Learn on PengiEureka Math, Grade 4Chapter 9: Multiplicative Comparison Word Problems

Lesson 3: Demonstrate understanding of area and perimeter formulas by solving multi-step real-world problems.

In this Grade 4 Eureka Math lesson from Chapter 9, students apply area and perimeter formulas to solve multi-step real-world word problems involving multiplicative comparisons. Using the RDW (Read, Draw, Write) approach, they work through scenarios such as comparing screen dimensions using the formula P = 2 × (l + w) and calculating remaining floor space by finding the difference between two rectangular areas. The lesson builds on prior work with unknown factors and prepares students to reason about how scaling dimensions affects both area and perimeter.

Section 1

Translate Word Problems for Area and Perimeter

Property

To solve word problems, first identify whether the context requires area (covering a surface) or perimeter (distance around an edge). Then, translate multiplicative comparison phrases into algebraic expressions to define the dimensions. For example, if a rectangle's length (ll) is described as 'nn times its width (ww)', the relationship is written as l=n×wl = n \times w.

Examples

Section 2

Calculate the Area of Composite Shapes by Subtraction

Property

To find the area of a composite shape formed by removing a smaller rectangle from a larger one, subtract the area of the smaller rectangle from the area of the larger rectangle.

Acomposite=AlargeAsmallA_{composite} = A_{large} - A_{small}

Examples

Book overview

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Chapter 9: Multiplicative Comparison Word Problems

  1. Lesson 1

    Lesson 1: Investigate and use the formulas for area and perimeter of rectangles.

  2. Lesson 2

    Lesson 2: Solve multiplicative comparison word problems by applying the area and perimeter formulas.

  3. Lesson 3Current

    Lesson 3: Demonstrate understanding of area and perimeter formulas by solving multi-step real-world problems.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Translate Word Problems for Area and Perimeter

Property

To solve word problems, first identify whether the context requires area (covering a surface) or perimeter (distance around an edge). Then, translate multiplicative comparison phrases into algebraic expressions to define the dimensions. For example, if a rectangle's length (ll) is described as 'nn times its width (ww)', the relationship is written as l=n×wl = n \times w.

Examples

Section 2

Calculate the Area of Composite Shapes by Subtraction

Property

To find the area of a composite shape formed by removing a smaller rectangle from a larger one, subtract the area of the smaller rectangle from the area of the larger rectangle.

Acomposite=AlargeAsmallA_{composite} = A_{large} - A_{small}

Examples

Book overview

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

Continue this chapter

Chapter 9: Multiplicative Comparison Word Problems

  1. Lesson 1

    Lesson 1: Investigate and use the formulas for area and perimeter of rectangles.

  2. Lesson 2

    Lesson 2: Solve multiplicative comparison word problems by applying the area and perimeter formulas.

  3. Lesson 3Current

    Lesson 3: Demonstrate understanding of area and perimeter formulas by solving multi-step real-world problems.