# MAFS.6.NS.2.4

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
General Information
Subject Area: Mathematics
Domain-Subdomain: The Number System
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Compute fluently with multi-digit numbers and find common factors and multiples. (Additional 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 :
Whole numbers less than or equal to 100. Least common multiple of two whole numbers less than or equal to 12.
• Calculator :

No

• Context :

No context

Sample Test Items (5)

• Test Item #: Sample Item 4
• Question:

An equation is shown. What factor is missing from the equation?

• Difficulty: N/A
• Type: EE: Equation Editor

## Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205020: M/J Grade 6 Accelerated Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond)
7912110: Fundamental Explorations in Mathematics 1 (Specifically in versions: 2013 - 2015, 2015 - 2017 (course terminated))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.6.NS.2.AP.4a: Find the greatest common factor of two numbers that are less than or equal to 50.
MAFS.6.NS.2.AP.4b: Find the least common multiple of two whole numbers that are less than or equal to 10.
MAFS.6.NS.2.AP.4c: Use the distributive property to express the sum of two whole numbers.

## Related Resources

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

## Assessments

Sample 2 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Sample 1 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

## Formative Assessments

Using the Distributive Property:

Students are asked to rewrite 36 + 42 in the form a(b + c) where a is the greatest common factor of 36 and 42.

Type: Formative Assessment

Least Common Multiples:

Students are asked to find the least common multiple of 8 and 12 and to explain how they found their answers.

Type: Formative Assessment

Greatest Common Factors:

Students are given two whole numbers less than or equal to 100 and asked to find the greatest common factor.

Type: Formative Assessment

## Lesson Plans

The Venn Factor:

This lesson plan provides the teacher with an activity to help students calculate the Greatest Common Factor of two or more positive integers and develop a definition based on their exploration. Students find the prime factorization of two positive numbers using factor trees and Venn diagrams to sort the prime factors. The plan includes learning objectives, materials needed, questions to ask students, assessment options, extensions, teacher self-reflection questions, and further references.

Type: Lesson Plan

Can You Find the Relationship?:

In this lesson students will first define in their own words what the greatest common factor (GCF) and least common multiple (LCM) mean. They will take this understanding and apply it to solving GCF and LCM word problems. Students will then illustrate their understanding by creating posters based on their word problems. There are examples of different types of methods, online games, a rubric, and a power point to summarize this two day lesson.

Type: Lesson Plan

Can you say that another way?:

This lesson covers the second part of this standard. Students rewrite the math standard in their own words to better understand what their learning goal is for the day. After this whole group discussion, students will model how to express an addition problem using the distributive property.

Type: Lesson Plan

Digesting the Distributive Property:

This lesson will show the student how to use the distributive property to express a sum of two whole numbers 1-100.

Type: Lesson Plan

You Can Never Have Too Many Shoes!:

This lesson teaches Least Common Multiples.

Type: Lesson Plan

Finding the Greatest Crush Factor:

This lesson uses a real life approach to exploring the use of Greatest Common Factors (GCF). The students will utilize math practice standards as they analyze math solutions and explain their own solutions.

Type: Lesson Plan

Factoring out the Greatest:

This lesson teaches students how to find the GCF and LCM by factoring. This is a different method than is normally seen in textbooks. This method easily leads into solving GCF word problems and using the distributive property to express a sum of two whole numbers.

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

The purpose of this task is to gain a better understanding of factors and common factors. Students should use the distributive property to show that the sum of two numbers that have a common factor is also a multiple of the common factor.

Bake Sale:

The purpose of this task requires students to apply the concepts of factors and common factors in a context. A version of this task could be adapted into a teaching task to help motivate the need for the concept of a common factor.

Multiples and Common Multiples:

This problem uses the same numbers and asks similar mathematical questions as "The Florist Shop" file, but that task requires students to apply the concepts of multiples and common multiples in a context.

The Florist Shop:

Students are asked to solve a real-world problem involving common multiples.

Factors and Common Factors:

This problem uses the same numbers and asks essentially the same mathematical questions as "Bake Sale," but that task requires students to apply the concepts of factors and common factors in a context.

## Tutorial

Least Common Multiple Exercise:

This video demonstrates the prime factorization method to find the lcm (least common multiple).

Type: Tutorial

## Video/Audio/Animation

LCM and GCF word problems:

Here we have a couple of word problems--one searching for the least common multiple and the other for the greatest common factor.

Type: Video/Audio/Animation

## Virtual Manipulatives

Factor Tree:

This virtual manipulative will help the students in exploring the prime factorization of numbers and see how to use the factorization of a pair of numbers to find the greatest common factor (GCF) and the least common factor (LCM). In the manipulative, the number pairs are presented randomly, so that a student returning to the factor tree will most likely begin with a pair of numbers not seen before.

Type: Virtual Manipulative

Factor Trees :

This virtual manipulative allows students to find the prime factorization of numbers by completing factor trees. Then they may use a venn diagram to sort the prime factors to find the greatest common factor and the least common multiple.

Type: Virtual Manipulative

## MFAS Formative Assessments

Greatest Common Factors:

Students are given two whole numbers less than or equal to 100 and asked to find the greatest common factor.

Least Common Multiples:

Students are asked to find the least common multiple of 8 and 12 and to explain how they found their answers.

Using the Distributive Property:

Students are asked to rewrite 36 + 42 in the form a(b + c) where a is the greatest common factor of 36 and 42.

## Student Resources

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

The purpose of this task is to gain a better understanding of factors and common factors. Students should use the distributive property to show that the sum of two numbers that have a common factor is also a multiple of the common factor.

The Florist Shop:

Students are asked to solve a real-world problem involving common multiples.

## Tutorial

Least Common Multiple Exercise:

This video demonstrates the prime factorization method to find the lcm (least common multiple).

Type: Tutorial

## Virtual Manipulative

Factor Tree:

This virtual manipulative will help the students in exploring the prime factorization of numbers and see how to use the factorization of a pair of numbers to find the greatest common factor (GCF) and the least common factor (LCM). In the manipulative, the number pairs are presented randomly, so that a student returning to the factor tree will most likely begin with a pair of numbers not seen before.

Type: Virtual Manipulative

## Parent Resources

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

The purpose of this task is to gain a better understanding of factors and common factors. Students should use the distributive property to show that the sum of two numbers that have a common factor is also a multiple of the common factor.

Bake Sale:

The purpose of this task requires students to apply the concepts of factors and common factors in a context. A version of this task could be adapted into a teaching task to help motivate the need for the concept of a common factor.

The Florist Shop:

Students are asked to solve a real-world problem involving common multiples.