the city has 6,789 students that go to the schools. If they want to figure out about how many backpacks to get so that every kid gets one, how many should they order?
• Write the number 6,789 on the board and think aloud about rounding to the nearest 10 (6,790) and the nearest 100 (6,800).
(12 minutes)
• Choose five student volunteers to stand at the front of the classroom and give each student a number card. Have them hold the card in front of them, and record the number on the Place Value Mat that is displayed. (e.g., Have students stand with number cards to create the number 57,291.)
• Initiate a discussion with the class by asking questions and providing sentence stems/frames to support their oral language. Revoice student ideas to model mathematical language use by restating a statement as a question in order to clarify, include vocabulary terms and phrases, and involve more students. Press for details in students' explanations by requesting for students to challenge an idea, elaborate on an idea, or give an example.
• Ask questions such as:
• What is the place of the digit ____ in the number? (The place of ____ is ____.)
• What is the value of the digit ____ in the number? (The value of ____ is ____.)
• What digit is in the ten thousands/thousands/hundreds/tens/ones place? (The ____ is in the ten thousands/thousands/hundreds/tens/ones place.)
• Call on nonvolunteers to share whether they agree or disagree with their peer's answers. Challenge them to add on or provide a different answer. (I agree/disagree with ____ because ____. I would like to also say ____.)
• Provide context for the number 57,291. Tell the class that there are 57,291 people that went to watch the hockey game. Ask them to round that number to the nearest 10 (57,290) and the nearest 100 (57,300).
• Invite a new set of five student volunteers to repeat the process with a new set of number cards to create a new number, if time allows.
(10 minutes)
• Give each student a copy of the Place Value Mat: Five-Digit Numbers worksheet.
• Divide the class into groups of five students, and give each group a baggie or envelope of the number cards. Tell each student in the group to get a number card to hold.
• Instruct groups to stand up in their area of the classroom and get in order from the oldest student to the youngest student in order to create their five-digit number.
• Remind students to write their number on their Place Value Mat and utilize the resource throughout the activity to help them use the correct terminology. Display the following questions and sentence stems/frames on the board for students to discuss as a group.
• What is the place of the digit ____ in the number? (The place of ____ is ____.)
• What is the value of the digit ____ in the number? (The value of ____ is ____.)
• What digit is in the ten thousands/thousands/hundreds/tens/ones place? (The ____ is in the ten thousands/thousands/hundreds/tens/ones place.)
• What is the number rounded to the nearest 10? (The number is ____.)
• What is the number rounded to the nearest 100? (The number is ____.)
• Gather students' attention and share what groups did well and provide any clarification or reteaching as necessary.

BEGINNING

• Allow access to reference materials in home language (L1).
• Have learners repeat instructions and key vocabulary to the teacher.
• Provide a word bank of key terms and phrases for students to use in group and class discussions.
• Group students intentionally based on academic and language needs.

• Allow learners to utilize glossaries and dictionaries for unfamiliar words.
• Encourage students to answer questions and participate in discussions without referring to the sentence stems or frames for support.
• Choose advanced ELs to share their ideas first in group and class discussions.
• Have learners repeat instructions and key vocabulary, summarizing important information for the class.
• Put students in mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
(3 minutes)
• Have students take out their whiteboards and whiteboard markers, and display a 5-digit number on the board. Tell learners that they will answer questions by writing their response on the whiteboard and displaying it as a check for understanding. Ask the following questions:
• What is the place of the digit ____ in the number?
• What is the value of the digit ____ in the number?
• What digit is in the ten thousands/thousands/hundreds/tens/ones place?
(2 minutes)
• Ask students to consider how place value plays a role in their number sense and understanding of math. Have students turn and talk to a partner before sharing with the whole group.
• Explain that place value plays a big role when adding, subtracting, multiplying, and dividing. Share that it helps us understand the meaning of a number, as well as the order of the numbers. Add that rounding is an important skill because it helps us find ways to work with numbers in an easier way. Tell them that we use it in our everyday lives, too!

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