# MAFS.4.OA.2.4

Investigate factors and multiples.

1. Find all factor pairs for a whole number in the range 1–100.
2. 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.
3. Determine whether a given whole number in the range 1–100 is prime or composite.
General Information
Subject Area: Mathematics
Domain-Subdomain: Operations and Algebraic Thinking
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Gain familiarity with factors and multiples. (Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Items may only contain whole numbers between 1—100. Vocabulary may include prime, composite, factor, or multiple.
• Calculator :

No

• Context :

Allowable

Sample Test Items (3)

• Test Item #: Sample Item 3
• Question:

Determine whether each number is prime or composite. • Difficulty: N/A
• Type: MI: Matching Item

## Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022 (current), 2022 and beyond)
5012055: Grade 3 Accelerated Mathematics (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.4.OA.2.AP.4a: Identify multiples for a whole number (e.g., The multiples of 2 are 2, 4, 6, 8, 10…).
MAFS.4.OA.2.AP.4b: Identify factors of whole numbers within 30.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Assessments

Sample 4 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 1 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

## Educational Games

Arithmetic Workout:

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game.

Type: Educational Game

Sigma Prime: A Prime Factorization Game:

This fun and engaging game will test your knowledge of whole numbers as prime or composite.  As you shoot the asteroids with a particular factor, the asteroids will break down by that chosen factor.  Keep shooting the correct factors to totally eliminate the asteroids.  But be careful, shooting the wrong factor has consequences!

Type: Educational Game

The Factor Game:

Test your factors skills with this fun factor game. Take turns choosing numbers from the board and identifying its factors. Outscore your opponent by identifying factors and using strategy to limit their score. Play against the computer or a friend.

Type: Educational Game

Product Game (Factors and Multiples):

This interactive game for two players develops students' fluency with multiplication facts, their understanding of the relationship between factors and products, and their strategic thinking. On a board displaying all the factors of the numbers 1-9, players take turns moving markers on the factor list and claiming their products. The first player to get four in a row wins the game.

Type: Educational Game

## Formative Assessments

Multiples of Six:

Students determine if a given number is a multiple of six, both with and without context.

Type: Formative Assessment

Find All the Factor Pairs:

Students are asked to find all the factor pairs for each of four given numbers.

Type: Formative Assessment

Factor Pairs:

Students are asked to find all the factor pairs of a given number and identify the number as a multiple of the factors.

Type: Formative Assessment

Prime or Composite:

Students are asked to determine whether each of four given numbers is prime or composite and justify their choices.

Type: Formative Assessment

## Lesson Plans

Factor Rainbows/Prime and Composite Story:

The students will learn one strategy for finding the factors of whole numbers. After creating factor rainbows students will learn the difference between prime and composite numbers. To integrate writing students will create a story using their chosen number.

Type: Lesson Plan

Fantastic Factors:

In this lesson, students will start out using manipulatives to create arrays which will be used to find factor pairs. Students will use a T-Chart to determine the factor pairs of numbers. Students will then use their T-Charts to determine if a number is prime or composite.

Type: Lesson Plan

Hooray for arrays!:

Students will identify prime and composite numbers through arrays. The lesson begins with a fun situational story.

Type: Lesson Plan

Finding a Few Friendly Factors:

Students will find factors for a given number 1-100. This activity should lead to prime and composite numbers.
Students will have the option of using manipulatives: counters, base ten blocks, Van De Walle matrix, foldables and or Geoboards.

Type: Lesson Plan

Using Rectangles to Find Prime and Composite Numbers:

In this lesson, students will be using rectangles to find prime and composite numbers.  Students will draw different rectangles for the area of a given set of numbers.  They will determine the factor pairs for each number in the given set and use them to discover the meaning of prime and composite numbers.

Type: Lesson Plan

Factor That! Part 1:

This is a foundational lesson in which the students will visually see the relationship between factors and multiples. As a result of this hands on lesson and guided discussion, they will learn to identify the factors of a given number.

This is lesson one of a 5 lesson unit. It can be used independently or as part of a week long unit.

Type: Lesson Plan

Creating Factor Pair "Trees":

In this lesson, students will practice identifying factor pairs of whole numbers. Students will then draw a triangle around their factor work so that it resembles a triangular tree. Students will then circle all of the prime numbers inside the tree. The circles might represent the balls or ornaments on a holiday tree if doing this lesson around the holidays. This lesson does not teach an understanding of factors or prime numbers but is, rather, a practice of the students' knowledge of these concepts.

Type: Lesson Plan

Fun with Factors:

This is an introductory lesson addressing factors for number 1-20. Factoring will lead students to discover differences and similarities between prime and composite numbers. Students will also discuss five claims about factors, prime, and composite numbers and create support from examples and non-examples to determine whether these claims are valid or invalid.

Type: Lesson Plan

Searching for the Primes:

Students will use a 100s chart to sort out the prime numbers under 100 using the Sieve of Eratosthenes method.

Type: Lesson Plan

Prime Factorization - From Fingerprints to Factorprints:

This activity provides an introduction to composite numbers and prime numbers through factorization.

Type: Lesson Plan

## Original Student Tutorial

Prime and Composite Backyard Dilemma :

Discover what makes prime and composite numbers unique thanks to an interesting backyard problem in this interactive tutorial.

Type: Original Student Tutorial

Identifying Multiples:

The goal of this task is to work on finding multiples of some whole numbers on a multiplication grid. After shading in the multiples of 2, 3, and 4 on the table, students will see a key difference.  The focus can be on identifying patterns or this can be an introduction or review of prime and composite numbers.

## Teaching Idea

Factors:

This lesson is designed to develop students' abilities to find factors of whole numbers. The lesson also introduces prime numbers. This lesson provides links to discussions and activities related to factors as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one. Note, reading level is not indicated because the lesson does not include student reading material.

Type: Teaching Idea

## Tutorials

Recognizing Prime and Composite Numbers:

This Khan Academy tutorial video reviews how to determine if a number is prime or composite.

Type: Tutorial

Factoring with the Factor Tree:

This Java applet presents a composite number, and prompts you to factor it -- one step at a time. Enter one factor, prime or another composite; the applet calculates the remaining factor, and branches two boxes below any composite factor so that you may proceed factoring until you obtain the full factorization into primes, which the applet colors in green. Click the "Repeat problem" button to see that different factor trees for a given number still result in the same prime factorization.

Type: Tutorial

## MFAS Formative Assessments

Factor Pairs:

Students are asked to find all the factor pairs of a given number and identify the number as a multiple of the factors.

Find All the Factor Pairs:

Students are asked to find all the factor pairs for each of four given numbers.

Multiples of Six:

Students determine if a given number is a multiple of six, both with and without context.

Prime or Composite:

Students are asked to determine whether each of four given numbers is prime or composite and justify their choices.

## Original Student Tutorials Mathematics - Grades K-5

Prime and Composite Backyard Dilemma :

Discover what makes prime and composite numbers unique thanks to an interesting backyard problem in this interactive tutorial.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorial

Prime and Composite Backyard Dilemma :

Discover what makes prime and composite numbers unique thanks to an interesting backyard problem in this interactive tutorial.

Type: Original Student Tutorial

## Educational Games

Arithmetic Workout:

This tutorial will help you to brush up on your multiplication, division and factoring skills with this exciting game.

Type: Educational Game

Sigma Prime: A Prime Factorization Game:

This fun and engaging game will test your knowledge of whole numbers as prime or composite.  As you shoot the asteroids with a particular factor, the asteroids will break down by that chosen factor.  Keep shooting the correct factors to totally eliminate the asteroids.  But be careful, shooting the wrong factor has consequences!

Type: Educational Game

The Factor Game:

Test your factors skills with this fun factor game. Take turns choosing numbers from the board and identifying its factors. Outscore your opponent by identifying factors and using strategy to limit their score. Play against the computer or a friend.

Type: Educational Game

Product Game (Factors and Multiples):

This interactive game for two players develops students' fluency with multiplication facts, their understanding of the relationship between factors and products, and their strategic thinking. On a board displaying all the factors of the numbers 1-9, players take turns moving markers on the factor list and claiming their products. The first player to get four in a row wins the game.

Type: Educational Game

Identifying Multiples:

The goal of this task is to work on finding multiples of some whole numbers on a multiplication grid. After shading in the multiples of 2, 3, and 4 on the table, students will see a key difference.  The focus can be on identifying patterns or this can be an introduction or review of prime and composite numbers.

## Tutorial

Recognizing Prime and Composite Numbers:

This Khan Academy tutorial video reviews how to determine if a number is prime or composite.

Type: Tutorial

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.