Standard

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.

Student language:

• "I can find all factor pairs for a number from 1 to 100."
• "I can determine whether a given whole number up to 100 is a prime or composite number."

Explanation

About the Math, Learning Targets, and Rigor

This standard requires students to demonstrate understanding of factors and multiples of whole numbers.

• Students should understand the process of finding factor pairs so they can do this for any number 1 – 100. For example, factor pairs for 96: 1 & 96, 2 & 48, 3 & 32, 4 & 24, 6 & 16, 8 & 12.
• To determine if a number between1-100 is a multiple of a given one-digit number, some helpful hints include the following:
  • all even numbers are multiples of 2
  • all even numbers that can be halved twice (with a whole number result) are multiples of 4
  • all numbers ending in 0 or 5 are multiples of 5

This standard also refers to prime and composite numbers.

• Prime numbers have exactly two factors, the number one and the number itself. For example, the number 17 has the factors of 1 and 17. (A common misconception is that the number 1 is prime, when in fact; it is neither prime nor composite. )
• Composite numbers have more than two factors. For example, 8 has the factors 1, 2, 4, and 8. (A common misconception is that all prime numbers are odd numbers. This is not true, since the number 2 has only 2 factors, 1 and 2, and is also an even number.)

Students investigate whether numbers are prime or composite by

• building rectangles (arrays) with the given area and finding which numbers have more than two rectangles (e.g. 7 can be made into only 2 rectangles, 1 x 7 and 7 x 1, therefore it is a prime number)
• finding factors of the number

Resources

Videos

• Khan Academy (scroll to find 4.OA.4, click on a skill, find videos on left side in each skill)
• Learn Zillion
  • Videos
• Virtual Nerd

EngageNY Lessons

• Module 3, Topic F, Lesson 22: Find factor pairs for numbers to 100 and use understanding of factors to define prime and composite.
• Module 3, Topic F, Lesson 23: Use division and the associative property to test for factors and observe patterns.
• Module 3, Topic F, Lesson 24: Determine whether a whole number is a multiple of another number.
• Module 3, Topic F, Lesson 25: Explore properties of prime and composite numbers to 100 by using multiples.

Extra Practice

• North Carolina Tasks
• Illustrative Math Tasks
• Howard County Tasks
  • Click on 4th grade at bottom, then 4.OA.4
• Common Core Sheets

Released Assessment Questions

PARCC

4.OA.4-1

Find all factor pairs for a whole number in the range 1–100.

4.OA.4-2

Recognize that a whole number is a multiple of each of its factors.

4.OA.4-3

Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number.

4.OA.4-4

Determine whether a given whole number in the range 1–100 is prime or composite.

Performance Indicators: 4.OA.4-1, 4.OA.4-2, 4.OA.4-3, 4.OA.4-4

Level 5: Exceeds Expectations

Recognizes that a whole number is a multiple of each of its factors, and within the range of 1-100, finds all factor pairs and determines multiples of whole numbers. Determines whether a whole number in the range 1-100 is prime or composite.

Level 4: Meets Expectations

Recognizes that a whole number is a multiple of each of its factors, and within the range of 1-100 finds factor pairs or determines multiples of whole numbers. Determines whether a whole number in the range 1-100 is prime or composite.

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