Learn on PengiPengi Math (Grade 4)Chapter 2: Algorithms, Fluency, and Multi-Step Problem Solving

Lesson 2: Standard Subtraction Algorithm and Decomposition

In this Grade 4 Pengi Math lesson, students learn to fluently subtract multi-digit whole numbers using the standard subtraction algorithm. The lesson focuses on proper digit alignment and systematic decomposition, commonly known as borrowing, to solve subtraction problems accurately. Part of Chapter 2 on algorithms and fluency, this lesson builds the foundational skills needed for multi-step problem solving.

Section 1

Standard Subtraction with Single Regrouping

Property

When subtracting vertically, if a digit in the top number (minuend) is smaller than the digit below it (subtrahend), you must regroup. To regroup, you decompose 1 from the next higher place value to the left and add 10 to the current place value. For example, 1 hundred becomes 10 tens, or 1 ten becomes 10 ones.

Examples

Section 2

Subtracting with Multiple Regroupings

Property

To subtract multi-digit numbers, align them by place value and subtract column by column from right to left. If a top digit is smaller than the bottom digit, decompose 1 unit from the place to the left, which is equivalent to adding 10 to the current place. This process may need to be repeated multiple times, including across places with a value of zero.

Examples

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Chapter 2: Algorithms, Fluency, and Multi-Step Problem Solving

  1. Lesson 1

    Lesson 1: Standard Addition Algorithm and Regrouping

  2. Lesson 2Current

    Lesson 2: Standard Subtraction Algorithm and Decomposition

  3. Lesson 3

    Lesson 3: Subtraction Across Zeros and Verification

  4. Lesson 4

    Lesson 4: Modeling Addition, Subtraction, and Comparison with Tape Diagrams

  5. Lesson 5

    Lesson 5: Multi-Step Problem Solving and Assessing Reasonableness

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Standard Subtraction with Single Regrouping

Property

When subtracting vertically, if a digit in the top number (minuend) is smaller than the digit below it (subtrahend), you must regroup. To regroup, you decompose 1 from the next higher place value to the left and add 10 to the current place value. For example, 1 hundred becomes 10 tens, or 1 ten becomes 10 ones.

Examples

Section 2

Subtracting with Multiple Regroupings

Property

To subtract multi-digit numbers, align them by place value and subtract column by column from right to left. If a top digit is smaller than the bottom digit, decompose 1 unit from the place to the left, which is equivalent to adding 10 to the current place. This process may need to be repeated multiple times, including across places with a value of zero.

Examples

Book overview

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

Continue this chapter

Chapter 2: Algorithms, Fluency, and Multi-Step Problem Solving

  1. Lesson 1

    Lesson 1: Standard Addition Algorithm and Regrouping

  2. Lesson 2Current

    Lesson 2: Standard Subtraction Algorithm and Decomposition

  3. Lesson 3

    Lesson 3: Subtraction Across Zeros and Verification

  4. Lesson 4

    Lesson 4: Modeling Addition, Subtraction, and Comparison with Tape Diagrams

  5. Lesson 5

    Lesson 5: Multi-Step Problem Solving and Assessing Reasonableness