Maryland Math 6.NOS.B.4

6.NOS.B.4 is a cluster heading. These are the individual standards under it.

• 6.NOS.B.4.a

  Identify the greatest common factor of two whole numbers within 100.

• 6.NOS.B.4.b

  Identify the least common multiple of two whole numbers within 12.

• 6.NOS.B.4.c

  Express the sum of two whole numbers within 100 using the distributive property to factor out the common factor of the addends (e.g., express 36 + 8 as 4(9 + 2)...

01

What Students Need to Do

Students list factors and multiples for two numbers and find the ones they share. They find the largest shared factor for numbers up to 100 and the first shared multiple for numbers up to 12. They rewrite sums by pulling a shared factor outside parentheses.

02

What Mastery Looks Like

Given 24 and 36, a student lists their shared factors and identifies 12 as the greatest. They find 12 as the first shared multiple of 4 and 6. They can also rewrite 36 + 8 as 4(9 + 2).

03

Common Misconceptions

Students may mix up factors and multiples, calling 24 a factor of 6. They may pick any shared factor or multiple without checking for the greatest or least. When factoring a sum, they may divide only one addend.

04

How to Assess It

Exit ticket: List the shared factors of 24 and 36 and circle the greatest. List multiples of 4 and 6 until they meet, then rewrite 36 + 8 by factoring out 4.

1. 01

   Give each pair 24 and 36 counters; have them make equal-size groups and record group sizes that work for both sets.

2. 02

   Write 36 + 8 = 4(9 + 2) and 36 + 8 = 2(18 + 4); ask which uses the greatest shared factor.

3. 03

   Draw two number cards from 1 to 12, list their multiples, and race to circle the least shared multiple.

4. 04

   Pencils come in packs of 4 and erasers in packs of 6; find the fewest of each to buy equal counts.

• 4.NOS.C.8.c

  Distinguish between factors and multiples and explain how they relate to a given number.

• 4.NOS.C.8

  Explain and apply concepts of factors, multiples, and prime and composite numbers for whole numbers in the range of 1-100.