6.13 Small Group · Group 1

Tier 2 Intervention · Concrete-Representational-Abstract (CRA) · Dual-Language Anchors

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

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

I want the prime factorization of 60. I start by splitting it: 60 = 6 × 10.
6 is not prime, so I break it: 6 = 2 × 3. Both 2 and 3 are prime, so I stop those branches.
10 is not prime, so I break it: 10 = 2 × 5. Both 2 and 5 are prime, so I stop.
Now every factor is prime: 60 = 2 × 2 × 3 × 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 DRAG SORT
Sort each expression: is it a COMPLETE prime factorization, or does it still have composite factors?

Target Categories: Complete Prime Factorization NOT Complete (Has Composite Factors)
2 MATCHING GAME
Match each number to its prime factorization.
1. 12
2. 18
3. 20
4. 28
5. 45
6. 50
- A2 × 2 × 3
- B2 × 3 × 3
- C2 × 2 × 5
- D2 × 2 × 7
- E3 × 3 × 5
- F2 × 5 × 5

SECTION 2 REAL-WORLD CONTEXTS & PROBLEM SOLVING [Applications]

🗣️ MATHEMATICAL DISCOURSE & TALK MOVES SMP.3 / Construct Viable Arguments

Group Discussion Prompt: How does your visual model justify your mathematical solution?

🗣️ Partner A:
Partner A: "I modeled this by identifying the relationship and..."

👂 Partner B:
Partner B: "I agree with your step because the standard mathematical rule states..."

✍️ The Writing Revolution (TWR) · Sentence Expansion Because · But · So

Complete each sentence stem to demonstrate precise mathematical reasoning:

BECAUSE The mathematical model proves the solution because each step preserves quantitative equivalence.

BUT An estimate provides a quick benchmark, but an exact proof is required for precision.

SO The quantities follow the standard rule, so the final result is verified with certainty.

📐 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