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# 6-N-1-6

last edited by 5 years, 4 months ago

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 two-digit 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.

## 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?)

## 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