Students use different methods to represent three-digit numbers in this unit. Students are going to:
- use base-10 blocks to depict a number.
- put numbers in the standard format.
- write the numbers in extended format.

- What mathematical representations exist for relationships? 
- How can the study of mathematics aid in clear communication? 
- How can identifying regularity or repetition help with problem-solving efficiency? 
- How are numbers represented, compared, quantified, and modeled using mathematics? 
- What does it mean to evaluate or estimate a numerical quantity? 
- What qualifies a tool or strategy as suitable for a particular task?

- Equivalent: Having the same value or amount. 
- Expanded Form: A way to write numbers that shows the value of each digit (e.g., 4,372 = 4,000 + 300 + 70 + 2).

- I Have, Who Has Base Ten cards (M-2-1-2_I Have, Who Has Base Ten) 
- number cards (M-2-1-1_Number Cards) 
- base-ten blocks 
- Place-Value Mat (M-2-1-1_Place-Value Mat) 
- whiteboards 
- whiteboard markers 
- whiteboard erasers, felt, or sock 
- Expanded Form Worksheet (M-2-1-2_Expanded Form Worksheet and Key) 
- Expanded Form Matching Game (M-2-1-2_Expanded Form Matching Game) 
- the Number-Cubes Game (M-2-1-2_The Number-Cubes Game) 
- index cards 
- pencils 
- Number Book worksheet (M-2-1-2_Number Book) 
- paper 
- crayons, colored pencils, and/or markers

- Examine students' work on the Expanded Form Worksheet (M-2-1-2_Expanded Form Worksheet and Key).
- Watch the students utilize M-2-1-2_I Have, Who Has Base Ten to play the game I Have, Who Has Base Ten.
- Throughout instructional procedures, watch how students react.

Direct Instruction, Modeling, Active Participation, and Scaffolding
W: Explain to the students that there are other ways to represent numbers besides base-ten blocks and number cards, like expanded form. 
H: Play I Have, Who Has Base Ten? 
E: Using base-ten blocks, students will represent multiple three-digit numbers and calculate each digit's value. Next, using the expanded form, the students will write the number.
R: The pre-, during--, and post-lesson questions will prompt students to consider how well they comprehend expanded form. 
E: Utilize the Expanded Form Worksheet and the answers to the questions asked during the class to gauge your students' comprehension of the expanded form. 
T: You can modify the lesson by implementing the ideas mentioned in the Extension section. 
O: The lesson aims to reinforce and expand on the idea of displaying numbers in various ways. The assignment requires students to write numbers in standard form, figure out the value of each digit, write expanded form, and represent numbers using base-ten blocks. 

Part 1

Get students to choral count as you start the lesson.

"Count forward by 100s, starting at 200." Ask pupils to end at 1000. (200, 300, 400, 500, 600, 700, 800, 900, 1,000)
“Count forward by 10s, starting at 47.” Stop the class at 127. (47, 57, 67, 77, 87, 97, 107, 117, 127)
"Count forward by 5s, starting at 65." Stop the class at 115 (65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115).
"Count backward by 5s, starting at 265." Stop the class at 230 (265, 260, 255, 250, 245, 240, 235, 230).
"Count backward by 10s, starting at 362." Make students stop at 292. (362, 352, 342, 332, 322, 312, 302, 292)
"Count backward by 100s, beginning at 999." Make students stop at 99. (999, 899, 799, 699, 599, 499, 399, 299, 199, 99)

[Or, you could also decide to play Cherry Pie to start the lesson (see Part 1 of Lesson 1).]

Part 2

Students form a circle. Until all of the cards have been distributed, distribute the I Have, Who Has Base Ten cards (M-2-1-2_I Have, Who Has Base Ten). Some students may have multiple cards. Allow one student to begin by reading his or her card. Continue until you've read every card.

"We used number cards and base-ten blocks to represent numbers in the previous lesson. We utilized number cards 3, 4, and 2 to represent the number 342′. Three is placed in the hundreds place, four is placed in the tens place, and two is placed in the ones place. Just like this." Display the number 342 using the Place-Value Mat (M-2-1-1_Place-Value Mat) and number cards (M-2-1-1_Number Cards). "Here is how the number 342 appears when written in standard form." On the board, write 342. "In addition, we utilized base-ten blocks to represent 342 by using 3 flats, 4 longs, and 2 cubes. Like this." Three hundred forty-two can be shown using base-ten blocks.

"The value of the 3 in the number 342 is 300. The 4 has a value of 40, and the 2 has a value of 2. Writing the number in the expanded form is an additional method of displaying 342 in text. When we write a number in expanded form, we do so in a manner that makes every digit visible. The number is divided into hundreds, tens, and ones in the expanded form. This is how the expanded form of the number 342 looks." Write on the board, 300 + 40 + 2.

Divide the base-ten blocks. Ask students to represent the number 126 using base-ten blocks. Ask,

"How much does the 1 mean?" (100)
"What does the 2 mean?" (20)
"How much does the 6 mean?" (6)
"What would the expanded form of this number be?" (20 + 100 + 6)

Use the subsequent numbers to repeat the previous process. Once students have demonstrated the number with base-ten blocks, ask them to write the expanded number on their whiteboards.

461
320
208
524

Give an Expanded Form Worksheet (M-2-1-2_Expanded Form Worksheet and Key) to every student. While students complete the worksheet, go around the classroom observing and clarifying questions for those who don't understand expanded notation and who need more time to figure it out.

Extension:

Routine: Partners play the Expanded Form Matching Game (M-2-1-2_Expanded Form Matching Game). M-2-1-2_The Number-Cubes Game is a game to play with others in pairs. More activities are listed under Related Resources.

Small Group: Base-ten blocks, index cards, pencils, whiteboards, markers, and erasers are needed for the students. Observe these actions:

1. "Get 6 cubes, 4 longs, and 3 flats."
2. "Enter the number of flats and record it on an index card." (300)
3. "Count the longs and write the number on an index card." (40)
4. "Write the number on an index card and count the cubes." (6)
5. "Set the index cards up in an expanded format." (300 40 6)
6. ”Write the plus sign on each of the two index cards.” (+ +)
7. "Put the plus signs in the appropriate places." (40+30+6)
8. "Write the expanded version of the number on your whiteboard." (40+30+6)

Continue with the following: 421, 293, 660, and 101.

Expansion: Students can make a Number Book (M-2-1-2_Number Book).