Maryland Math 4.NOS.C.8.c
The Standard
- 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.
Distinguish between factors and multiples and explain how they relate to a given number.
Maryland College and Career Ready Standards for Mathematics (2025) · GAIN FAMILIARITY WITH FACTORS AND MULTIPLES.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find numbers that divide a given number evenly. They find multiples by multiplying that number by 1, 2, 3, and so on. They use multiplication equations to explain the connection.
What Mastery Looks Like
- A student lists 1, 2, 3, 4, 6, and 12 as factors of 12, and 12, 24, and 36 as multiples. They explain that 3 is a factor of 12 because 3 × 4 = 12, so 12 is a multiple of 3.
Common Misconceptions
- Students may call 24 a factor of 12 because it appears when counting by 12s. Some leave 12 off both lists. Others miss that 3 can be a factor of 12 while 12 is a multiple of 3.
How to Assess It
- On an exit ticket, ask: “List three factors and the first three positive multiples of 18. Use an equation to explain why 3 is a factor of 18.”
Lesson moves
Ways to Teach It
Make arrays of 12 with counters, record the side lengths as factors, then combine two and three groups of 12 to model multiples.
Ask partners, “Can 12 be both a factor and a multiple of 12?” Have them defend their answers with equations.
Give students cards numbered 1 through 24; call out 6 and have them sort cards into factor, multiple, both, or neither piles.
Use a bakery sign for six-packs of rolls; find totals for one, two, and three packs, then explain why 6 divides each total.
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Related Standards
- 6.NOS.B.4
Identify the common factors and multiples of two whole numbers.
- 3.NOS.B.2
Represent and interpret multiplication of two factors (0- 10) as equal groups or as a composed unit that can be repeated/iterated. Explain the relationship betw...
- 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.
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