6.N.1.6 Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of twodigit numbers with a common factor using the distributive property.
In a Nutshell
The greatest common factor (largest factor common to a pair or set of numbers) and the least common multiple (smallest number that is a multiple of a pair or set of numbers) will be used to create equivalent fractions and simplify fractions to their simplest form. The greatest common factor (GCF) is used to reduce a fraction to its simplest form. The least common multiple (LCM) is used to create equivalent fractions with a common denominator for the purpose of comparing fractions and adding/subtracting fractions. The distributive property helps students understand how a common factor relates to two separate numbers.
Student Actions

Teacher Actions


Develop procedural fluency by finding factors and multiples of whole numbers and sets of numbers. (Ex: Students could set up factor rainbows to find factors of two numbers, then compare to find the GCF.)

Develop procedural fluency to simplify fractions using GCF and generate equivalent fractions using common multiples.

Develop mathematical reasoning through discussions as students compare strategies for using common factors and multiples as an efficient procedure to calculate with fractions.

Develop strategies for problem solving by using factors, multiples, GCF and LCMs to solve a variety of problems.

Develop mathematical reasoning of the concept of common factors by using the distributive property.

 Use and connect mathematical representations of prime and composite numbers to develop procedural fluency of finding factors and multiples. (Ex: factor rainbows, Venn Diagram, etc.)

Build procedural fluency for using GCF and common multiples to create equivalent fractions.

Implement tasks that promote reasoning and problem solving by comparing strategies to solve various types of problems using equivalent fractions. (Ex: Ethan has ⅔ cup of juice in his cup, Nate has ⅚ cup of juice left. Who has more juice left in their cup? One strategy that could be used in this problem would be to make ⅔ equivalent to 4/6 to then compare each fraction.)

Pose purposeful questions when using the distributive property to help students understand how a common factor relates to two separate numbers (Ex: What number should be “factored out?” Why?)

Key Understandings

Misconceptions


Understand how to use a variety of strategies to determine factors, multiples, least common multiples, and greatest common factors, including prime factorization.

Understand that dividing the numerator and denominator of a fraction by their greatest common factor results in a fraction in simplest form.

Understand common multiples as common denominators and find equivalent fractions.

solve a variety of problems involving factors, greatest common factors, multiples, and least common multiples.

Recognize the sum of two numbers can be written as the product of a common factor and a sum. (Ex: 28 + 12 = 4(7 + 3)).


Confuse the terms multiples and factors.

Believe that factors of a given number must be smaller than the given number (Ex: Students may not realize that 36 is a factor of 36.)

Believe that multiples of a given number must be larger than the given number (Ex: Students may not recognize 36 as a multiple of 36.)

Use a decimal as a factor (Ex: They believe 2.5 is a factor of 10 since 4 x 2.5 =10.)

Use additive method instead of multiplicative method to find equivalent fractions (Ex: ½ = ⅔ instead of 2/4).

Not recognize that a common factor exists within the sum of two composite numbers.

OKMath Framework Introduction
6th Grade Introduction
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