Understanding Place Value

Curriculum Area and Level

This lesson is designed for Year 4 students in New Zealand and aligns with Mathematics and Statistics in the New Zealand Curriculum, Level 2-3. The focus is on Number and Algebra – Place value, addition, and subtraction. Students will develop an understanding of place value in numbers up to four digits and apply their understanding to expanding numbers effectively.

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Lesson Objectives

By the end of this 60-minute lesson, students will be able to:

• Recognise and understand the place value of digits in numbers up to 9,999.
• Expand numbers into thousands, hundreds, tens, and ones (e.g. 3,482 = 3000 + 400 + 80 + 2).
• Use concrete materials to build and deconstruct numbers for deeper understanding.
• Demonstrate their learning through activities and discussion.

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Lesson Structure

1. Introduction and Warm-Up (10 mins)

Objective: Activate prior knowledge and engage students with a quick interactive exercise.

Game: "Sky-High Numbers"

• Write a four-digit number on the board (e.g., 2,746).
• Ask students to identify the place value of each digit (e.g., "What digit is in the hundreds place?").
• Call on students to come up and underline the value of different digits.
• Extend for higher ability learners by having them write the expanded form on mini whiteboards.

📢 Teacher Prompt:
"Who can tell me what the '4' represents in our number? Can you explain why?"

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2. Whole-Class Teaching (15 mins)

Objective: Introduce the concept of expanding four-digit numbers using concrete materials.

Demonstration: Using Place Value Blocks

• Show students physical place value blocks (or printed cut-outs if unavailable).
• Model how to represent a number like 3,482 using thousands, hundreds, tens, and ones.
• Record the expanded form on the board: 3000 + 400 + 80 + 2.
• Repeat with another number, eliciting responses from students to guide the process.

📢 Teacher's Questioning:
"What happens if you take away 10 from 3,482? Which digit will change?"

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3. Hands-On Activity: "Place Value Builders" (20 mins)

Objective: Reinforce place value understanding using hands-on exploration.

Activity Instructions

• Paired Work: Each pair of students receives a tray of place value blocks (or number cards with thousands, hundreds, tens, and ones).
• Teacher announces a number (e.g., 5,326).
• Students work together to build the number using materials and write the expanded form in their maths books.
• Higher-ability students can create their own numbers and challenge a partner.
• Provide direct teacher support to struggling learners by focusing on two-digit and three-digit expansion before moving to larger numbers.

✅ Success Criteria:

• Students correctly match place value materials to the written number.
• Students can write their number in expanded form accurately.

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4. Wrap-Up and Reflection (10 mins)

Objective: Consolidate learning and check understanding.

Class Discussion & Exit Ticket

• Ask volunteers to share one number they represented and explain its expanded form.
• Quick-fire round: Teacher calls out a number, and students write expanded form on whiteboards.
• Exit Ticket Question: Each student writes down one thing they learned about place value on a sticky note and places it on the board.

📢 Teacher's Reflection Prompts:
"What helped you understand place value better today?"
"Can you think of a real-life example where place value is important?"

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Extension for Early Finishers and Higher Ability Learners

• Challenge: "Missing Number Puzzle"—Give students an expanded number (e.g., 4000 + ? + 30 + 2) and ask them to determine the missing value.
• Introduce rounding to the nearest ten/hundred and discuss how it connects to place value.

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Assessment & Differentiation

Formative Assessment Throughout the Lesson:

• Observations during activities
• Student explanations of their thinking
• Exit tickets evaluating student understanding

Differentiation Strategies:

• Struggling Learners: Start with two- or three-digit numbers before moving to larger values, using concrete materials for support.
• Advanced Learners: Introduce decimal place values (tenths/hundredths) or allow them to create their own problems to challenge a partner.

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Resources & Materials Required

✅ Whiteboard & markers
✅ Place value blocks or printed number cards
✅ Mini whiteboards and markers for student responses
✅ Sticky notes for exit tickets

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Teacher Reflection After the Lesson

• Which students demonstrated a solid understanding of place value?
• Were concrete materials effective for struggling learners?
• How engaged were students during paired activities?
• What adjustments should be made in the next lesson?

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Final Thoughts

This engaging and interactive lesson not only strengthens Year 4 students’ place value understanding but encourages deeper thinking through discussions and hands-on learning. Teachers will love how immersive and adaptable this lesson is, making it effective for a diverse range of learners in a New Zealand classroom. 😊🎉