## Engage NY Eureka Math 4th Grade Module 3 Lesson 25 Answer Key

### Eureka Math Grade 4 Module 3 Lesson 25 Problem Set Answer Key

Question 1.
a. Circle the first unmarked number.
b. Cross off every multiple of that number except the one you circled. If it’s already crossed off, skip it.
c. Repeat Steps (a) and (b) until every number is either circled or crossed off.
d. Shade every crossed out number in orange.

a. Circled the first unmarked numbers
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,

b. Crossed off every multiple of that number except the one I circled as 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99 and 100, and If it’s already crossed off, skipped it.

c. Repeated Steps (a) and (b) until every number is either circled or crossed off,

Explanation:
Repeated Steps (a) and (b) until every number is either circled or crossed off as shown above.

d. Shaded every crossed out number in orange,

Explanation:
Shaded every crossed out number in orange as shown in the picture above.

Question 2.
a. List the circled numbers.
The circled numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 respectively,

b. Why were the circled numbers not crossed off along the way?
The circled numbers were not crossed off along the way because they are not the multiples of any other numbers except 1 and themselves,

Explanation:
As shown above the circled numbers were not crossed off along the way because they are not the multiples of any other numbers except 1 and themselves, these numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 respectively.

c. Except for the number 1, what is similar about all of the numbers that were crossed off?
The crossed off numbers are all composite numbers,

Explanation:
Except for the number 1, the similarity about all of the numbers that were crossed off are composite numbers, composite numbers are the numbers which have more than two factors they are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99 and 100 all these numbers have more than two factors.

d. What is similar about all of the numbers that were circled?
The circled numbers are all prime numbers,

Explanation:
The similarity  about all of the numbers that were circled are they are all prime numbers.
Prime numbers are numbers that have only 2 factors:
1 and themselves, So all these numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 are prime numbers.

### Eureka Math Grade 4 Module 3 Lesson 25 Exit Ticket Answer Key

Use the calendar below to complete the following:

1. Cross off all composite numbers.
2. Circle all of the prime numbers.
3. List any remaining numbers.

1. Crossed off all composite numbers as 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28 and 30,
2. Circled all of the prime numbers as 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and 31,
3. 1 is the only remaining number,

### Eureka Math Grade 4 Module 3 Lesson 25 Homework Answer Key

Question 1.
A student used the sieve of Eratosthenes to find all prime numbers less than 100. Create a step-by-step set of directions to show how it was completed.
Use the word bank to help guide your thinking as you write the directions. Some words may be used just once, more than once, or not at all.

Directions for completing the sieve of Eratosthenes activity:
A student used the sieve of Eratosthenes to find all prime numbers less than 100. Created a step-by-step set of directions to show how it is completed,
prime numbers are numbers that have only 2 factors: 1 and themselves, So all these numbers 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 are prime numbers.

Question 2.
What do all of the numbers that are crossed out have in common?
The numbers that are crossed out have in common are composite numbers,

Explanation:
The numbers that are crossed out have in common are composite numbers they are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99 and 100.

Question 3.
What do all of the circled numbers have in common?
The circled numbers are all prime numbers,

Explanation:
The similarity  about all of the numbers that were circled are they are all prime numbers.
Prime numbers are numbers that have only 2 factors: 1 and themselves, So all these numbers 2, 3, 5, 7, 11, 13, 17,
19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 are prime numbers.

Question 4.
There is one number that is neither crossed out nor circled.
Why is it treated differently?