Standard #: MAFS.6.NS.2.4 (Archived 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: 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
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    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 # Question Difficulty Type
Sample Item 1

What is the greatest common factor of 15 and 20?

N/A EE: Equation Editor
Sample Item 2

What is the least common multiple of 7 and 12?

N/A EE: Equation Editor
Sample Item 3

Which expression is equivalent to 8 + 20?

 

N/A MC: Multiple Choice
Sample Item 4

An equation is shown.

begin mathsize 12px style 30 space plus space 12 space equals space square left parenthesis 5 space plus space 2 right parenthesis end style

What factor is missing from the equation?

N/A EE: Equation Editor
Sample Item 5

Fill in the bubbles to match the equivalent expression.

 

N/A MI: Matching Item


Related Courses

Course Number1111 Course Title222
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 Resources

Formative Assessments

Name Description
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.

Least Common Multiples

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

Greatest Common Factors

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

Lesson Plans

Name Description
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.

Can you say that another way?

Students will model how to express an addition problem using the distributive property.

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.

You Can Never Have Too Many Shoes!

This lesson teaches Least Common Multiples.

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.

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.

Prime Factorization - From Fingerprints to Factorprints

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

Original Student Tutorials

Name Description
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.

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.

Problem-Solving Tasks

Name Description
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.

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

Name Description
Least Common Multiple

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

Video/Audio/Animation

Name Description
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. 

Student Resources

Original Student Tutorials

Name Description
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.

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.

Problem-Solving Tasks

Name Description
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.

The Florist Shop:

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

Tutorial

Name Description
Least Common Multiple:

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



Parent Resources

Problem-Solving Tasks

Name Description
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.

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.



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