6.12 Small Group · Group 1

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

Visual Models · Least Common Multiple · Multiple · Procedural Fluency

Name: Date: Period: Learning Goal:

■ CONCEPT SUMMARY & GUIDED NOTES: Let's build it together — What is the least common multiple (LCM)?

1The LCM is the FIRST number that shows up in both numbers' multiple lists.

A multiple is what you get when you count by a number: 4, 8, 12, 16. The least common multiple is the smallest multiple that two numbers share. 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 LCM of 4 and 6. I skip count the multiples of 4: 4, 8, 12, 16, 20, 24.
Then I skip count the multiples of 6: 6, 12, 18, 24.
I look for the first number in BOTH lists. 12 is in both lists, and it comes before 24.
So the LCM of 4 and 6 is 12. I check: 12 ÷ 4 = 3 and 12 ÷ 6 = 2, so both go into 12 evenly.

3Mathematical Word Bank

Least Common Multiple (Mínimo común múltiplo) — The least positive number that is a multiple of two or more numbers.
Multiple (Múltiplo) — What you get when you multiply a number by 1, 2, 3, and so on.
Common multiple (Múltiplo común) — A number that two or more numbers both go into.
Skip counting (Conteo salteado) — Counting by a number, like 2, 4, 6, to list its multiples.
Prime factorization (Factorización prima) — Writing a number as prime numbers multiplied together. It helps you find the LCM.

4Watch out

A common mistake in Least Common Multiple is multiplying the two numbers together instead of listing multiples to find the smallest shared one. For example, for 4 and 6, a student calculates 4 × 6 = 24 and calls that the LCM, but the actual least common multiple is 12 (multiples of 4: 4, 8, 12; multiples of 6: 6, 12 — 12 is the first number that appears in both lists). This shortcut only works when the two numbers share no common factors (like 4 and 9, where the LCM really is 36 = 4 × 9); for numbers like 4 and 6 that share a factor of 2, multiplying overshoots the true LCM. Always list multiples of both numbers and pick the first one that appears in both lists.

SECTION 1 CONCEPTUAL UNDERSTANDING & VISUAL MODELS [Visual Modeling]

1 NUMBER LINE

Find the LCM of 5 and 6 on the number line
✏️ Workspace & Solution Steps
2 MATCHING GAME
Match each pair of numbers to their LCM.
1. LCM(2, 5)
2. LCM(4, 10)
3. LCM(3, 8)
4. LCM(6, 9)
5. LCM(5, 7)
6. LCM(4, 6)
- A10
- B20
- C24
- D18
- E35
- F12

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