6.NOS.4 Lesson 6-13-part2 Apply Day · Version A
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.13 · Part II

Supported Application · Guided Entry to Today's Problem

Prime Factorization · Prime number

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ CONCEPT SUMMARY & GUIDED NOTES: 6.13 · Part II
1Prime Factorization & Factor Trees
2Strategy Model — step by step
  1. Prime Number: Has exactly two factors (1 and itself, e.g. 2, 3, 5, 7, 11)
  2. Split composite number into factor pairs until every branch ends in a prime
  3. Write final product using exponents in ascending order (e.g. 60 = 2² × 3 × 5)
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.
  1. 1 MULTIPLE CHOICE

    Which of these numbers is composite?

    1. A27
    2. B23
    3. C29
    4. D31
    ✏️ Workspace & Solution Steps
  2. 2 GUIDED FILL
    42

    Build a new factor tree for 42. Write the prime factorization.

    1. 1The smallest prime factor of 42 is ___.
    2. 242 ÷ 2 = ___.
    3. 3Keep splitting until every end number is prime. Write the prime factorization: ___.
    Final answer:
  3. 3 GUIDED FILL
    54

    Build a new factor tree for 54. Write the prime factorization.

    1. 1The smallest prime factor of 54 is ___.
    2. 254 ÷ 2 = ___.
    3. 3Keep splitting until every end number is prime. Write the prime factorization: ___.
    Final answer:
📐 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 6-13-part2 Apply Day · Version B
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.13 · Part II

On-Level Application · Standard Rigor

Prime Factorization · Prime number

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.13 · Part II
1Prime Factorization & Factor Trees
2The Structural Procedure
  1. Prime Number: Has exactly two factors (1 and itself, e.g. 2, 3, 5, 7, 11)
  2. Split composite number into factor pairs until every branch ends in a prime
  3. Write final product using exponents in ascending order (e.g. 60 = 2² × 3 × 5)
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
📐 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 6-13-part2 Apply Day · Challenge
MASTERY CHECK
☐ Exceeds☐ Meets Target☐ Needs Practice

6.13 · Part II

Extension & Non-Routine Application

Prime Factorization · Prime number

Interactive Workbench & Models →
Name: Date: Period: Learning Goal:
■ ADVANCED CONCEPT ANCHOR: 6.13 · Part II
1Prime Factorization & Factor Trees
2The Structural Procedure
  1. Prime Number: Has exactly two factors (1 and itself, e.g. 2, 3, 5, 7, 11)
  2. Split composite number into factor pairs until every branch ends in a prime
  3. Write final product using exponents in ascending order (e.g. 60 = 2² × 3 × 5)
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.
  1. 1 MULTIPLE CHOICE

    What is the prime factorization of 72?

    1. A2³ × 3²
    2. B2² × 3³
    3. C2 × 3 × 12
    4. D8 × 9
    ✏️ 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