6.NOS.4 Lesson 6-7-part2 Apply Day · Set B
MASTERY CHECK
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6.7 · Part II

Second Practice Form · Independent Application and Spiral Review

Find Factors and Multiples · Factor

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.7 · Part II
1Greatest Common Factor (GCF) & Least Common Multiple (LCM)
2The Structural Procedure
  1. GCF: Largest factor shared by two numbers — used to simplify fractions or divide into equal groups
  2. LCM: Smallest shared multiple — used to find common denominators
  3. Use prime factor trees or list method to find common factors/multiples
3Mathematical Word Bank
  • Find Factors and Multiples (Hallar factores y múltiplos) — Listing what divides a number evenly (its factors) and what it divides into evenly (its multiples), then finding what two numbers share.
  • Factor (Factor) — A whole number that divides another number evenly, with no remainder.
  • Multiple (Múltiplo) — The result of multiplying a number by 1, 2, 3, and so on — where you land when you skip-count by it.
  • Greatest common factor (GCF) (Máximo común divisor (MCD)) — The largest number that is a factor of two or more numbers. It answers “how many equal groups can I make?”
  • Least common multiple (LCM) (Mínimo común múltiplo (mcm)) — The smallest number that is a multiple of two or more numbers. It answers “when will these line up again?”
  • Factor pair (Par de factores) — Two factors that multiply to make a number. In a word problem, one is the number of groups and the other is the size of each group.
4Watch out
  • A common mistake is reaching for the wrong tool: listing FACTORS for a problem about repeating cycles. Ayasha's classes repeat every 6 and 8 weeks, so the weeks they land on are multiples — answering with the GCF of 2 claims a class that meets every 8 weeks happens in week 2. Use the size of the answer as a check: a GCF is never larger than the smaller number, and an LCM is never smaller than the larger one.
  1. 1 MULTIPLE CHOICE

    Is 4 a factor or a multiple of 12?

    1. AA factor
    2. BA multiple
    3. CBoth
    4. DNeither
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    What is the GCF of 10 and 15?

    1. A5
    2. B1
    3. C30
    4. D10
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Two buses leave the depot together. One returns every 12 minutes, the other every 18. A student wants to know when they next leave together and answers 6. What went wrong?

    1. AThey found the GCF. Meeting again needs the LCM, 36 minutes
    2. BNothing — 6 minutes is correct
    3. CThey should have added 12 + 18 to get 30 minutes
    4. DThey should have multiplied 12 × 18 to get 216 minutes
    ✏️ Workspace & Solution Steps
  4. 4 MULTIPLE CHOICE

    Which list shows all the factors of 12?

    1. A1, 2, 3, 4, 6, 12
    2. B12, 24, 36, 48
    3. C1, 12
    4. D2, 3, 4, 6
    ✏️ Workspace & Solution Steps
  5. 5 MULTIPLE CHOICE

    Which list shows the first four multiples of 8?

    1. A8, 16, 24, 32
    2. B1, 2, 4, 8
    3. C8, 9, 10, 11
    4. D2, 4, 6, 8
    ✏️ Workspace & Solution Steps
  6. 6 MULTIPLE CHOICE

    What is the greatest common factor of 12 and 18?

    1. A6
    2. B3
    3. C36
    4. D2
    ✏️ Workspace & Solution Steps
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

Writing Task: Justify why your mathematical solution is accurate and complete.

C Claim
State your direct mathematical answer/claim with units.
E Evidence
Cite exact numbers, calculations, dimensions, or graph data.
R Reasoning
Explain the mathematical theorem, property, or definition connecting evidence to claim.
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It