6.NS.4 - About the Math, Learning Targets, and Increasing Rigor

Grade 5AGL The Number System

6.NS.4

Full Standard

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).

 

Learning Targets (I can)

  • Find factor pairs for any number between 1 and 100.
  • Find multiples of a number (multiples up to 100).
  • Explain what the greatest common factor is.
  • Find the greatest common factor of two numbers less than or equal to 100.
  • Explain what a least common multiple is.
  • Find the least common multiple of two numbers less than or equal to 12.
  • Express two addends with a common multiple using the distributive property (i.e. 36 + 8 is the same 4(9 + 2), note: this standard is explored during daily number routines).

 

About the Math

  • Find factor pairs for any number between 1 and 100.

Factor pairs can be found in a variety of ways. Students should have many opportunities to find factor pairs and look for patterns within factor pairs. Finding and using factor pairs is more than creating "rainbows." Instead, students should reason about why a halfway number is useful for finding factor pairs and how knowing factor pairs of some numbers can help with others. For example, knowing the factors of 40 can help with finding the factors of 80. Explicit instruction of divisibility rules is not appropriate, however student discovery of these rules could be an enrichment within this standard for students who show proficiency with factors, multiples, and prime/composite numbers.

  • Find multiples of a number (multiples up to 100).

0 is often overlooked as a multiple. 0 is in fact a multiple of any whole number. However, it is often ignored as it isn't useful or practical. However, 1 is not a multiple yet many students often believe that it is.

  • Explain what the greatest common factor is.
  • Find the greatest common factor of two numbers less than or equal to 100.

In the earlier grades, students identified primes, composites, and factor pairs. In 6th grade students will find the greatest common factor of two whole numbers less than or equal to 100. For example, the greatest common factor of 40 and 16 can be found by:

Listing factors of 40 (1, 2, 4, 5, 8, 10, 20, 40) and 16 (1, 2, 4, 8, 16), then taking the greatest common factor (8). Eight is also the largest number such that the other factors are relatively prime (two numbers with no common factors other than one). For example, 8 would be multiplied by 5 to get 40; 8 would be multiplied by 2 to get 16. Since the 5 and 2 are relatively prime, then 8 is the greatest common factor. If students think 4 is the greatest, then show that 4 would be multiplied by 10 to get 40, while 16 would be 4 times 4. Since 10 and 4 are not relatively prime (have 2 in common), the 4 cannot be the greatest common factor.

Listing the prime factors of 40 (2 x 2 x 2 x 5) and 16 (2 x 2 x 2 x 2) and then multiplying the common factors (2 x 2 x 2 = 8).

For this standard, students should also understand that the greatest common factor of two prime numbers is 1.

  • Explain what a least common multiple is.
  • Find the least common multiple of two numbers less than or equal to 12.

Common multiples can be used for various purposes. Here they are useful for finding common denominators. Often, the least common multiple is used so that a fraction is in simplest form. However, students can find common denominators without using LCMs. Often, students need to find common denominators or common multiples before then finding a least common multiple.

  • Express two addends with a common multiple using the distributive property (i.e. 36 + 8 is the same 4(9 + 2), note: this standard is explored during daily number routines).

Common multiples can be used to simplify equations and expressions among other things in later grades. As noted with this learning target, students can use common multiples, even greatest common multiples to find express addends.

Essential vocabulary for this standard includes greatest common factor, least common multiple, distributive property, prime numbers, composite numbers, relatively prime, factors, multiples, and prime factorization. 

 

 

Progression of Standard within Grade 6 (5 AGL)

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Find factor pairs for any number between 1 and 100.
  • Find multiples of a number (multiples up to 100).
  • Explain what the greatest common factor is.
  • Find the greatest common factor of two numbers less than or equal to 100.
  • Explain what a least common multiple is.
  • Find the least common multiple of two numbers less than or equal to 12.
  • Express two addends with a common multiple using the distributive property (i.e. 36 + 8 is the same 4(9 + 2), note: this standard is explored during daily number routines).
 

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 5 Grade 7
  • Write simple expressions (5.OA.2)
  • Apply properties of operations to linear expressions (7.EE.1)

 

 

Back to Top