6.NOS.4 Lesson 6-7-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.7 Small Group · Group 2

Second Challenge Form · Non-Routine Extension · Same Standard, New Problems

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — 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 — and you can say why it is true, and where it would stop being true.
  • You already can do this. So we go up a level, not up a number: find what is always true, show it a second way, and be ready to defend it with a reason instead of an answer.
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.
3Second Model — Try it together — then prove it
  1. A factor tree breaks each number into primes. 48 = 2 × 2 × 2 × 2 × 3, and 36 = 2 × 2 × 3 × 3.
  2. Now look at what the two share: two 2s and one 3.
  3. Multiply the shared primes: 2 × 2 × 3 = 12.
  4. Same answer as the lists, 12 — which is the check. For big numbers, the factor tree is usually the faster road.
  5. Now prove it: say why that move had to work at all — not just that it did.
  6. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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

    Asking for the LCM of 4 and 6, Kai lists multiples until they match: 4, 8, 12 and 6, 12. Nia multiplies 4 × 6 = 24. Whose method gives the least common multiple?

    1. AKai — 12 is the first shared multiple; Nia's 24 is a common multiple but not the least
    2. BNia — multiplying the two numbers always gives the LCM
    3. CBoth — 12 and 24 are equally correct answers
    4. DNeither — the LCM of 4 and 6 is 2
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    What is the least common multiple of 4 and 6?

    1. A12
    2. B24
    3. C2
    4. D10
    ✏️ Workspace & Solution Steps
  3. 3 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
  4. 4 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
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:Ayasha has painting every 8 weeks and pottery every 6 weeks, both this week. When do they next fall in the same week?
    2. 2A classmate at our table answered:In 48 weeks

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Find the error

    1. 1Problem:Ayasha has painting every 8 weeks and pottery every 6 weeks. When do both fall in the same week?
    2. 2Step 1:Factors of 8: 1, 2, 4, 8
    3. 3Step 2:Factors of 6: 1, 2, 3, 6
    4. 4Step 3:The greatest common factor is 2, so both classes meet in week 2.

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

    ✏️ Corrected Mathematical Work & Explanation
📐 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