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Understanding Place Value

Mathematics • Year 4 • 45 • 14 students • Created with AI following Aligned with Common Core State Standards

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Mathematics
4Year 4
45
14 students
22 March 2025

Teaching Instructions

Class description and setting: needs to be included on all lesson plans

Rationale Curricular rationale: Developmental and Pedagogy rationale NOTE: if the lesson plan is part of a larger unit – the class rationale can be noted as addressed in the unit plan.

Title

Grade Level 4th Grade Time allotted for lesson 45 Minutes

Topic and Theme/Big Idea

Standards NY-4.NBT.2 : Generalize place value understanding for multi-digit whole numbers. 2a. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. 2b. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Instructional Objectives

Cognitive Objectives (Knowledge):

Behavioral/Psychomotor Objectives (Skills):

Affective Objectives (Attitude):

Aim/Goal/Teaching Point/I can Statement/Do Now/Learning Target/Essential Question

Assessments Assessments Plan

Objectives What to assess How to assess Criteria used to assess When to assess Cognitive (What you wrote for objectives) (Identify the specific tools or methods you will use to assess; Formal and/or informal assessment) Specifics you will look for in order to assess (Describe when you will assess during the procedure of your lesson) Behavioral/ Psychomotor

Affective

Assessment Tool(s)

Prerequisite Knowledge/Skills/Gaps.

Vocabulary Place Value: How much each digit in a number represents. We start from left to right when finding out which number is larger / smaller.

we start a number from left to right when finding out which number is larger

Part B. Plans for Learning Segment

Instructional Procedure Mini-Lesson/Introduction/Motivation/I Do-We Do (10 - 15 Minutes) Students will begin with a large number on the sideshow (e.g., 54,321). The number will be within a “house,” with empty spots underneath it. Students will read the number aloud together. Students will answer questions: “What place is the 5 in?” “What place is the 4 in?” “What pace is the 3 in?” “What place is the 2 in?” “What place is the 1 in?” Students will be re-introduced to what place value means. Students will move onto the different forms to write the initial number in: Standard form (54,321) Word form (Fifty thousand, Four thousand, two hundred, thirty-one) Expanded form (50,000 + 4,000 + 300 + 20 + 1) Students will be introduced to comparison symbols (> < =). They can use tricks to help them meorize the signs: Memory Trick #1: Explain that the less-than symbol < can be remembered because it looks like an "L" for "Less.” The smaller number always goes on the left side of the symbol. Memory Trick #2: Explain that the greater-than symbol > can be remember as an alligator mouth. The alligator always wants to eat the bigger number! Students will then work through comparing two numbers (ex. 54,321 ___ 53,123): “Which place value do we start at? (Let’s start at the tens thousands place.) Which number is bigger there when we compare the two?” “Is it bigger, smaller, or the same? If it’s the same we move onto the next place value. “Which number is less? Which side should it go on?”

Developmental Application – Independent and/or small group learning activities/You do (20 Minutes): [Content Outline] Activity 1: Place Value Form Sort Students receive a worksheet with mixed-up number forms (standard, word, expanded). Students job is to match each set by drawing lines, coloring matching groups, or circling it using squares, shapes or circles. Key Questions: How do these forms match? What helped you figure it out? Activity 2: Compare & Color Students continue work on their worksheets. Below will be number pairs and comparison boxes. Students will write <, >, or = between the numbers and color a smiley if they’re confident. Key Questions: What place value helped you compare the numbers? How do you know if they’re equal? Activity 3: Number Challenge Each student picks two numbers from a box. Students will write both numbers in expanded and word form. Students will next, underneath, choose the correct symbol and write a full comparison statement (Ex. 54,321 > 53,123), (54,321 is greater than 53,123 because …) Key Questions: Which place value helped you compare? What does the symbol mean in your example?

Culminating Application – Whole Class Share (10-15 Minutes): [Key Questions] Students will have to have finished activity 3 to be able to present. Each group will come up with their whiteboards. Each student’s whiteboard will show their chosen number, the comparison sign, and the other number from their worksheet (e.g., 54,321 > 53,123). The group will then explain why they chose that symbol and why it’s accurate. After presentations, students will complete a short exit ticket to review what they’ve learned. The exit ticket will ask students to: Write two number’s (of their own choice) in standard, word, and expanded form. Compare the two numbers using <, >, or =. Key Questions: What did you learn about numbers today? Why is place value important? How do we decide which comparison symbol to use?

Extension/ Home work Roll & Compare (Dice Game) Each group (or students) will have two dice to share (or take home). Students will roll each dice 5 times to create two 5-digit numbers. Students will next, write both numbers in standard and expanded form. Students will then compare both numbers using >, <, or =. Students will last, circle the place value that helped them decide which number was bigger/smaller (or equal).

Part C. Instructional Resources

Materials/Environment

Attachments/Handouts

References Fill everything that's blank out!!!!!!!

Understanding Place Value

Class Description and Setting

This math lesson is designed for a 4th grade class of 14 students, taking place in a traditional classroom with desks arranged into small groups to facilitate collaboration. The lesson utilizes a whiteboard, projector, and student whiteboards for interactive engagement. The teacher employs a student-centered approach, incorporating visuals, hands-on activities, and group discussions to ensure comprehension.

Rationale

Curricular Rationale

This lesson aligns with the NY-4.NBT.2 standard, ensuring that students can read, write, and compare multi-digit numbers in different forms. Mastering place value is foundational for future mathematical concepts, such as rounding, addition, and subtraction of large numbers.

Developmental and Pedagogy Rationale

At age 9-10, fourth graders develop the ability to understand abstract numerical concepts. This lesson leverages concrete representations (visual models), interactive discussions, and peer collaboration to bridge the gap between concrete and abstract thinking.

Title

Understanding Place Value

Grade Level

4th Grade

Time Allotted

45 Minutes

Topic and Theme/Big Idea

  • Understanding place value of multi-digit numbers
  • Reading and writing numbers in different forms
  • Comparing numbers using place value

Standards

NY-4.NBT.2: Generalize place value understanding for multi-digit whole numbers.

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

Instructional Objectives

Cognitive Objectives (Knowledge)

  • Identify the value of each digit in a multi-digit number.
  • Convert numbers between standard, expanded, and word forms.
  • Compare two multi-digit numbers using place value.

Behavioral/Psychomotor Objectives (Skills)

  • Accurately place numbers in correct forms.
  • Use comparison symbols correctly in numerical comparisons.
  • Explain their reasoning for comparing numbers verbally and in writing.

Affective Objectives (Attitude)

  • Develop confidence in working with large numbers.
  • Engage in discussions with peers to justify reasoning.
  • Show curiosity in number relationships through hands-on activities.

Aim/Goal/Teaching Point

I can compare multi-digit numbers using place value and explain my reasoning.

Assessment Plan

ObjectivesWhat to AssessHow to AssessCriteriaWhen to Assess
CognitiveUnderstanding place value and number formsObservation during class discussions & worksheetsCorrectly converting numbers & using comparison symbolsDuring the lesson and exit ticket
Behavioral/PsychomotorAccurately placing numbers and using symbolsStudents’ worksheets & presentationsProper number placement & symbol useDuring activities & presentations
AffectiveStudent engagement & confidence in explaining reasoningSelf-assessment smiley faces on worksheetsStudent participation & explanation qualityThroughout the lesson, discussions, and exit ticket

Assessment Tools

  • Worksheet Checklists – Checking students’ answers for accuracy
  • Class Discussion Observation – Informal observation of participation and engagement
  • Exit Ticket Review – A final check for understanding

Prerequisite Knowledge/Skills/Gaps

  • Knowledge of digits and basic place value (ones, tens, hundreds).
  • Ability to read and write basic multi-digit numbers.
  • Some students may still struggle with expanded form.

Vocabulary

  • Place Value: The value a digit holds in a number, based on its position.
  • Standard Form: The usual way we write numbers (e.g., 54,321).
  • Word Form: Writing numbers in words (e.g., Fifty-four thousand, three hundred twenty-one).
  • Expanded Form: Breaking numbers into their place values (e.g., 50,000 + 4,000 + 300 + 20 + 1).
  • Comparison Symbols: > (greater than), < (less than), = (equal to).

Part B: Plans for Learning Segment

Instructional Procedure

Mini-Lesson (10 - 15 Minutes) – "I Do, We Do"

  1. Project the number 54,321 onto the board inside a visual "house" with spaces underneath each digit.
  2. Ask guided questions:
    • What place is the 5 in?
    • What place is the 4 in?
    • Continue through each digit.
  3. Introduce the different forms of numbers:
    • Standard (54,321)
    • Word (Fifty-four thousand, three hundred twenty-one)
    • Expanded (50,000 + 4,000 + 300 + 20 + 1)
  4. Introduce comparison symbols using tricks and visuals:
    • "<" looks like an "L" for "Less Than"
    • ">" is an alligator mouth that eats the bigger number!
  5. Compare two numbers (e.g., 54,321 vs. 53,123) using:
    • Guided questioning:
      • Which digit helps us decide? (Start with the leftmost digit)
    • Discuss choices as a class.

Developmental Application – "You Do" (20 Minutes)

Activity 1: Place Value Form Sort (5-7 Mins)

  • Students receive mixed number forms (standard, expanded, and word).
  • Match them by drawing lines or circling groups in different colors.
  • Key Questions:
    • How do you know these forms match?
    • What clues helped you?

Activity 2: Compare & Color (5-7 Mins)

  • Compare number pairs using <, >, or =.
  • Confidence Check – Students color a smiley face if they’re sure of their answer.
  • Key Questions:
    • Which place value helped you compare?
    • What does the symbol mean?

Activity 3: Number Challenge (5-7 Mins)

  • Each student picks two numbers from a container.
  • Convert both into expanded and word forms.
  • Write a comparison statement (e.g., 54,321 > 53,123 because the tens thousand place is larger).
  • Key Questions:
    • Which digit told you the correct comparison?
    • How can we explain this to someone else?

Culminating Application – Whole Class Share (10 - 15 Minutes)

  • Students choose a whiteboard to present their comparison problem.
  • Explain their choice of symbol aloud.
  • Complete an exit ticket with two self-chosen numbers, written in all three forms, and compared.
  • Key Questions:
    • Why do we compare numbers starting from the left?
    • How do we know which symbol to use?

Extension/Homework

Roll & Compare (Dice Game)

  1. Roll two dice (5 times each) to create two 5-digit numbers.
  2. Write them in standard and expanded form.
  3. Compare using <, >, or =.
  4. Circle the place value that determined the comparison.

Part C: Instructional Resources

Materials/Environment

  • Projector/Whiteboard
  • Student whiteboards & markers
  • Worksheets (comparison problems, number sort)
  • Dice for extension activity

Attachments/Handouts

  • Place Value Form Sort worksheet
  • Compare & Color worksheet
  • Exit Ticket

References

  • New York State Next Generation Mathematics Standards (NY-4.NBT.2)
  • Developmentally Appropriate Practices for 4th Grade Mathematics

This highly engaging and standards-aligned lesson plan ensures students build deep conceptual understanding and confidence in place value and number comparison. 🚀

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