6.NOS.4 Lesson 6-7-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.7 · Part II

Supported Application · Guided Entry to Today's Problem

Find Factors and Multiples · Factor

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 6.7 · Part II
1Greatest Common Factor (GCF) & Least Common Multiple (LCM)
2Strategy Model — step by step
  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.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each number by its relationship to 10.

    Target Categories: A factor of 10 A multiple of 10
    • 2
    • 20
    • 5
    • 30
    • 10
    • 50
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE

    What is the least common multiple of 4 and 6?

    1. A12
    2. B24
    3. C2
    4. D10
    ✏️ 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 6-7-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.7 · Part II

On-Level Application · Standard Rigor

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.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 DRAG SORT

    Sort each real problem by the tool that solves it.

    Target Categories: Use the GCF Use the LCM
    • Split 48 pencils and 36 notebooks into identical packs
    • Two classes repeat every 6 and 8 weeks — when do they meet?
    • Cut two ribbons into the longest equal pieces with none left over
    • Hot dogs in packs of 10, buns in packs of 8 — when do they match?
    • The answer is at most the smaller number
    • The answer is at least the larger number
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 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. 3 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
📐 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 6-7-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.7 · Part II

Extension & Non-Routine Application

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.
SECTION 1 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 1 MULTIPLE CHOICE

    What is the greatest common factor of 18 and 24?

    1. A6
    2. B72
    3. C3
    4. D2
    ✏️ Workspace & Solution Steps
  2. 2 MULTIPLE CHOICE

    Claim: “The GCF of two numbers is always smaller than both of them.” Always, sometimes, or never true?

    1. ASometimes — it equals the smaller number whenever that number divides the larger one
    2. BAlways — a common factor has to be smaller than what it divides
    3. CNever — the GCF is always one of the two numbers
    4. DSometimes — it depends whether the numbers are even
    ✏️ Workspace & Solution Steps
SECTION 2 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 3 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
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