6.NOS.4 Lesson 6-12-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.12 · Part II

Supported Application · Guided Entry to Today's Problem

Least Common Multiple · Multiple

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 6.12 · Part II
1Least Common Multiple (LCM)
2Strategy Model — step by step
  1. Skip count multiples of each number starting with the larger number
  2. Identify the first non-zero multiple that appears in both lists
  3. Prime factorization method: Product of highest powers of all prime factors
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.
  1. 1 MULTIPLE CHOICE

    What is the LCM of 2 and 7?

    1. A14
    2. B7
    3. C2
    4. D9
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    (Lesson 6.7) 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
  3. 3 MULTIPLE CHOICE

    (Lesson 6.7) 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
📐 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
6.NOS.4 Lesson 6-12-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.12 · Part II

On-Level Application · Standard Rigor

Least Common Multiple · Multiple

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.12 · Part II
1Least Common Multiple (LCM)
2The Structural Procedure
  1. Skip count multiples of each number starting with the larger number
  2. Identify the first non-zero multiple that appears in both lists
  3. Prime factorization method: Product of highest powers of all prime factors
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.
  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
📐 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
6.NOS.4 Lesson 6-12-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.12 · Part II

Extension & Non-Routine Application

Least Common Multiple · Multiple

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.12 · Part II
1Least Common Multiple (LCM)
2The Structural Procedure
  1. Skip count multiples of each number starting with the larger number
  2. Identify the first non-zero multiple that appears in both lists
  3. Prime factorization method: Product of highest powers of all prime factors
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.
  1. 1 MULTIPLE CHOICE

    What is the least common multiple of 6 and 8?

    1. A24
    2. B48
    3. C2
    4. D14
    ✏️ 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