# Multi-Digit Multiplication

## Objective

Identify multiples and determine if a whole number is a multiple of another number.

## Common Core Standards

### Core Standards

?

• 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.

?

• 3.OA.C.7

## Criteria for Success

?

1. Understand that a multiple is a product of a given number and any other whole number.
2. Find multiples of whole numbers.
3. Determine whether a number is a multiple of another number.
4. Recognize and analyze patterns in the multiples of a number (e.g., all the multiples of 9 have digits whose sum is a multiple of 9).

## Tips for Teachers

?

• The following material is needed for today's lesson:
• Lessons 4—8 focus on gaining familiarity with factors and multiples, which supports the major work of the rest of the unit on multi-digit multiplication by reviewing basic facts within 100 from Grade 3 through the lens of factors and multiples, since “one component of understanding general methods for multiplication is understanding how to compute products of one-digit numbers and multiples of 10, 100, and 1000, [which] extends work in Grade 3 on products of one-digit numbers” (NBT Progression, p. 15).

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 2 (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

?

### Problem 1

Look at the patterns that a skip-counting sequence made:

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
1. What will the next three numbers in the sequence be?
2. Will 62 be in the pattern? How do you know?
3. How many fours are equal to the number 32?

### Problem 2

Which of the following numbers are multiples of 6? Explain or show how you know.

A.  0

B.  3

C.  36

D.  56

E.  72

F.  95

### Problem 3

I am an even number. I am a multiple of 5. I am less than 28. What am I?

#### References

Massachusetts Department of Elementary and Secondary Education Spring 2014 Grade 4 Mathematics TestQuestion 19

Spring 2014 Grade 4 Mathematics Test is made available by the Massachusetts Department of Elementary and Secondary Education. © 2017 Commonwealth of Massachusetts. Accessed Jan. 8, 2018, 1:15 p.m..

Modified by The Match Foundation, Inc.

## Problem Set & Homework

#### Discussion of Problem Set

• In #2, which multiples were the easiest to write: the fives, fours, or sixes? Why?
• What strategy did you use in #3?
• In #5, why isn’t 42 a multiple of 21?
• What number did you come up with for #6? Is there more than one correct answer?
• Which number is a multiple of every number?
• In Anchor Task #1, we found that when counting by fours, the multiples followed a pattern of having 0, 4, 8, 2, and 6 in the ones digit. Does that mean any even number is a multiple of 4?

?

### Problem 1

Select the list of number that are all multiples of 9.

A. 9, 27, 35, 63

B. 9, 48, 81, 90

C. 18, 36, 45, 64

D. 18, 54, 72, 99

#### References

Smarter Balanced Assessment Consortium: Sample Items Item #3527

Item #3527 from Smarter Balanced Assessments' Sample Items is made available by Smarter Balanced Assessment Consortium. © The Regents of the University of California – Smarter Balanced Assessment Consortium. Accessed Dec. 14, 2018, 2:32 p.m..

### Problem 2

What numbers have 24 as a multiple?

?