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

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

In this Grade 5 Eureka Math lesson, students connect area models and the distributive property to partial products of the standard algorithm with renaming. Using problems like 64 × 73, they decompose multi-digit factors, identify how each partial product from the area model corresponds to a step in the standard algorithm, and practice renaming tens and hundreds during multiplication. The lesson builds fluency with multi-digit whole number multiplication while reinforcing the relationship between visual models and symbolic procedures.

Section 1

Multiplying Mixed Numbers with an Area Model

Property

To multiply two numbers using an area model, decompose each factor into its place value components.
The total product is the sum of the partial products obtained by multiplying each component of the first factor by each component of the second factor.
For factors (a+b)(a+b) and (c+d)(c+d), the product is:

(a+b)×(c+d)=(a×c)+(a×d)+(b×c)+(b×d)(a+b) \times (c+d) = (a \times c) + (a \times d) + (b \times c) + (b \times d)

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Multiplying Mixed Numbers with an Area Model

Property

To multiply two numbers using an area model, decompose each factor into its place value components.
The total product is the sum of the partial products obtained by multiplying each component of the first factor by each component of the second factor.
For factors (a+b)(a+b) and (c+d)(c+d), the product is:

(a+b)×(c+d)=(a×c)+(a×d)+(b×c)+(b×d)(a+b) \times (c+d) = (a \times c) + (a \times d) + (b \times c) + (b \times d)

Examples