6.NOS.4 Lesson 6-12-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.12 Small Group · Group 1

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

Visual Models · Least Common Multiple · Multiple · Procedural Fluency

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What is the least common multiple (LCM)?
1The LCM is the FIRST number that shows up in both numbers' multiple lists.
  • A multiple is what you get when you count by a number: 4, 8, 12, 16. The least common multiple is the smallest multiple that two numbers share. 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
  1. I want the LCM of 4 and 6. I skip count the multiples of 4: 4, 8, 12, 16, 20, 24.
  2. Then I skip count the multiples of 6: 6, 12, 18, 24.
  3. I look for the first number in BOTH lists. 12 is in both lists, and it comes before 24.
  4. So the LCM of 4 and 6 is 12. I check: 12 ÷ 4 = 3 and 12 ÷ 6 = 2, so both go into 12 evenly.
3Mathematical Word Bank
  • Least Common Multiple (Mínimo común múltiplo) — The least positive number that is a multiple of two or more numbers.
  • Multiple (Múltiplo) — What you get when you multiply a number by 1, 2, 3, and so on.
  • Common multiple (Múltiplo común) — A number that two or more numbers both go into.
  • Skip counting (Conteo salteado) — Counting by a number, like 2, 4, 6, to list its multiples.
  • Prime factorization (Factorización prima) — Writing a number as prime numbers multiplied together. It helps you find the LCM.
4Watch out
  • A common mistake in Least Common Multiple is multiplying the two numbers together instead of listing multiples to find the smallest shared one. For example, for 4 and 6, a student calculates 4 × 6 = 24 and calls that the LCM, but the actual least common multiple is 12 (multiples of 4: 4, 8, 12; multiples of 6: 6, 12 — 12 is the first number that appears in both lists). This shortcut only works when the two numbers share no common factors (like 4 and 9, where the LCM really is 36 = 4 × 9); for numbers like 4 and 6 that share a factor of 2, multiplying overshoots the true LCM. Always list multiples of both numbers and pick the first one that appears in both lists.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    Two buses leave the station at 8:00 AM. Bus A returns every 15 minutes and Bus B returns every 20 minutes. When is the next time both buses are at the station together?

    1. A9:00 AM (60 minutes later)
    2. B8:30 AM (30 minutes later)
    3. C8:40 AM (40 minutes later)
    4. D9:20 AM (80 minutes later)
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    One machine runs every 4 min, another every 6 min. They just ran together. In how many minutes do they run together again?

    1. A12
    2. B10
    3. C24
    4. D6
    ✏️ Workspace & Solution Steps
  3. 3 MULTIPLE CHOICE

    One ship docks every 8 min, another every 12 min. They just docked together. In how many minutes do they dock together again?

    1. A24
    2. B20
    3. C48
    4. D16
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Spot Riley's Mistake — LCM of 4 and 6

    1. 1Problem:Find the LCM of 4 and 6.
    2. 2Multiples of 4:4, 8, 12, 16
    3. 3Multiples of 6:6, 12, 18
    4. 4Choose the answer:Riley added the two numbers: 4 + 6 = 10, so LCM = 10.

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot Maya's Mistake — LCM of 6 and 9

    1. 1Problem:Find the LCM of 6 and 9.
    2. 2Multiples of 6:6, 12, 18, 24
    3. 3Multiples of 9:9, 18, 27
    4. 4Choose the answer:Maya saw that 9 is bigger than 6, so she wrote LCM = 9.

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Level 2 Extension — Crew Member's Schedule Sync Mistake

    1. 1Problem:The water recycler cycles every 8 minutes and the heat exchanger cycles every 12 minutes. They just ran together. When do they next sync?
    2. 2List multiples of 8:8, 16, 24, 32
    3. 3List multiples of 12:12, 24, 36
    4. 4Pick the number to use:The greatest factor that 8 and 12 share is 4.
    5. 5Answer:They next sync in 4 minutes.

    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
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