Understanding Place Value

Grade Level

4th Grade

Time Allotted

45 Minutes

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Topic and Theme/Big Idea

Topic: Place Value and Comparing Multi-Digit Numbers
Big Idea: Understanding place value helps us read, write, and compare large numbers accurately.

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Standards

New York State Mathematics Learning Standards (NY-4.NBT.2)

• NY-4.NBT.2a: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.
• NY-4.NBT.2b: Compare two multi-digit numbers based on meanings of the digits using >, =, and < symbols.

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Instructional Objectives

Cognitive Objectives (Knowledge):

• Identify place value in multi-digit numbers (up to the hundred-thousands place).
• Read, write, and represent multi-digit numbers in standard, word, and expanded form.
• Compare two multi-digit numbers using place value understanding.

Behavioral/Psychomotor Objectives (Skills):

• Correctly write numbers in three different forms (standard, word, expanded).
• Use manipulatives (base-ten blocks or digit cards) to represent and compare numbers physically.
• Apply symbols >, <, and = accurately in number comparisons.

Affective Objectives (Attitude):

• Show confidence in working with large numbers.
• Participate in group discussions and collaborate with peers.
• Recognize real-world applications of place value understanding.

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Aim/Goal/Teaching Point/I Can Statement

I Can Statement: "I can use place value to read, write, and compare multi-digit numbers."

Essential Question:

• How does place value help us read, write, and compare numbers?

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Assessments Plan

Cognitive Assessment

Objective	What to Assess	How to Assess	Criteria	When to Assess
Identify place value in multi-digit numbers	Recognition of digit values	Informal questioning	Accuracy of responses	During lesson (mini-lesson & independent work)
Read, write, and represent numbers	Standard, word, and expanded forms	Student workbook exercises	Completeness and correctness	Independent work
Compare numbers	Use of >, =, < symbols correctly	Partner activity	Proper placement of symbols	Partner activity and closing review

Behavioral/Psychomotor Assessment

Objective	What to Assess	How to Assess	Criteria	When to Assess
Use manipulatives to represent numbers	Hands-on use of base-ten blocks/digit cards	Observation	Correct representation	Group work section
Apply symbols accurately in direct comparison	Placement and reasoning behind >, <, =	Written activity and peer discussion	Justification of choice	Independent work and partner activity

Affective Assessment

Objective	What to Assess	How to Assess	Criteria	When to Assess
Participation level	Engagement in activities	Teacher observation	Willingness to engage	Throughout the lesson
Confidence in working with large numbers	Verbal and written responses	Group discussion & reflection	Demonstration of understanding	Closing discussion

Assessment Tool(s):

• Observation checklists
• Student work samples
• Quick informal "thumbs up/down" checks

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Prerequisite Knowledge/Skills/Gaps

• Understanding of ones, tens, hundreds place value (review from previous grade).
• Basic knowledge of multi-digit numbers (reading/writing up to four digits).
• Familiarity with comparing smaller numbers (students may need reinforcement).

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Vocabulary

• Place Value – the value of a digit based on its position in a number
• Standard Form – writing the number normally (e.g., 4,523)
• Word Form – writing the number in words (e.g., four thousand five hundred twenty-three)
• Expanded Form – breaking the number down into place values (e.g., 4,000 + 500 + 20 + 3)
• Greater Than (>) – when one number is larger than another
• Less Than (<) – when one number is smaller than another
• Equal To (=) – when two numbers have the same value

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Part B: Plans for Learning Segment

Instructional Procedure

Mini-Lesson/Introduction ("I Do") – 10 Minutes

1. Display a large multi-digit number (e.g., 56,234) and ask:
   • "What do you notice about this number?"
   • "Can you identify the value of each digit?"
2. Demonstrate how to write the number in:
   • Standard Form: 56,234
   • Word Form: Fifty-six thousand, two hundred thirty-four
   • Expanded Form: 50,000 + 6,000 + 200 + 30 + 4
3. Model comparing two numbers (e.g., 56,234 and 56,543). Think aloud:
   • "I compare starting from the largest place value."

Key Questions:

• "Why do we start comparing from the left digit?"
• "How do we know which number is greater?"

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Guided Practice ("We Do") – 10 Minutes

1. Group Discussion:

   • Display two numbers on the board (e.g., 74,128 and 74,182).
   • Ask students to discuss in pairs:
     • "Which number is greater? How do you know?"
   • Call on students to explain their thinking.

2. Activity – Base-Ten Block Representation:

   • Give students digit cards (1–9) and ask them to build a five-digit number.
   • In pairs, they compare their numbers using >, <, and = symbols.

Key Questions:

• "How does the place value impact which number is larger?"
• "Did changing just one digit affect the comparison?"

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Independent/Small Group Work ("You Do") – 15 Minutes

1. Students complete a workbook exercise:

   • Writing given numbers in standard, word, and expanded form.
   • Comparing pairs of numbers using >, <, and =.

2. Challenge Activity (Extension for Early Finishers):

   • "Think of a real-world place where we use large numbers. Create a math problem using place value."

Key Questions:

• "Why is it important to understand place value?"
• "Can you think of a time outside math class when you compare big numbers?"

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Culminating Application – 5 Minutes

1. Whole-Class Share-Out

   • Have students read one of their compared numbers aloud.
   • Ask them to explain their reasoning behind using >, <, or =.

2. Reflection:

   • "What is one thing you learned about place value today?"

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Extension/Homework

• Practice Worksheet:
  • Read and write five multi-digit numbers in all three forms.
  • Compare five pairs of numbers, explaining the reasoning in one sentence.
• Real-World Application: Bring in an example of a large number found at home (e.g., population size, banknote value, sports scores).

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Part C: Instructional Resources

Materials/Environment

• Classroom setup: Students seated in pairs
• Materials:
  • Base-ten blocks
  • Digit cards (for building numbers)
  • Whiteboards & markers
  • Student workbooks

Safety Plan

No safety concerns for this lesson.

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Attachments/Handouts

• Place Value Chart
• Number Comparison Reference Sheet
• Multi-Digit Practice Worksheet

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References

• New York State Next Generation Mathematics Learning Standards (NY-4.NBT.2)
• National Council of Teachers of Mathematics (NCTM) recommendations for place value instruction
• Classroom-tested best practices for elementary mathematics instruction

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This lesson plan is highly structured, engaging, and aligned with US standards, ensuring students develop deep conceptual understanding of place value. 🚀 🎯