MAFS.6.NS.2.4Archived Standard

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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
Grade: 6
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 Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
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)

Related Courses

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

Related Resources

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

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

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?:

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 to 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

Original Student Tutorials

Homework Help: Least Common Multiple Part 2:

Use the least common multiple to solve real-life problems with Brady and Natalia in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Homework Help: Least Common Multiple Part 1:

Learn how to find the least common multiple by helping Brady and Natalia work through some homework questions in this interactive student tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

Problem-Solving Tasks

Adding Multiples:

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

The Florist Shop:

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Tutorial

Least Common Multiple:

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 searching for the least common multiple and the other for the greatest common factor. 

Type: Video/Audio/Animation

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.

Original Student Tutorials Mathematics - Grades 6-8

Homework Help: Least Common Multiple Part 1:

Learn how to find the least common multiple by helping Brady and Natalia work through some homework questions in this interactive student tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Homework Help: Least Common Multiple Part 2:

Use the least common multiple to solve real-life problems with Brady and Natalia in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Student Resources

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

Original Student Tutorials

Homework Help: Least Common Multiple Part 2:

Use the least common multiple to solve real-life problems with Brady and Natalia in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Homework Help: Least Common Multiple Part 1:

Learn how to find the least common multiple by helping Brady and Natalia work through some homework questions in this interactive student tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

Problem-Solving Tasks

Adding Multiples:

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.

Type: Problem-Solving Task

The Florist Shop:

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

Type: Problem-Solving Task

Tutorial

Least Common Multiple:

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

Type: Tutorial

Parent Resources

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

Problem-Solving Tasks

Adding Multiples:

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

The Florist Shop:

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

Type: Problem-Solving Task