Learn on PengiEureka Math, Grade 4Chapter 16: Multiplication of Two-Digit by Two-Digit Numbers

Lesson 1: Multiply two-digit multiples of 10 by two-digit numbers using a place value chart.

In this Grade 4 Eureka Math lesson, students learn to multiply two-digit multiples of 10 by two-digit numbers using a place value chart, building on their understanding of unit form and the associative property. Students explore how expressions like (4 × 10) × 22 and 40 × 22 represent the same product, reinforcing place value concepts such as tens multiplied by ones yielding hundreds. The lesson connects area models from prior topics to the place value chart as a new strategy for solving two-digit by two-digit multiplication problems.

Section 1

Visualizing the Associative Property on a Place Value Chart

Property

The associative property of multiplication allows us to regroup factors. When multiplying by a multiple of 10, we can change the order of operations to make the problem easier to model on a place value chart:

(a×10)×b=a×(10×b)(a \times 10) \times b = a \times (10 \times b)

Examples

Section 2

Multiplying Using Unit Form

Property

To multiply numbers in unit form, multiply the digits and then multiply the place value units.

(a tens)×(b tens)=(a×b) hundreds(a \text{ tens}) \times (b \text{ tens}) = (a \times b) \text{ hundreds}
(a tens)×(b ones)=(a×b) tens(a \text{ tens}) \times (b \text{ ones}) = (a \times b) \text{ tens}

Examples

Section 3

Multiply Using the Distributive Property

Property

The distributive property of multiplication states that multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.

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

Examples

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Chapter 16: Multiplication of Two-Digit by Two-Digit Numbers

  1. Lesson 1Current

    Lesson 1: Multiply two-digit multiples of 10 by two-digit numbers using a place value chart.

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  2. Lesson 2

    Lesson 2: Multiply two-digit multiples of 10 by two-digit numbers using the area model.

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  3. Lesson 3

    Lesson 3: Multiply two-digit by two-digit numbers using four partial products.

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  4. Lesson 4

    Lesson 4: Transition from four partial products to the standard algorithm for two-digit by two-digit multiplication.

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  5. Lesson 5

    Lesson 5: Transition from four partial products to the standard algorithm for two-digit by two-digit multiplication.

    LearnPractice

Lesson overview

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Section 1

Visualizing the Associative Property on a Place Value Chart

Property

The associative property of multiplication allows us to regroup factors. When multiplying by a multiple of 10, we can change the order of operations to make the problem easier to model on a place value chart:

(a×10)×b=a×(10×b)(a \times 10) \times b = a \times (10 \times b)

Examples

Section 2

Multiplying Using Unit Form

Property

To multiply numbers in unit form, multiply the digits and then multiply the place value units.

(a tens)×(b tens)=(a×b) hundreds(a \text{ tens}) \times (b \text{ tens}) = (a \times b) \text{ hundreds}
(a tens)×(b ones)=(a×b) tens(a \text{ tens}) \times (b \text{ ones}) = (a \times b) \text{ tens}

Examples

Section 3

Multiply Using the Distributive Property

Property

The distributive property of multiplication states that multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products.

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

Examples

Book overview

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

Continue this chapter

Chapter 16: Multiplication of Two-Digit by Two-Digit Numbers

  1. Lesson 1Current

    Lesson 1: Multiply two-digit multiples of 10 by two-digit numbers using a place value chart.

    LearnPractice
  2. Lesson 2

    Lesson 2: Multiply two-digit multiples of 10 by two-digit numbers using the area model.

    LearnPractice
  3. Lesson 3

    Lesson 3: Multiply two-digit by two-digit numbers using four partial products.

    LearnPractice
  4. Lesson 4

    Lesson 4: Transition from four partial products to the standard algorithm for two-digit by two-digit multiplication.

    LearnPractice
  5. Lesson 5

    Lesson 5: Transition from four partial products to the standard algorithm for two-digit by two-digit multiplication.

    LearnPractice