# Understanding Place Value

This lesson can be used as a pre-lesson for the Place Value HopLesson plan.

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This lesson can be used as a pre-lesson for the Place Value HopLesson plan.

Students will be able to identify different place value digits within a number.

##### Language

Students will be able to compare the worth of digits within three-digit numbers with content specific vocabulary using place value mats and base-ten blocks for support.

(8 minutes)
• Write the number 159 on the whiteboard. Pass out personal whiteboards and whiteboard markers to each student. Provide students with access to base-ten blocks (enough for each student to create the number 159).
• Say, "I want you to think about which DigitIn this number is WorthThe MostIn the number, and which digit is worth the LeastIn this number. I'm not going to explain what these words mean yet, I want to see what you already know!"
• Allow the students a few minutes to solve the problem. Rotate around the room and ask students to explain their thinking to you. If a student is confused and doesn't know where to start, support them by reminding them that each digit is in a different place value (e.g. 9 ones, 5 tens, 1 hundred). Don't give students the correct answer, instead, gently guide them as they think about the question.
• Put students in partnerships and have students first identify what is similar and what is different about their approaches to solving the problem. This can also be an initial discussion about what worked well in this or that approach, and what might make this or that approach more complete or easy to understand.
• Provide a sentence frame to support students in discussing their ideas, and ask a partnership to model reading and completing the sentence frame in front of the rest of the students. An example sentence frame is:
• The digit that is worth the most is ____. I know this because ____.
• The digit that is worth the least is ____. I know this because ____.
• My partner and I both used ____To solve the problem.
• I used ____To solve the problem, but my partner used ____Instead.
• Allow the students a few minutes to discuss the similarities and differences of their approaches.
(8 minutes)
• Ask a few partnerships to share their ideas with the rest of the class.
• Encourage students to come up to the front of the classroom to elaborate their ideas with pictures, words, and models, and add on to their ideas as appropriate to introduce different strategies (e.g. build the number with blocks, sketch the number, write the number using expanded notation, etc.)
• Use active questioning techniques to get students to elaborate their thinking and encourage discussion amongst peers. Example questions include:
• Who can restate ____’s reasoning in a different way?
• Did anyone solve the problem the same way, but would explain it differently?
• Did anyone solve the problem in a different way?
• Does anyone want to add on to ____’s strategy?
• Do you agree or disagree? Why?
• Which number is worth the most? Why?
• Which number is worth the least? Why?
• Pass out the Vocabulary Cards worksheet to each partnership. Read through the student-friendly definitions, referring to the visuals to support student understanding.
• Pause after reading each definition and encourage students to explain the meaning of each vocabulary word in their own words to their partner.
(8 minutes)
• Project the Place Value Mat: Three-Digit Numbers on the whiteboard and create 159 using base-ten blocks, putting each digit in the corresponding place value space on the mat. Count the base-ten blocks from left to right saying, "One hundred, ten-twenty-thirty-forty-fifty, one-two-three-four-five-six-seven-eight-nine. I have one group of one hundred, five groups of ten, and nine ones."
• Ask students to think about the meaning of the words Digit, Worth, Most, and Least. Write the following sentence frame on the whiteboard:
• I used to think ____But now I know ____.
• Encourage the students to think about the approach they used to figure out the digit that was worth the most and the least in the previous activity. Ask the students, "Now that you know the meaning of the words, and you see the number created with base-ten blocks on the place value mat, would you like to change your answer about which digit is worth the least or the most? Why or why not?"
• Model completing the sentence frame with an example (e.g. "I used to think the 9 was worth the most but know I know the 9 is only worth 9 ones.")
• Give students a few minutes to share their ideas in their partnerships.
• Allow students to share their ideas with the rest of the class. Elaborate the the 1 is worth the most, because it represents 1 group of hundreds. The 9 is worth the least because it represents only 9 ones. Relate this to money by asking the students if they would rather have \$9 or \$100. Encourage students to justify their reasoning.
(10 minutes)
• Put students into small groups of about 4–5 students. Assign each group a letter (A, B, C, etc).
• Write 951 on the whiteboard. Ask a student volunteer to read the number aloud.
• Pass out the Place Value Mat: Three-Digit Numbers to each small group along with one set of base-ten blocks.
• Create the following checklist on the whiteboard.
1. Which digit is worth the most?
2. Which digit is worth the least?
• Write the following sentence frames on the whiteboard:
• The ____That is ____The ____Is ____. We know this because ____.
• The ____That is ____The ____Is ____. We know this because ____.
• Create a word bank on the whiteboard with the words Digit, Worth, Most, and Least.
• Section off the whiteboard into 5–6 squares with ample room for students to record their answers. Write down each group's letter on the top of the square so students know where to record their work.
• Allow the students time to figure out the answer to the problem. Once students are finished, assist students in choosing a group member to come to the board to record their answers.

Beginning

• Define the vocabulary words in English and student's home language (L1).
• Allow students to work in a small group with students who speak the same L1, if possible.
• Emphasize the word FiftyBy having the students repeat, "Fifty (fif-tee) is the same as five groups of ten."

• Instruct students to explain the steps to figure out the digit that is worth the least and the most using sequencing words.
• Challenge students to share their answer orally to the class without relying on the sentence frames for support.
• Observe students as they are working in their small groups and jot down important observations of language used, collaboration skills, and ability to finish the sentence frame using the words in the word bank. Use the observations to inform future lessons on understanding the worth of digits in three-digit numbers.
(6 minutes)
• Have each group come up to the front of their classroom to share their answers with the rest of the class.
• Use the question stems from explicit instruction to encourage students to compare and contrast their answers with their peers as well as justify their own.
• Ask students, "Why is it important to undestand place value and the worth of digits?" Listen to student responses and elaborate that it is important because it is the starting point for understanding regrouping, multiple-digit multiplication, and understanding decimals.

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