# Multi-Digit Multiplication

## Objective

Multiply multiples of 10, 100, and 1,000 by one-digit numbers. Estimate multi-digit products by rounding numbers to their largest place value.

## Common Core Standards

### Core Standards

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• 4.NBT.B.5 — Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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• 3.NBT.A.3

• 4.NBT.A.1

• 3.OA.C.7

## Criteria for Success

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1.  Multiply multiples of 10, 100, and 1,000 by single digits.
2. Identify patterns in multiplication of multiples of 10, 100, and 1,000 by single digits.
3. Estimate products of one-digit by two-digit, three-digit, and four-digit multiplication by rounding the multi-digit values to their largest place value.
4. Understand that just rounding the multi-digit factor and not changing the one-digit factor will result in the most accurate estimate.

## Tips for Teachers

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• The following material is needed for today's lesson: base ten blocks

In Lessons 10—15, students estimate products of a whole number of up to four digits by a one-digit whole number by rounding the largest factor, thus connecting the work of 4.NBT.3 across clusters to the work of 4.NBT.4, as well as preparing students to assess reasonableness in the context of multi-step word problems (4.OA.3).

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 1 and Anchor Task 3 (benefit from worked examples). Find more guidance on adapting our math curriculum for remote learning here.

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## Anchor Tasks

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### Problem 1

1. Solve.

a. 4 x 3

b. 4 x 30

c. 4 x 300

d. 4 x 3,000

2. What do you notice about #1? What do you wonder?

#### Guiding Questions

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#### References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic B > Lesson 5Concept Development

Grade 4 Mathematics > Module 3 > Topic B > Lesson 5 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

### Problem 2

1. Solve.

a. 5 x 4

b. 5 x 40

c. 5 x 400

d. 5 x 4,000

2. What do you notice about #1? What do you wonder?

#### Guiding Questions

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#### References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic B > Lesson 5Concept Development

Grade 4 Mathematics > Module 3 > Topic B > Lesson 5 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

### Problem 3

Estimate the following products.

a. 4 x 42

b. 783 x 7

c. 5,182 x 8

#### Guiding Questions

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## Problem Set & Homework

#### Discussion of Problem Set

• What pattern did you notice while solving #1?
• What made #2 (i)–(l) particularly more challenging?
• How did the last lesson prepare you for this lesson?
• Think about the problems we solved during the lesson and the problems you solved in the Problem Set. When does the number of zeros in the factors not equal the number of zeros in the product?
• For each problem in #4, would you expect the actual product to be greater or less than your estimate? Why?
• How can you tell, just by looking at the size of the factors and the size of the product Peter found, that his answer is unreasonable?

## Target Task

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### Problem 1

Find the following products.

 a.   30 x 3 b.   6 x 400 c.   8 x 5,000

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic B > Lesson 5Exit Ticket, Question #3

Grade 4 Mathematics > Module 3 > Topic B > Lesson 5 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

### Problem 2

Estimate the following products.

 a.   8 x 84 b.   458 x 4 c.   2 x 9,340

### Mastery Response

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## Additional Practice

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