# Multi-Digit Multiplication

## Objective

Determine whether a given number is prime or composite.

## 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 prime number is a whole number that has exactly two factors, 1 and itself.
2. Understand that a composite number is a whole number that can be written as a product of two whole numbers, neither of which is itself.
3. Understand that a square number is a whole number that has a factor whose factor pair is itself.
4. Determine whether a given number is prime or composite.
5. Determine whether a given number is a square number.
6. Understand 0 and 1 as special cases that are neither prime nor composite, but both are square.

## Tips for Teachers

?

• The following material is needed for today's lesson: Dice

Students will need a die or, ideally, a pair of dice for the Problem Set.

#### 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

Ms. Cole also wants to set up the desks in her room in rows and columns. There are 23 desks in her classroom. What are the different ways she could make rows and columns with 23 desks? Draw arrays to represent the possible arrangements.

### Problem 2

A composite number is a whole number that can be written as a product of two whole numbers, neither of which is itself.

Is 28, the number of students in Mr. Duffy’s class from Lesson 6, a prime or composite number? How do you know?

#### 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

A square number is a whole number that has a factor whose factor pair is itself.

Is 81 a prime, composite, or square number, or some combination of the above?

### Problem 4

Determine whether each of the following numbers are prime, composite, and/or square.

a.  74

b.  61

c.  49

d.  30

e.  2

f.  1

g.  0

## Problem Set & Homework

#### Discussion of Problem Set

• Look at #5. What types of numbers appeared only once in the table? Was this true of all square numbers? Why or why not? Which numbers appeared most frequently? What numbers did not appear at all?
• Look at #6. What number did you use to prove that Bryan’s claim is false? Are there other numbers that would have worked?
• Do even or odd numbers have more prime numbers? Why?
• Were each of the statements in #8 always, sometimes, or never true?

?

Determine whether the following numbers are prime or composite. Explain your reasoning.

1.      17
2.      32
3.      53

### Mastery Response

? 