6.NOS.4 Lesson 6-13-group2 🟣 Group 2 · Set B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.13 Small Group · Group 2

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

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

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: Push further — What is prime factorization?
1Keep breaking a number apart until every factor is a prime number you cannot split anymore — 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
  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.
3Second Model — Try it together — then prove it
  1. Let's factor 12 together. What is one way to split 12 into two factors? (You might say 3 × 4.)
  2. Is 3 prime? Yes, so we keep it. Is 4 prime? No — what is 4 split apart? (4 = 2 × 2.)
  3. So put the prime factors together: 12 = 2 × 2 × 3. Every factor is prime, so we are done.
  4. Now prove it: say why that move had to work at all — not just that it did.
  5. Sentence frame — convince a skeptic: "My method works because ___ . It would stop working if ___ ."
4Mathematical 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.
5Watch 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

    Which of the following is a prime number?

    1. A17
    2. B15
    3. C21
    4. D9
    ✏️ Workspace & Solution Steps
  2. 3 MULTIPLE CHOICE

    What is the prime factorization of 30?

    1. A2 × 3 × 5
    2. B5 × 6
    3. C2 × 15
    4. D3 × 10
    ✏️ Workspace & Solution Steps
SECTION 3 MATHEMATICAL WRITING & ERROR ANALYSIS [Reasoning & Critique]
  1. 4 ERROR ANALYSIS

    Fix our table's thinking

    1. 1The problem:The first lock panel shows 90. What is the prime factorization of 90?
    2. 2A classmate at our table answered:2 × 45

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

    ✏️ Corrected Mathematical Work & Explanation
  2. 5 ERROR ANALYSIS

    Spot the Common Mistake

    1. 1Find the prime factorization of 45, using exponents:Start: 45
    2. 2First split:45 = 5 × 9
    3. 3Break down 9:9 = 3 × 3, so 45 = 5 × 3 × 3
    4. 4Write with exponents:45 = 3² × 5²

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

    ✏️ Corrected Mathematical Work & Explanation
  3. 6 ERROR ANALYSIS

    Find Marcus's Mistake

    1. 1Find prime factorization of 48:Start: 48
    2. 2First split:48 = 6 × 8
    3. 3Break down 6:6 = 2 × 3
    4. 4Break down 8:8 = 2 × 4
    5. 5Final answer:48 = 2 × 3 × 2 × 4

    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