6.NOS.4 Lesson 6-13-group1 🟡 Group 1 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.13 Small Group · Group 1

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

Prime Factorization · Prime number · Procedural Fluency · Reasoning & Critique

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What is prime factorization?
1Keep breaking a number apart until every factor is a prime number you cannot split anymore.
  • Prime factorization means writing a number as a product of prime numbers only. A prime number can be divided only by 1 and itself, like 2, 3, 5, and 7. 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 prime factorization of 60. I start by splitting it: 60 = 6 × 10.
  2. 6 is not prime, so I break it: 6 = 2 × 3. Both 2 and 3 are prime, so I stop those branches.
  3. 10 is not prime, so I break it: 10 = 2 × 5. Both 2 and 5 are prime, so I stop.
  4. Now every factor is prime: 60 = 2 × 2 × 3 × 5.
  5. Using exponents, I write it as 2² × 3 × 5. I check: 2 × 2 × 3 × 5 = 60. Correct.
3Mathematical Word Bank
  • Prime Factorization (Factorización prima) — Writing a whole number as a product of only prime numbers.
  • Prime number (Número primo) — A number bigger than 1 that you can only divide by 1 and itself.
  • Composite number (Número compuesto) — A number bigger than 1 that you can divide by more than just 1 and itself.
  • Factor (Factor) — A factor of a whole number divides it evenly, with no remainder. For example, 3 is a factor of 12 because 12 ÷ 3 = 4.
  • Factor tree (Árbol de factores) — A picture that splits a number into its prime numbers, step by step.
  • Exponent (Exponente) — A small number that tells how many times to multiply a number by itself.
4Watch out
  • A common mistake in Prime Factorization is stopping the factor tree too soon — leaving a composite number like 4, 6, 8, or 9 in the final answer instead of continuing to split it. For example, writing 20 = 4 × 5 as the prime factorization (4 is composite) instead of finishing with 20 = 2 × 2 × 5. Before you submit, check every number in your final answer: if any factor can still be broken into smaller factors, the tree isn't finished yet.
SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]
  1. 1 MULTIPLE CHOICE

    Two students found different factor trees for 60. Student A started with 2 × 30. Student B started with 6 × 10. Which statement is true?

    1. ABoth get the same prime factorization: 2 × 2 × 3 × 5
    2. BOnly Student A gets the correct prime factorization
    3. COnly Student B gets the correct prime factorization
    4. DThey will get different prime factorizations
    ✏️ Workspace & Solution Steps
SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]
  1. 2 MULTIPLE CHOICE
    Factor Tree for 90
    909331025

    The first lock panel shows 90. What is the prime factorization of 90?

    1. A2 × 3 × 3 × 5
    2. B2 × 45
    3. C9 × 10
    4. D3 × 30
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    The second panel needs a number whose prime factorization is 2² × 3². Which number unlocks it?

    1. A36
    2. B24
    3. C12
    4. D18
    ✏️ Workspace & Solution Steps
  3. 4 MULTIPLE CHOICE
    Factor Tree for 78
    7862313

    The final lock asks for the prime factorization of 78 written as a product of primes. Which is correct?

    1. A2 × 3 × 13
    2. B2 × 39
    3. C3 × 26
    4. D6 × 13
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Find the prime factorization of 20:Start: 20
    2. 2First split:20 = 4 × 5
    3. 3Check each factor:5 is prime, so that branch is done.
    4. 4Final answer:20 = 4 × 5

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 6 ERROR ANALYSIS

    Level 2 Extension — Fix the Broken Factor Tree

    1. 1Find prime factorization of 96:Start: 96
    2. 2First split:96 = 8 × 12
    3. 3Break down 8:8 = 2 × 2 × 2
    4. 4Break down 12:12 = 2 × 6
    5. 5Final answer:96 = 2 × 2 × 2 × 2 × 6

    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