Learn on PengienVision, Mathematics, Grade 4Chapter 1: Generalize Place Value Understanding

Lesson 2: Place Value Relationships

In this Grade 4 lesson from enVision Mathematics Chapter 1, students learn that a digit in one place has ten times the value of the same digit in the place to its right, exploring place value relationships across ones, tens, hundreds, thousands, and beyond. Using place-value blocks and real-world problems, students practice multiplying and dividing by 10 to understand how place values scale. The lesson builds students' ability to generalize patterns in multi-digit numbers and compare the values of repeated digits within the same number.

Section 1

The 10-to-1 Relationship Between Places

Property

In our base-10 number system, the value of each place is 10 times greater than the value of the place to its immediate right.

Value of a place=10×Value of the place to its right \text{Value of a place} = 10 \times \text{Value of the place to its right}

Examples

Section 2

The 1-to-10 Relationship Between Places

Property

The value of a digit in a given place is equal to the value of the same digit in the place to its immediate left divided by 10.

Value of a digit=Value of the digit to the left÷10\text{Value of a digit} = \text{Value of the digit to the left} \div 10

Examples

  • In the number 770, the value of the 7 in the tens place (70) is the value of the 7 in the hundreds place (700) divided by 10. So, 70=700÷1070 = 700 \div 10.
  • In the number 2,245, the value of the 2 in the hundreds place (200) is the value of the 2 in the thousands place (2000) divided by 10. So, 200=2000÷10200 = 2000 \div 10.

Explanation

This property explains the relationship between adjacent place values as you move from left to right. Each time you move one place to the right, the value of the digit becomes ten times smaller. This is the same as dividing the value of the digit by 10. Understanding this division relationship is key to comparing the value of digits within a number.

Book overview

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Chapter 1: Generalize Place Value Understanding

  1. Lesson 1

    Lesson 1: Numbers Through One Million

  2. Lesson 2Current

    Lesson 2: Place Value Relationships

  3. Lesson 3

    Lesson 3: Compare Whole Numbers

  4. Lesson 4

    Lesson 4: Round Whole Numbers

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

The 10-to-1 Relationship Between Places

Property

In our base-10 number system, the value of each place is 10 times greater than the value of the place to its immediate right.

Value of a place=10×Value of the place to its right \text{Value of a place} = 10 \times \text{Value of the place to its right}

Examples

Section 2

The 1-to-10 Relationship Between Places

Property

The value of a digit in a given place is equal to the value of the same digit in the place to its immediate left divided by 10.

Value of a digit=Value of the digit to the left÷10\text{Value of a digit} = \text{Value of the digit to the left} \div 10

Examples

  • In the number 770, the value of the 7 in the tens place (70) is the value of the 7 in the hundreds place (700) divided by 10. So, 70=700÷1070 = 700 \div 10.
  • In the number 2,245, the value of the 2 in the hundreds place (200) is the value of the 2 in the thousands place (2000) divided by 10. So, 200=2000÷10200 = 2000 \div 10.

Explanation

This property explains the relationship between adjacent place values as you move from left to right. Each time you move one place to the right, the value of the digit becomes ten times smaller. This is the same as dividing the value of the digit by 10. Understanding this division relationship is key to comparing the value of digits within a number.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 1: Generalize Place Value Understanding

  1. Lesson 1

    Lesson 1: Numbers Through One Million

  2. Lesson 2Current

    Lesson 2: Place Value Relationships

  3. Lesson 3

    Lesson 3: Compare Whole Numbers

  4. Lesson 4

    Lesson 4: Round Whole Numbers