Understanding Place Value

Overview

This 60-minute lesson for Year 3 students focuses on developing a secure understanding of place value, specifically working confidently with numbers up to 1,000. The lesson aligns with the New Zealand Curriculum Refresh and aims to build students' mathematical thinking through interactive, hands-on games that foster engagement and conceptual understanding of the base 10 number system.

Curriculum Links

• Achievement Objective: Number and Algebra - Understand the place value system and use it with increasing whole numbers. Represent numbers using concrete, pictorial, and symbolic forms up to at least 1,000.
• Specific Learning Objectives:
• Identify the value of digits in hundreds, tens, and ones places in numbers up to 1,000.
• Partition numbers into hundreds, tens, and ones systematically.
• Read, write, and order numbers up to 1,000.
• References to the New Zealand Curriculum Refresh (Te Mātaiaho Mathematics and Statistics in the New Zealand Curriculum Years 0–8, 2024) underpin this plan.

Competencies

• Thinking: Students use logical thinking to understand and explain place value concepts.
• Using language, symbols, and texts: Communicate their understanding of numbers using correct mathematical vocabulary and representations.
• Managing self: Engage with collaborative games, managing time and rules effectively.

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Learning Objectives

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

• Explain the value of digits in three-digit numbers (hundreds, tens, ones).
• Partition three-digit numbers into hundreds, tens, and ones using physical materials and diagrams.
• Demonstrate their knowledge of place value through interactive games.

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Lesson Flow

1. Introduction to Place Value (10 minutes)

• Begin with a brief, concrete introduction using physical base 10 materials (e.g., place value blocks or PV money — hundreds flats, tens rods, ones units).
• Demonstrate the number 243 by building it with blocks: 2 hundreds, 4 tens, 3 ones.
• Explain that each digit has a different value depending on its position (place value).
• Use place-value language: "This '2' means 2 hundreds, or 200; this '4' means 4 tens, or 40; and this '3' means 3 ones, or 3."
• Show how numbers can be split into parts (partitioning) and recorded in equations: 243 = 200 + 40 + 3.
• Use a place value chart or house diagram on the board to visually reinforce the concept.

2. Activity 1: Place Value Build-Up Game (15 minutes)

Objective: Reinforce the concept of place value by building numbers with physical materials.

Setup:

• Divide the class into groups of 4–5 students.
• Each group receives a set of place value blocks (hundreds, tens, ones) or laminated place value cards and a blank place value house mat.

Instructions:

• Teacher calls out a three-digit number (e.g., 376).
• Each group works together to build that number using their blocks/cards.
• Groups then write the number in expanded form (e.g., 300 + 70 + 6) and say the number aloud, explaining digit values.
• Rotate through a series of numbers increasing in complexity.

Teacher’s role: Circulate, prompt students' explanations, and check understanding.

3. Activity 2: Digit Swap Challenge (15 minutes)

Objective: Understand how changing digit positions affects the value of the number.

Setup:

• Each student receives a printable paper place-value house sheet with blank hundreds, tens, and ones boxes.
• Provide digit cards numbered 0–9 for students to select.

Instructions:

• Teacher calls out a three-digit number or writes it on the board.
• Students place digit cards in the correct place according to the number.
• After confirming the initial number, students swap two digits and write the new number on their sheet.
• Discuss how the value of the number changed (e.g., 352 swapped tens and ones becomes 325, changing the value of digits).
• Optional: Students work in pairs to challenge each other by creating numbers and swapping digits.

4. Activity 3: Place Value Bingo (15 minutes)

Objective: Reinforce place value knowledge by recognising and matching numbers.

Setup:

• Prepare Bingo cards for each student with various three-digit numbers.
• Teacher has a deck of place-value description cards (e.g., “2 hundreds, 5 tens, 1 one” or “3 hundreds, 0 tens, 4 ones”).

Instructions:

• Teacher draws a place-value description card and reads it aloud.
• Students identify the corresponding number on their bingo card and mark it.
• First to complete a line shouts “Bingo!” and explains one number they marked in terms of hundreds, tens, and ones.
• Continue for several rounds.

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Conclusion and Reflection (5 minutes)

• Regroup and discuss the games: What did students learn about place value?
• Ask volunteers to share one new thing they understood about the value of digits in numbers.
• Reinforce that understanding place value helps with many maths skills like addition, subtraction, and estimating.
• Remind students to look for numbers in their environment and think about the value of each digit.

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Assessment

• Observe students during activities focusing on correct use of place value language and accurate building/writing of numbers.
• Use questioning during group work to assess individual understanding.
• Collect a quick snapshot of students’ digit swap sheets or place value houses for evidence of learning.

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Materials Needed

• Base 10 blocks or place value money sets
• Laminated digit cards (0-9)
• Printable place value house mats/work sheets
• Place value bingo cards and place value description cards
• Whiteboard and markers

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This lesson plan brings place value to life with physical, visual, and auditory elements infused with playful learning, ensuring every Year 3 student gains a robust grasp of this foundational concept as prescribed by the New Zealand Curriculum Refresh.

By using manipulatives and peer interaction, the lesson nurtures key competencies such as communication, managing self, and thinking, building a confident mathematical foundation linked to achievement objectives in Number and Algebra for Year 3.

Teachers are encouraged to adapt the activities as needed to suit their class dynamics and resources.