Learn on PengiEureka Math, Grade 5Chapter 8: The Standard Algorithm for Multi-Digit Whole Number Multiplication

Lesson 1: Write and interpret numerical expressions, and compare expressions using a visual model.

In this Grade 5 Eureka Math lesson from Chapter 8, students learn to write and interpret numerical expressions using parentheses, translating word phrases like "3 times the sum of 26 and 4" into expressions such as 3 × (26 + 4) and modeling them with tape diagrams. Students practice the distributive property by decomposing factors and build estimation skills by rounding multi-digit numbers to find reasonable products. The lesson connects verbal descriptions, symbolic notation, and visual models to deepen understanding of how grouping and order of operations affect the value of an expression.

Section 1

Writing Expressions from Verbal Phrases

Property

To translate verbal phrases that group quantities, use parentheses ()(). Phrases like "the sum of..." or "the difference between..." that are then multiplied or divided require parentheses to ensure the addition or subtraction is performed first. For example, "the sum of aa and bb, times cc" is written as (a+b)×c(a + b) \times c.

Examples

Section 2

Applying the Order of Operations

Property

To evaluate numerical expressions, apply the order of operations:

  1. Parentheses: Calculate any operations inside parentheses first.
  2. Multiplication and Division: Perform these operations from left to right.
  3. Addition and Subtraction: Perform these operations from left to right.

Examples

Book overview

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Chapter 8: The Standard Algorithm for Multi-Digit Whole Number Multiplication

  1. Lesson 1Current

    Lesson 1: Write and interpret numerical expressions, and compare expressions using a visual model.

  2. Lesson 2

    Lesson 2: Convert numerical expressions into unit form as a mental strategy for multi-digit multiplication.

  3. Lesson 3

    Lesson 3: Connect visual models and the distributive property to partial products of the standard algorithm without renaming.

  4. Lesson 4

    Lesson 4: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.

  5. Lesson 5

    Lesson 5: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems.

  6. Lesson 6

    Lesson 6: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.

  7. Lesson 7

    Lesson 7: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Writing Expressions from Verbal Phrases

Property

To translate verbal phrases that group quantities, use parentheses ()(). Phrases like "the sum of..." or "the difference between..." that are then multiplied or divided require parentheses to ensure the addition or subtraction is performed first. For example, "the sum of aa and bb, times cc" is written as (a+b)×c(a + b) \times c.

Examples

Section 2

Applying the Order of Operations

Property

To evaluate numerical expressions, apply the order of operations:

  1. Parentheses: Calculate any operations inside parentheses first.
  2. Multiplication and Division: Perform these operations from left to right.
  3. Addition and Subtraction: Perform these operations from left to right.

Examples

Book overview

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

Continue this chapter

Chapter 8: The Standard Algorithm for Multi-Digit Whole Number Multiplication

  1. Lesson 1Current

    Lesson 1: Write and interpret numerical expressions, and compare expressions using a visual model.

  2. Lesson 2

    Lesson 2: Convert numerical expressions into unit form as a mental strategy for multi-digit multiplication.

  3. Lesson 3

    Lesson 3: Connect visual models and the distributive property to partial products of the standard algorithm without renaming.

  4. Lesson 4

    Lesson 4: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.

  5. Lesson 5

    Lesson 5: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems.

  6. Lesson 6

    Lesson 6: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to check for reasonableness of the product.

  7. Lesson 7

    Lesson 7: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step word problems.