6.NOS.4 Lesson 6-7-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.7 Small Group · Group 1

Second Practice Form · Re-Teach, Homework or Retake · Same Standard, New Problems

Find Factors and Multiples · Factor · Procedural Fluency · Real-World Applications

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — Factors split things up; multiples count forward
1GCF = the biggest number that divides BOTH — use it to split into equal groups. LCM = the smallest number BOTH divide into — use it to find when cycles meet again.
  • A factor divides a number evenly, so factors answer questions about splitting a stock into equal groups. A multiple is where you land when you skip-count, so multiples answer questions about when repeating events line up. We'll walk through a worked example, try one together, then you'll try a few with hints right there when you need them.
2Worked Example — Watch me build the combo packs
  1. The store has 48 pencils and 36 notebooks. Every combo pack must hold the same number of each, with nothing left over — so the number of packs has to be a factor of BOTH quantities.
  2. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Listing them in order is what makes the comparison easy.
  3. The numbers in both lists are the common factors: 1, 2, 3, 4, 6, and 12.
  4. The greatest of those is 12, so the GCF of 48 and 36 is 12. The manager can make 12 combo packs — each holding 48 ÷ 12 = 4 pencils and 36 ÷ 12 = 3 notebooks.
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.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Using prime factors, 48 = 2 × 2 × 2 × 2 × 3 and 36 = 2 × 2 × 3 × 3. What is their GCF?

    1. A12, from the shared 2 × 2 × 3
    2. B144, from multiplying all the primes
    3. C6, from one 2 and one 3
    4. D2, the only prime they share
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Ayasha has painting every 8 weeks and pottery every 6 weeks, both this week. When do they next fall in the same week?

    1. AIn 24 weeks
    2. BIn 48 weeks
    3. CIn 14 weeks
    4. DIn 2 weeks
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    Is 4 a factor or a multiple of 12?

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

    What is the GCF of 10 and 15?

    1. A5
    2. B1
    3. C30
    4. D10
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Find the error

    1. 1Problem:Find the GCF of 12 and 18.
    2. 2Step 1:Factors of 12: 1, 2, 3, 4, 6, 12
    3. 3Step 2:Factors of 18: 1, 2, 3, 6, 9, 18
    4. 4Step 3:The GCF is 36, because 36 is in both times tables.

    Which step contains the error? Explain the mathematical misconception and write the correct calculation below.

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 OPEN RESPONSE

    Reginald is having hot dogs for 24 guests and wants the same number of hot dogs and buns, with none left over. Hot dogs come in packs of 10 and buns in packs of 8. How many packs of each should he buy, and how many will he have? Explain which tool you used and why.

    ✏️ Mathematical Justification & Response
📐 CER MATHEMATICAL PROOF MATRIX (CER 2.0) SMP.3 / Proof & Justification

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

C Claim
Starter: My mathematical claim is that the solution is...
E Evidence
Starter: The evidence from the model/table demonstrates that...
R Reasoning
Starter: This proves my answer because the standard mathematical definition of...
Student Mastery Self-Assessment:
1 · Need More Support
2 · Getting Closer
3 · Got It / Solid
4 · Master / Can Teach It