Place Value and Rounding

Explicit Instruction/Teacher modeling

• 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).

Guided Practice

• 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.

Group work time

• 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.