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

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

In this Grade 4 Pengi Math lesson from Chapter 2, students learn to solve addition, subtraction, and additive comparison word problems using the Read-Draw-Write (RDW) process. They use tape diagrams to model part-whole relationships and interpret comparison situations, such as finding a difference or calculating a total when a difference is known.

Section 1

Solving Addition Word Problems Using Tape Diagrams

Property

A tape diagram models an addition problem by representing the addends as parts of a whole. The total, or sum, is the unknown whole. This relationship can be shown with the equation: $Part + Part = Whole$ .

Examples

Section 2

Modeling Subtraction with Tape Diagrams

Property

A tape diagram for subtraction illustrates the relationship $Whole = Part + Part$ . In a subtraction problem, the total amount is the $Whole$ , and the number being subtracted is a known $Part$ . The goal is to find the unknown $Part$ , which is the difference:

Whole - Part_{known} = Part_{unknown}

Examples

Section 3

Modeling Additive Comparisons with Tape Diagrams

Property

To find the difference ( $D$ ) between a larger quantity ( $L$ ) and a smaller quantity ( $S$ ) in an additive comparison problem, you subtract the smaller quantity from the larger quantity.

L - S = D

Examples

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

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Lesson 1
Lesson 1: Standard Addition Algorithm and Regrouping
Learn Practice
Lesson 2
Lesson 2: Standard Subtraction Algorithm and Decomposition
Learn Practice
Lesson 3
Lesson 3: Subtraction Across Zeros and Verification
Learn Practice
Lesson 4Current
Lesson 4: Modeling Addition, Subtraction, and Comparison with Tape Diagrams
Learn Practice
Lesson 5
Lesson 5: Multi-Step Problem Solving and Assessing Reasonableness
Learn Practice

Lesson overview

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Section 1

Solving Addition Word Problems Using Tape Diagrams

Property

Examples

Section 2

Modeling Subtraction with Tape Diagrams

Property

Whole - Part_{known} = Part_{unknown}

Examples

Section 3

Modeling Additive Comparisons with Tape Diagrams

Property

To find the difference ( $D$ ) between a larger quantity ( $L$ ) and a smaller quantity ( $S$ ) in an additive comparison problem, you subtract the smaller quantity from the larger quantity.

L - S = D

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

Back to Pengi Math (Grade 4)

Lesson 1
Lesson 1: Standard Addition Algorithm and Regrouping
Learn Practice
Lesson 2
Lesson 2: Standard Subtraction Algorithm and Decomposition
Learn Practice
Lesson 3
Lesson 3: Subtraction Across Zeros and Verification
Learn Practice
Lesson 4Current
Lesson 4: Modeling Addition, Subtraction, and Comparison with Tape Diagrams
Learn Practice
Lesson 5
Lesson 5: Multi-Step Problem Solving and Assessing Reasonableness
Learn Practice

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Solving Addition Word Problems Using Tape Diagrams

Property

Examples

Section 2

Modeling Subtraction with Tape Diagrams

Property

Whole - Part_{known} = Part_{unknown}

Examples

Section 3

Modeling Additive Comparisons with Tape Diagrams

Property

To find the difference ( $D$ ) between a larger quantity ( $L$ ) and a smaller quantity ( $S$ ) in an additive comparison problem, you subtract the smaller quantity from the larger quantity.

L - S = D

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

Back to Pengi Math (Grade 4)

Lesson 1
Lesson 1: Standard Addition Algorithm and Regrouping
Learn Practice
Lesson 2
Lesson 2: Standard Subtraction Algorithm and Decomposition
Learn Practice
Lesson 3
Lesson 3: Subtraction Across Zeros and Verification
Learn Practice
Lesson 4Current
Lesson 4: Modeling Addition, Subtraction, and Comparison with Tape Diagrams
Learn Practice
Lesson 5
Lesson 5: Multi-Step Problem Solving and Assessing Reasonableness
Learn Practice

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

Property

Examples

Property

Examples

Property

Examples

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

Lesson 1: Standard Addition Algorithm and Regrouping

Lesson 2: Standard Subtraction Algorithm and Decomposition

Lesson 3: Subtraction Across Zeros and Verification

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

Lesson 5: Multi-Step Problem Solving and Assessing Reasonableness

Lesson overview

Property

Examples

Property

Examples

Property

Examples

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

Lesson 1: Standard Addition Algorithm and Regrouping

Lesson 2: Standard Subtraction Algorithm and Decomposition

Lesson 3: Subtraction Across Zeros and Verification

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

Lesson 5: Multi-Step Problem Solving and Assessing Reasonableness

Lesson 1: Standard Addition Algorithm and Regrouping

Lesson 2: Standard Subtraction Algorithm and Decomposition

Lesson 3: Subtraction Across Zeros and Verification

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

Lesson 5: Multi-Step Problem Solving and Assessing Reasonableness