Learn on PengiPengi Math (Grade 4)Chapter 3: Understanding Multiplication and Division

Lesson 2: Multiplicative Comparison

In this Grade 4 lesson from Pengi Math Chapter 3, students learn to model multiplicative comparison problems using tape diagrams, bar models, and equations. They practice distinguishing multiplicative comparison from additive comparison and apply multiplication and division to solve real comparison problems.

Section 1

Identifying Additive and Multiplicative Comparisons

Property

An additive comparison shows how much more or less one quantity is than another. It involves adding a difference to a smaller quantity to find a larger quantity.

smaller quantity+difference=larger quantity \text{smaller quantity} + \text{difference} = \text{larger quantity}

A multiplicative comparison shows how many times as many one quantity is than another. It involves multiplying a smaller quantity by a factor to find a larger quantity.

smaller quantity×factor=larger quantity \text{smaller quantity} \times \text{factor} = \text{larger quantity}

Examples

Section 2

Writing Equations for Multiplicative Comparisons

Property

A multiplicative comparison can be represented by the equation:

Larger Quantity=Multiplier×Smaller Quantity \text{Larger Quantity} = \text{Multiplier} \times \text{Smaller Quantity}

If we let LL be the larger quantity, SS be the smaller quantity, and nn be the multiplier, the general form is L=n×SL = n \times S.

Examples

Book overview

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Chapter 3: Understanding Multiplication and Division

  1. Lesson 1

    Lesson 1: Understanding Multiplication and Division as Equal Groups

  2. Lesson 2Current

    Lesson 2: Multiplicative Comparison

  3. Lesson 3

    Lesson 3: Estimation and Reasonableness in Operations

  4. Lesson 4

    Lesson 4: Interpreting Remainders

  5. Lesson 5

    Lesson 5: Multi-Step Word Problems

Lesson overview

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Section 1

Identifying Additive and Multiplicative Comparisons

Property

An additive comparison shows how much more or less one quantity is than another. It involves adding a difference to a smaller quantity to find a larger quantity.

smaller quantity+difference=larger quantity \text{smaller quantity} + \text{difference} = \text{larger quantity}

A multiplicative comparison shows how many times as many one quantity is than another. It involves multiplying a smaller quantity by a factor to find a larger quantity.

smaller quantity×factor=larger quantity \text{smaller quantity} \times \text{factor} = \text{larger quantity}

Examples

Section 2

Writing Equations for Multiplicative Comparisons

Property

A multiplicative comparison can be represented by the equation:

Larger Quantity=Multiplier×Smaller Quantity \text{Larger Quantity} = \text{Multiplier} \times \text{Smaller Quantity}

If we let LL be the larger quantity, SS be the smaller quantity, and nn be the multiplier, the general form is L=n×SL = n \times S.

Examples

Book overview

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

Continue this chapter

Chapter 3: Understanding Multiplication and Division

  1. Lesson 1

    Lesson 1: Understanding Multiplication and Division as Equal Groups

  2. Lesson 2Current

    Lesson 2: Multiplicative Comparison

  3. Lesson 3

    Lesson 3: Estimation and Reasonableness in Operations

  4. Lesson 4

    Lesson 4: Interpreting Remainders

  5. Lesson 5

    Lesson 5: Multi-Step Word Problems