# Multi-Digit Multiplication

## Objective

Find factor pairs for numbers to 100 and recognize that a whole number is a multiple of each of its factors.

## Common Core Standards

### Core Standards

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• 4.OA.A.3 — Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

• 4.OA.B.4 — Find all factor pairs for a whole number in the range 1—100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1—100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1—100 is prime or composite.

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• 3.OA.C.7

## Criteria for Success

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1. Understand that factors are numbers that when multiplied together give a certain product (e.g., 3 is a factor of 24 since 3 x 8 = 24).
2. Understand that a factor pair is the pair of numbers that when multiplied together give a certain product (e.g., 2 and 12 are a factor pair of 24 since 2 x 12 = 24).
3. Find all factors of a certain number, ensuring that the list is comprehensive.
4. Understand that a whole number is a multiple of each of its factors (e.g., 24 is a multiple of 2, 3, and 12 [among other numbers] since they are each a factor of 24).

## Tips for Teachers

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• The following material is needed for today's lesson: Square tiles
• Students learned the term “factor” in Grade 3 but not the term “factor pair”.
• Most, but not all, of the values here for which students have to find factors are ones whose factors are less than 10 to be within the scope of 3.OA.7 and in some cases less than 12 to approach 4.OA.3a. This serves two purposes: (1) it allows students to continue to review the basic facts, which they’ll depend on later in the unit when they get to multi-digit multiplication, and (2) while they have strategies for determining whether a number, a, is a multiple of another number, b, (i.e., whether b is a factor of a), they don’t yet have the computational skills to find a’s factor pair. Students can find it using brute force (e.g., skip-counting by one factor to see how many count-bys are needed to reach the target value), but since this isn’t the main purpose of this lesson, cases involving factors beyond 10 are limited. Students will see more examples involving factor pairs that are beyond their 1–10 facts later in this unit and in Unit 3.
• Before the Problem Set, you could have students play the "Factor Game" by NCTM.

#### Remote Learning Guidance

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

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Mr. Duffy wants to set up the desks in his room in rows and columns. There are 28 desks in his classroom. What are the different ways he could make rows and columns with 28 desks? Draw arrays to represent the possible arrangements.

### Problem 2

1. Find all of the factors of 18.
2. How can you be sure your list is exhaustive? In other words, how can you be sure there are no other factors that you haven’t listed?

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic F > Lesson 22Concept Development

Grade 4 Mathematics > Module 3 > Topic F > Lesson 22 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

1. Find all of the factors of 60.
2. Find all of the numbers that have 60 as a multiple.
3. What do you notice about both of your lists above? What do you wonder?

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic F > Lesson 22Concept Development

Grade 4 Mathematics > Module 3 > Topic F > Lesson 22 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 Set & Homework

#### Discussion of Problem Set

• Which number is a factor of every number?
• What were the factors of 13 in #1f? How do you know there aren’t any more factors than that?
• Compare the factors in #1(e) and 1(k). Twenty-four is double 12. What do you notice about their factors? Compare the factors in Problem 1(d) and 1(i). Eighteen is double 9. What do you notice about their factors?
• In #1, what numbers have an odd number of factors? Why is that so? How is this related to your answer in #4?
• What do you notice about the answers to each part of #3? What do you wonder?
• Explain the difference between factors and multiples.
• Are the following true?
• 3 is a factor of 12.
• 12 is a multiple of 3.
• 12 is divisible by 3.

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### Problem 1

Record the factors of the given numbers as multiplication sentences and as a list in order from least to greatest.

 Multiplication Sentences Factors a. 9 The factors of 9 are: b 12 The factors of 12 are: c. 19 The factors of 19 are:

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 3 > Topic F > Lesson 22Exit Ticket

Grade 4 Mathematics > Module 3 > Topic F > Lesson 22 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. List the numbers that have 42 as a multiple.
2. What are the factors of 42?
3. Are your two lists the same? Why or why not?

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