Learn on PengiPengi Math (Grade 4)Chapter 1: Place Value Fundamentals and Estimation

Lesson 1: The Base-Ten System's Ten-Times Relationship

In this Grade 4 Pengi Math lesson, students explore the base-ten system's ten-times relationship, learning how a digit in any place represents ten times the value of the same digit one place to its right. The lesson uses hands-on bundling models to show how 10 smaller units combine to form 1 larger unit, such as 10 tens equaling 1 hundred. This foundational concept prepares students to work confidently with multi-digit numbers throughout Chapter 1.

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

Bundling Place Value Units

Property

When you bundle 10 of a specific place value unit, you create 1 of the next larger place value unit.

10 ones=1 ten10 \text{ ones} = 1 \text{ ten}
10 tens=1 hundred10 \text{ tens} = 1 \text{ hundred}
10 hundreds=1 thousand10 \text{ hundreds} = 1 \text{ thousand}

Examples

Section 3

Dividing by 10 by Unbundling Units

Property

Dividing a number by 10 is equivalent to unbundling each of its place value units into 10 units of the next smaller place value. This causes each digit to shift one place to the right, making its value 10 times smaller.

1 larger unit=10 smaller units to the right1 \text{ larger unit} = 10 \text{ smaller units to the right}
(Value)÷10=Value shifted one place to the right(\text{Value}) \div 10 = \text{Value shifted one place to the right}

Examples

Book overview

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

Continue this chapter

Chapter 1: Place Value Fundamentals and Estimation

  1. Lesson 1Current

    Lesson 1: The Base-Ten System's Ten-Times Relationship

    LearnPractice
  2. Lesson 2

    Lesson 2: Reading and Writing Large Numbers

    LearnPractice
  3. Lesson 3

    Lesson 3: Representing Multi-Digit Numbers in Different Forms

    LearnPractice
  4. Lesson 4

    Lesson 4: Comparing Multi-Digit Numbers Place by Place

    LearnPractice
  5. Lesson 5

    Lesson 5: Comparing and Ordering Numbers in Various Forms

    LearnPractice
  6. Lesson 6

    Lesson 6: Rounding Multi-Digit Numbers to Any Place Value

    LearnPractice
  7. Lesson 7

    Lesson 7: Estimation for Sums, Differences, and Reasonableness

    LearnPractice

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

Bundling Place Value Units

Property

When you bundle 10 of a specific place value unit, you create 1 of the next larger place value unit.

10 ones=1 ten10 \text{ ones} = 1 \text{ ten}
10 tens=1 hundred10 \text{ tens} = 1 \text{ hundred}
10 hundreds=1 thousand10 \text{ hundreds} = 1 \text{ thousand}

Examples

Section 3

Dividing by 10 by Unbundling Units

Property

Dividing a number by 10 is equivalent to unbundling each of its place value units into 10 units of the next smaller place value. This causes each digit to shift one place to the right, making its value 10 times smaller.

1 larger unit=10 smaller units to the right1 \text{ larger unit} = 10 \text{ smaller units to the right}
(Value)÷10=Value shifted one place to the right(\text{Value}) \div 10 = \text{Value shifted one place to the right}

Examples

Book overview

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

Continue this chapter

Chapter 1: Place Value Fundamentals and Estimation

  1. Lesson 1Current

    Lesson 1: The Base-Ten System's Ten-Times Relationship

    LearnPractice
  2. Lesson 2

    Lesson 2: Reading and Writing Large Numbers

    LearnPractice
  3. Lesson 3

    Lesson 3: Representing Multi-Digit Numbers in Different Forms

    LearnPractice
  4. Lesson 4

    Lesson 4: Comparing Multi-Digit Numbers Place by Place

    LearnPractice
  5. Lesson 5

    Lesson 5: Comparing and Ordering Numbers in Various Forms

    LearnPractice
  6. Lesson 6

    Lesson 6: Rounding Multi-Digit Numbers to Any Place Value

    LearnPractice
  7. Lesson 7

    Lesson 7: Estimation for Sums, Differences, and Reasonableness

    LearnPractice