Session 1 Discussion

Objectives

• Label each column of the place value chart (Hundreds, Tens, Ones)
• Break down three-digit numbers into hundreds, tens, and ones

Materials

• Place Value Chart
• Digital Number Paddle
• Whiteboards & Markers

Discussion Guidelines

• Listen respectfully when classmates share ideas
• Raise your hand to speak
• Use complete sentences to explain your thinking

Discussion Flow

1. Introduce the Chart (3 minutes)
   • Display the blank Place Value Chart.
   • Teacher asks: “What labels belong at the top of each column?”
     • Follow-up: “How does each label help us read a number?”
   • Class chorally labels columns: Hundreds │ Tens │ Ones
2. Model with 345 (5 minutes)
   • Teacher writes 345 beneath the chart.
   • Ask: “How many hundreds does this number have? Tens? Ones?”
     • Student volunteers place 3 in Hundreds, 4 in Tens, 5 in Ones.
     • Follow-up: “Why didn’t we put 34 in the Hundreds column?”
   • Connect to expanded form: “How could we write 345 as a sum?” → 300 + 40 + 5
3. Guided Practice (7 minutes)
   • Project 482 using Digital Number Paddle.
   • Students draw chart on whiteboards, break 482 into H–T–O, then show boards.
     • Teacher selects 2–3 volunteers to explain their placements.
     • Follow-up: “How do you know you have exactly eight tens?”
   • Repeat with 269 and 503.
4. Think-Pair-Share Extension (5 minutes)
   • Pose comparison question: “Which number is larger—324 or 294?”
     • Students think silently, then turn to a partner to discuss.
     • Pairs share reasoning: focus on Hundreds first, then Tens.
   • Whole-class debrief: “How can knowing place value help us compare numbers?”
5. Dynamic Place Value Question (3 minutes)
   • Ask: “If I trade 10 ones for one ten, what happens on the chart?”
     • Encourage students to adjust entries and explain the exchange.
     • Follow-up: “Why is that trade helpful when adding or subtracting?”
6. Closure (2 minutes)
   • Ask volunteers: “What is one new thing you learned about place value today?”
     
     
     

Teacher Reflection Prompts:

• Which questions sparked the most student thinking?
• Were any students still uncertain about labeling columns or exchanging units?
• Plan to revisit exchanges or comparisons in small groups if needed.

Session 1 Activity

Objective

Students will use base-ten blocks to represent three-digit numbers and record their expanded form in their math journals.

Time

20 minutes

Materials

• Base-Ten Blocks Template
• Pencils
• Math Journals
• Digital Number Paddle

Setup

• Distribute one sheet of cut-out base-ten blocks and scissors to each student.
• Ensure each student has a pencil and their math journal open to a fresh page.
• Load the Digital Number Paddle with preselected three-digit numbers.

Steps

1. Number Call (4 minutes)
   • Project a three-digit number (e.g., 427) on the Digital Number Paddle.
   • Say: “Build this number using your base-ten blocks.”
2. Build Model (5 minutes)
   • Students cut or select the appropriate hundreds, tens, and ones blocks and arrange them on their desks.
3. Record in Journal (6 minutes)
   • In their math journals, students draw a quick sketch of the blocks, write the number in standard form, and write the expanded form (e.g., 400 + 20 + 7).
     
     
     
     
     
     
4. Share & Check (5 minutes)
   • Invite 2–3 volunteers to show their block arrangement and read their journal entries aloud.
   • Ask: “How did you know to use ___ tens?” or “Why is expanded form useful?”

Differentiation

• Support: Provide a partially built model (e.g., pre-placed hundreds blocks) and have students complete the tens and ones.
• Extension: Challenge advanced students to build a four-digit number (e.g., 1,234) and record its expanded form.

Formative Assessment

• Circulate and ask guiding questions:
  • “How many tens are in your model? How do you know?”
  • “Can you explain the exchange between ones and tens?”
• Note any students who hesitate; plan to pair them for extra practice in Session 2.

Session 1 Game

Objective

Reinforce breaking three-digit numbers into hundreds, tens, and ones while practicing expanded form in a fun, competitive setting.

Time

10 minutes

Materials

• Place Value Number Cards
• Base-Ten Blocks Template
• Whiteboards & Markers (or paper and pencils)
• Score sheet (optional)

Setup

1. Shuffle the Place Value Number Cards and place them face down in the center of each pair’s workspace.
2. Ensure each student has a whiteboard (or paper) and a marker (or pencil).
3. Optional: Provide each pair a simple score sheet to track points.

How to Play

1. Draw & Model (2 minutes per round)
   • Player A draws a number card without showing it to Player B.
   • Both players build the number using their Base-Ten Blocks Template.
   • On their whiteboards, they sketch the blocks and write the expanded form (e.g., 500 + 30 + 6).
     
     
     
2. Compare & Score
   • Players reveal their models and expanded forms to each other.
   • If both models and expanded forms are correct, each student earns 1 point. If one or both make an error, no points are awarded that round.
3. Switch Roles
   • Player B draws a new card, and steps repeat.
4. Play Continuously
   • Continue for as many rounds as time allows (approximately 4–6 rounds).

Winning the Game

• The pair adds their points at the end of the game. Celebrate pairs that demonstrate accuracy and speed.

Differentiation

• Support: For students needing extra support, provide hint cards showing place-value breakdown (e.g., “300 + 20 + 5”).
• Extension: Challenge pairs to draw a four-digit number from a custom deck and model it.

Formative Assessment

• Circulate to observe students’ block arrangements and expanded-form writing.
• Ask quick-check questions:
  • “How did you decide on three hundreds?”
  • “Why is your expanded form 400 + 20 + 7?”
• Note students who consistently need guidance and plan small-group practice in Session 2.

Session 2 Warm-Up

Objective

Activate prior knowledge of place value to compare and order three-digit numbers.

Time

10 minutes

Materials

• Digital Comparison Paddle
• Whiteboards & Markers

Steps

1. Display the following pairs of numbers one pair at a time on the Digital Comparison Paddle:
   • 318 __ 381
   • 245 __ 254
   • 407 __ 470
   • 329 __ 329
2. Students use whiteboards to write the correct inequality symbol (>, <, or =) between each pair.
3. On signal, students hold up their boards. Quickly scan responses to identify common errors.
4. Invite 2–3 volunteers to explain their reasoning, focusing on comparing hundreds first, then tens, then ones.

Transition: Point out how understanding place value helps us determine which number is larger. Move into the Discussion to explore ordering numbers in more depth.

Session 1 Warm-Up

Objective

Activate students’ understanding of place value by representing three-digit numbers as hundreds, tens, and ones.

Time

10 minutes

Materials

• Digital Number Paddle
• Whiteboards & Markers

Steps

1. Project the numbers 141, 308, and 256 one at a time on the Digital Number Paddle.
2. Students draw the corresponding hundreds, tens, and ones on their whiteboards.
3. On signal, students hold up their whiteboards for a quick check.
4. Invite 2–3 volunteers to explain how they modeled each number.

Transition: Use students’ models to introduce the Place Value Chart in the upcoming Discussion.

Session 2 Discussion

Objectives

• Compare two three-digit numbers using place value (Hundreds, Tens, Ones)
• Explain reasoning for which number is larger or smaller

Materials

• Digital Comparison Paddle
• Place Value Chart
• Whiteboards & Markers

Discussion Guidelines

• Listen to classmates and build on their ideas
• Speak clearly and use complete sentences
• Ask clarifying questions if you’re unsure

Discussion Flow

1. Review the Chart (3 minutes)

   • Display the blank Place Value Chart.
   • Ask: “What do the column labels tell us about a number?”
   • Students chorally name: Hundreds │ Tens │ Ones

2. Model Comparing 642 vs. 569 (5 minutes)

   • Project 642 and 569 side by side on the Digital Comparison Paddle.
   • Ask: “Which number is larger? How do you know?”
     • Guide students to compare hundreds (6 vs. 5), then tens if needed.
   • Record reasoning on chart: 642 > 569 because 6 hundreds > 5 hundreds

3. Guided Practice (7 minutes)

   • Project 738 __ 783 on the paddle.
   • Students draw the chart on whiteboards, fill in digits, and write >, <, or =.
   • Invite 2–3 volunteers to explain their choice, focusing on place-value steps.
   • Repeat with 421 __ 412.

4. Think-Pair-Share Extension (6 minutes)

   • Pose: “Order these numbers from least to greatest: 295, 259, 352.”
   • Students think silently and jot a quick list:
     
     
     
   • Turn to partners to compare lists and discuss strategies.
   • Pairs share their ordered list and explain why they started with that number.

5. Dynamic Place-Value Question (4 minutes)

   • Ask: “If I trade 1 ten for 10 ones in the number 430, what number do I get?”
   • Students adjust the chart and share their new number and reasoning.
     
     
     

6. Closure (3 minutes)

   • Ask: “What’s one strategy that helps you compare numbers?”
     
     
     
     
     
     
     
   • Invite 2–3 students to share their strategies with the class.

Teacher Reflection Prompts:

• Which students needed more support identifying place values?
• Which prompts generated the richest discussion?
• How might small-group work reinforce strategies before Session 3?

Session 2 Activity

Objective

Students will sort and order sets of three-digit numbers using place-value reasoning and write explanations for their strategies.

Time

20 minutes

Materials

• Three-Digit Ordering Cards
• Base-Ten Blocks Template (optional for modeling)
• Math Journals
• Pencils

Setup

• Arrange students in small groups of 3–4.
• Place a shuffled deck of Three-Digit Ordering Cards at each group’s workspace.
• Ensure each student has a math journal and pencil.

Steps

1. Draw a Hand (2 minutes)
   • Each student draws 5 cards from the deck without showing peers.
   • Students quickly glance at their numbers and return extras to the bottom of the deck.
2. Group Sort (8 minutes)
   • In groups, students reveal their 5 cards and work together to arrange all 20 cards (if 4 students) in ascending order.
   • Encourage use of place-value thinking: compare hundreds first, then tens, then ones.
   • Optional: Use the Base-Ten Blocks Template to model tricky numbers.
3. Record & Explain (6 minutes)
   • In math journals, groups list the ordered sequence and write one sentence explaining how they decided which number came first.
     
     
     
4. Gallery Share (4 minutes)
   • Groups exchange journals with a neighboring group.
   • Each reviewer scans the sequence and explanation, placing a ✔️ if correct or a ❓ if there’s a question.
   • Briefly discuss any ❓ marks and clarify reasoning.

Differentiation

• Support: Provide a small set of 3 cards instead of 5 and a partially ordered exemplar list.
• Extension: Challenge students to order in descending order or to create their own set of 5 cards to stump another group.

Formative Assessment

• Circulate and listen for language like “six hundreds” or “two tens.”
• Ask guiding questions:
  • “Why did you place 472 before 447?”
  • “How did you decide between 528 and 582?”
• Note groups that need extra practice for targeted small-group work in Session 3.

Session 2 Game

Objective

Students will reinforce comparing and ordering three-digit numbers through a fast-paced group race.

Time

10 minutes

Materials

• Three-Digit Ordering Cards
• Timer or stopwatch (optional)
• Whiteboards & Markers (or paper and pencils)
• Score sheet (optional)

Setup

1. Divide the class into small groups of 3–4 students.
2. At each group’s table, place a shuffled deck of Three-Digit Ordering Cards.
3. Ensure each group has a whiteboard (or paper) and marker (or pencil).
4. (Optional) Provide each group with a simple score sheet to record their wins.

How to Play

1. Draw & Arrange (2 minutes per round)
   • On “Go,” each group draws 3 cards from their deck—no peeking at other groups’ cards.
   • Groups collaborate to arrange the three numbers in ascending order using place-value reasoning (compare hundreds first, then tens, then ones).
   • Groups write their ordered sequence on their whiteboard or paper.
2. Reveal & Verify (1 minute)
   • When a group finishes, they call out “Done!” and hold up their sequence.
   • Teacher or a peer referee checks for accuracy.
     • If correct, the group earns 1 point for that round.
     • If incorrect, they discuss mistakes briefly (with teacher support) and earn 0 points.
3. Reset & Repeat
   • Groups return their cards to the bottom of the deck, reshuffle if needed, and prepare for the next round.
   • Play as many rounds as time allows (approximately 3–4 rounds).

Winning the Game

• After the final round, groups tally their points.
• Celebrate the group(s) with the highest score and highlight examples of clear place-value reasoning.

Differentiation

• Support: Provide hint strips with labeled place-value prompts (e.g., “Compare hundreds, then tens, then ones”).
• Extension: Increase challenge by having groups draw 4 cards instead of 3, or order cards in descending order.

Formative Assessment

• Circulate to listen for language like “four hundreds,” “six tens,” or “two ones.”
• Ask groups:
  • “How did you decide which number came first?”
  • “What made this set tricky?”
• Note any recurring errors to address in small groups during Session 3.

Session 1 Cool-Down

Objective

Reflect on today’s learning and solidify understanding of place value.

Time

5 minutes

Materials

• Math Journals
• Pencils

Steps

1. In your math journal, write one thing you learned about place value today and one question you still have.
   
   
   
2. Draw a quick sketch showing the place-value breakdown of a three-digit number of your choice (e.g., 274 as 200 + 70 + 4).
   
   
   
3. When time is up, volunteer to share your reflection or sketch with the class.

Session 2 Cool-Down

Objective

Reflect on today’s learning and solidify strategies for comparing and ordering numbers.

Time

5 minutes

Materials

• Math Journals
• Pencils

Steps

1. In your math journal, write one strategy that helped you compare and order numbers correctly and explain why it worked.
   
   
   
2. Draw two three-digit numbers of your choice, place the correct inequality symbol (>, <, or =) between them, and label your thinking.
   
   
   
3. Share your strategy or drawing with a partner or volunteer to share with the class.

Session 3 Warm-Up

Objective

Activate students’ understanding of place-value trading in addition and subtraction using base-ten block models.

Time

10 minutes

Materials

• Addition and Subtraction Paddle
• Base-Ten Blocks Template
• Whiteboards & Markers

Steps

1. Display the following problems one at a time on the Addition and Subtraction Paddle:
   • 24 + 38
   • 57 – 29
   • 46 + 18
   • 63 – 47
2. Students draw hundreds (if needed), tens, and ones on their whiteboards using block sketches. Trade 10 ones for 1 ten or 10 tens for 1 hundred to compute each answer.
3. On your signal, hold up your whiteboard for a quick check and self-assessment.
4. Invite 2–3 volunteers to explain one trading step they used (e.g., “I traded 10 ones for one ten to solve 24 + 38”).

Transition: Use these models and trades as we explore addition and subtraction strategies in our Discussion.

Session 3 Discussion

Objectives

• Use place-value trading to add and subtract three-digit numbers accurately
• Explain each trading step and why it’s necessary

Materials

• Place Value Chart
• Addition and Subtraction Paddle
• Base-Ten Blocks Template
• Whiteboards & Markers

Discussion Guidelines

• Listen and build on classmates’ ideas
• Speak clearly and use complete sentences
• Ask questions when you need clarification

Discussion Flow

1. Review the Chart (3 minutes)
   • Display the blank Place Value Chart.
   • Ask: “What do the Hundreds, Tens, and Ones columns represent?”
   • Students chorally name each column and give an example.
2. Model Addition with Trading (5 minutes)
   • Project 146 + 275 on the Addition and Subtraction Paddle.
   • Use the chart and Base-Ten Blocks Template to model 146.
   • Add 5 ones to 6 ones → trade 10 ones for 1 ten. Show the trade on the chart and blocks.
   • Add tens (now 4 + 7 + 1 traded ten) → trade 10 tens for 1 hundred.
   • Record each step and final sum. → 421
   • Ask: “Why did we trade 10 ones before adding tens?”
3. Model Subtraction with Decomposing (5 minutes)
   • Project 302 – 127.
   • Model 302 on the chart. Ask: “Do we have enough ones to subtract 7?”
   • Decompose 1 ten into 10 ones; show trade. Subtract ones, then tens, then hundreds.
   • Record each decomposition and the result. → 175
   • Follow-up: “What happens if we don’t trade when needed?”
4. Guided Practice (7 minutes)
   • Project 83 + 29 and 105 – 48 (one at a time).
   • Students sketch charts on whiteboards, show blocks, perform trades, and write answers.
   • Invite 2–3 volunteers to explain their trading steps and reasoning.
   • Follow-up: “How did the chart help you keep track of trades?”
5. Think-Pair-Share Extension (4 minutes)
   • Pose: “Add 154 + 187 using trading. Which column required trading first, and why?”
   • Students think and jot steps:
     
     
     
   • Turn to a partner to compare trade strategies and sums.
   • Pairs share one insight with the class.
6. Dynamic Trade Question (3 minutes)
   • Ask: “If you convert 1 hundred into 10 tens in the number 200, what does your chart show now?”
   • Students adjust charts and explain: 1 hundred → 10 tens, so Hundreds=1→0, Tens=0→10.
   • Follow-up: “How might that help with subtraction?”
7. Closure (3 minutes)
   • Ask volunteers: “What is one trading step you’ll remember when adding or subtracting?”
     
     
     

Teacher Reflection Prompts:

• Which trading steps were students most comfortable with? Which caused confusion?
• Did students accurately record each decomposition/trade?
• How will you reinforce or reteach trading strategies in follow-up lessons?

Session 3 Activity

Objective

Students will practice adding and subtracting three-digit numbers using place-value trading by modeling problems with base-ten blocks and recording each trade step in their journals.

Time

20 minutes

Materials

• Place Value Trading Cards (each card has one three-digit addition or subtraction problem)
• Base-Ten Blocks Template
• Math Journals
• Pencils

Setup

• Arrange students in pairs.
• Give each pair a shuffled deck of Place Value Trading Cards.
• Ensure each student has a math journal and pencil.

Steps

1. Choose Roles (1 minute)
   • Student A will be the Modeler, Student B will be the Recorder.
   • Roles flip after each problem.
2. Draw & Model (4 minutes per round)
   • Student A draws the top card and reads the problem aloud (e.g., 154 + 187 or 302 – 127).
   • Both students use cut-out blocks from the Base-Ten Blocks Template to build the first number, then model the operation step by step:
     • Addition: add ones, trade 10 ones → 1 ten, then add tens, trade 10 tens → 1 hundred, then add hundreds.
     • Subtraction: check ones; if not enough, decompose 1 ten → 10 ones, subtract ones, then tens, then hundreds.
3. Record Trades (4 minutes per round)
   • Student B sketches the block setup and each trade on their journal page.
   • Write the problem, show each step (e.g., “6 ones + 7 ones = 13 ones → trade 10 ones for 1 ten”), and record the final answer.
     
     
     
     
     
     
4. Share & Switch (2 minutes per round)
   • Student A explains their trading steps and final answer to Student B.
   • Partners check accuracy together.
   • Swap roles and repeat with a new card. Aim to solve three to four cards total.

Differentiation

• Support: Provide cards with two-digit problems and pre-printed block diagrams to label trades.
• Extension: Challenge students with four-digit addition/subtraction cards or ask them to create their own problems for peers.

Formative Assessment

• Circulate to observe block models and journal entries.
• Ask guiding questions:
  • “Which column did you trade first, and why?”
  • “How did the decomposition help you subtract?”
• Note any misconceptions to address during the Game or Cool-Down.

Session 3 Game

Objective

Reinforce place-value trading in addition and subtraction through a fast-paced team relay.

Time

10 minutes

Materials

• Place Value Trading Cards
• Base-Ten Blocks Template
• Timer or stopwatch (optional)
• Whiteboards & Markers (or paper and pencils)
• Score sheet (optional)

Setup

1. Divide the class into teams of three students.
2. At each team’s table, place a shuffled deck of Place Value Trading Cards.
3. Provide each team with the Base-Ten Blocks Template, a whiteboard, and markers.
4. (Optional) Give each team a simple score sheet to record points.

How to Play

1. On “Go,” Student 1 draws the top card, reads the problem aloud (e.g., 154 + 187 or 302 – 127), and uses blocks to model and perform necessary trades.
2. Student 1 writes the final answer and key trading steps on the team whiteboard, then tags Student 2.
3. Student 2 draws a new card and repeats the process, then tags Student 3.
4. Continue rotating through team members until time is up or each member has completed two to three cards.

Scoring

• Each correct solution (accurate model, trades, and answer) earns 1 point for the team.
• At the end of the game, teams total their points. Celebrate the team with the highest score and highlight clear trading strategies.

Differentiation

• Support: Provide trading hint strips (e.g., “Trade 10 ones for 1 ten”) or two-digit problems.
• Extension: Increase challenge with four-digit addition/subtraction cards or require each student to solve additional cards.

Formative Assessment

• Circulate and listen for language like “traded 10 ones for one ten” or “decomposed one hundred into ten tens.”
• Ask quick-check questions:
  • “Which trade did you perform first and why?”
  • “How did your model help you keep track of the exchange?”
• Note any misconceptions to address in the Cool-Down or follow-up instruction.

Session 3 Cool-Down

Objective

Reflect on today’s learning and solidify understanding of place-value trading in addition and subtraction.

Time

5 minutes

Materials

• Math Journals
• Pencils

Steps

1. In your math journal, write one thing you learned about trading ones or tens when adding or subtracting and explain why it helps you compute accurately.
   
   
   
2. Draw a quick base-ten block sketch for 83 + 29 (or choose another problem), showing each trade you made (e.g., trading 10 ones for 1 ten) and label each step.
   
   
   
3. Share your reflection or sketch with a partner or volunteer to share with the class.